/* 
==========Equation for modular curve X_H(l)=========

Let l be a prime number, H a subgroup of (Z/lZ)^*.

This table contains equations for modular curves X_H(l), in some cases, 
more than one equations are found for one modular curve X_H(l). Eqautions marked with "used" are 
used for computing Galois representations associated to discriminant modular forms.

1. f_N(x,y), N>3 is an equation for moduar curve X_1(N), computed by Sutherland, see http://math.mit.edu/~drew/X1_altcurves.html 

2. f_l_k(X,Y) is an equation for modular X_H(l) of level l subgroup H with [(Z/lZ)^*:H]=k.

3. The map between function fields
 
pi: Q(x)[y]/(f_N(x,y)) -> Q(X)[Y]/(f_l_k(X,Y)),

is given by

x mapsto X(x,y) and y mapsto Y(x,y) .

4. P_Xx is a polynomial relation between X(x,y) and x in Q(x)[y]/(f_N(x,y)). (P_Xy, P_Yx, P_Yy similar)

5. In some cases, a chang of variables (X,Y)->(1/X, Y) or (X,Y)->(X, 1/Y) or (X,Y)->(1/X, 1/Y) may lower the total degree
   of the equations, but the degrees w.r.t X and Y do not change.
*/

r:=(x^2*y-x*y+y-1)/(x*(x*y-1));
s:=(x*y-y+1)/(x*y);
b:=r*s*(r-1);
c:=s*(r-1);
f_2 := b/(16*b^2+(1-20*c-8*c^2)*b+c*(c-1)^3);
f_3 := b;
f_4 := c;
f_5 := b-c;
f_6 := s-1;
f_7 := s-r;
f_8 := r*s-2*r+1;
f_9 := s^2-s-r+1;
f_10 := x-y+1;
f_11 := x^2*y-x*y^2+y-1;
f_12 := x-y;
f_13 := x^3*y-x^2*y^2-x^2*y+x*y^2-y+1;
f_14 := x^2*y-x*y^2-x*y+y^2-1;
f_15 := x^2*y-x^2-x*y^2+x*y-x+y-1;
f_16 := x^2*y^2-2*x^2*y-x*y^3+2*x*y^2-y+1;
f_17 := x^4*y-x^3*y^3-x^3*y+x^2*y^4+x^2*y-x^2-x*y^4+x*y^3-x*y^2+x*y+y^3-2*y^2+y;
f_18 := x^4*y-3*x^3*y^2+x^3*y+2*x^2*y^3+x^2*y^2-2*x^2*y-2*x*y^3+2*x*y^2+y^2-2*y+1;
f_19 := x^5*y^2-3*x^4*y^3+3*x^3*y^4+2*x^3*y^2-2*x^3*y-x^2*y^5-x^2*y^4-x^2*y^3+x^2*y^2+x^2*y+x*y^5-x*y^4+2*x*y^3-2*x*y^2-x*y+x-y^4+2*y^3-y^2;
f_20 := x^4*y-2*x^3*y^2-x^3*y+x^2*y^3+x^2*y^2+2*x^2*y-x^2-2*x*y^2+x*y+y-1;
f_21 := x^5*y^2-3*x^4*y^3-x^4*y^2+3*x^3*y^4+3*x^3*y^3-x^2*y^5-3*x^2*y^4-2*x^2*y^2+3*x^2*y+x*y^5+3*x*y^3-4*x*y^2-y^4+y^3+y-1;
f_22 := x^5*y^2-x^5*y-2*x^4*y^3+2*x^4*y+x^3*y^4+3*x^3*y^3-4*x^3*y^2+x^3-2*x^2*y^4+x^2*y^3+x^2*y^2-x^2*y+x*y^4-x*y^3+x*y^2-x*y-y^3+2*y^2-y;
f_23:=x^7*y^4 - 2*x^7*y^3 + x^7*y^2 - 3*x^6*y^5 + 4*x^6*y^4 + 3*x^5*y^6 - 5*x^5*y^4 -     3*x^5*y^3 + 3*x^5*y^2 - x^5*y - x^4*y^7 - 4*x^4*y^6 + 5*x^4*y^5 + 6*x^4*y^4     - x^4*y^3 - x^4*y^2 - x^4*y + 2*x^3*y^7 - 3*x^3*y^5 - 6*x^3*y^4 + 2*x^3*y^3     + 5*x^3*y^2 - x^3*y - x^2*y^7 + 3*x^2*y^5 + 2*x^2*y^4 - x^2*y^3 - 7*x^2*y^2     + 4*x^2*y + x*y^6 - 2*x*y^5 - 3*x*y^4 + 8*x*y^3 - 4*x*y^2 + y^3 - 3*y^2 +     3*y - 1;
f_24:=x^5*y^4 - 3*x^5*y^3 + 3*x^5*y^2 - 2*x^4*y^5 + 5*x^4*y^4 - 5*x^4*y^3 + x^3*y^6 -     x^3*y^5 + x^3*y^4 - x^3*y^3 + 4*x^3*y^2 - 3*x^3*y - x^2*y^6 + x^2*y^5 -     x^2*y^4 + x^2*y^3 - x^2*y^2 + x^2*y + 2*x*y^5 - 5*x*y^4 + 5*x*y^3 - 2*x*y^2     - x*y + x - y^4 + 3*y^3 - 3*y^2 + y;
f_25:=x^8*y^2 + x^7*y^5 - 4*x^7*y^4 - x^7*y^2 - 3*x^6*y^6 + 11*x^6*y^5 - 2*x^6*y^4 +     2*x^6*y^2 - 2*x^6*y + 3*x^5*y^7 - 9*x^5*y^6 - 4*x^5*y^5 + 4*x^5*y^4 -     2*x^5*y^3 + 4*x^5*y^2 - x^4*y^8 + x^4*y^7 + 9*x^4*y^6 - 5*x^4*y^5 +     6*x^4*y^4 - 15*x^4*y^3 + 7*x^4*y^2 - 2*x^4*y + x^4 + x^3*y^8 - 4*x^3*y^7 +     3*x^3*y^6 - 14*x^3*y^5 + 26*x^3*y^4 - 15*x^3*y^3 + 7*x^3*y^2 - 5*x^3*y + x^3    - x^2*y^7 + 8*x^2*y^6 - 13*x^2*y^5 + 12*x^2*y^4 - 18*x^2*y^3 + 19*x^2*y^2 -     8*x^2*y + x^2 - 4*x*y^5 + 13*x*y^4 - 16*x*y^3 + 10*x*y^2 - 4*x*y + x + y^4 -    4*y^3 + 6*y^2 - 4*y + 1;
f_26:=x^6*y^2 - 5*x^5*y^3 + 2*x^5*y^2 + x^4*y^5 + 5*x^4*y^4 - 2*x^4*y^2 - x^4*y -     2*x^3*y^6 - 4*x^3*y^4 + 9*x^3*y^2 - 4*x^3*y + x^2*y^7 + 5*x^2*y^4 -     11*x^2*y^3 + 4*x^2*y^2 + x^2*y - x*y^7 + 2*x*y^6 - 4*x*y^5 + 6*x*y^4 -     3*x*y^3 + x*y^2 - 2*x*y + x + y^6 - 3*y^5 + 3*y^4 - y^3;
f_27:=x^10*y^3 - 6*x^9*y^4 + 15*x^8*y^5 + 3*x^8*y^3 - 3*x^8*y^2 - 19*x^7*y^6 -     6*x^7*y^5 - 3*x^7*y^4 + 5*x^7*y^3 + 3*x^7*y^2 + 12*x^6*y^7 + 18*x^6*y^6 -     6*x^6*y^5 + 3*x^6*y^4 - 12*x^6*y^3 - 3*x^6*y^2 + 3*x^6*y - 3*x^5*y^8 -     18*x^5*y^7 + 6*x^5*y^6 - 12*x^5*y^5 + 27*x^5*y^4 - 3*x^5*y^3 - x^5*y^2 -     2*x^5*y + 6*x^4*y^8 + 3*x^4*y^7 + 10*x^4*y^6 - 24*x^4*y^5 + 3*x^4*y^4 -     2*x^4*y^3 + 5*x^4*y^2 + x^4*y - x^4 - 3*x^3*y^8 - 3*x^3*y^7 + 15*x^3*y^5 -     6*x^3*y^4 - 3*x^3*y^3 - x^3*y^2 + x^3*y + 6*x^2*y^7 - 12*x^2*y^6 +     10*x^2*y^5 - 13*x^2*y^4 + 15*x^2*y^3 - 7*x^2*y^2 + x^2*y - 4*x*y^6 +     13*x*y^5 - 16*x*y^4 + 10*x*y^3 - 4*x*y^2 + x*y + y^5 - 4*y^4 + 6*y^3 - 4*y^2    + y;
f_28:=x^8*y^2 - 5*x^7*y^3 + 10*x^6*y^4 + 2*x^6*y^2 - x^6*y - 10*x^5*y^5 - 10*x^5*y^3 +    8*x^5*y^2 - x^5*y + 5*x^4*y^6 + x^4*y^5 + 13*x^4*y^4 - 9*x^4*y^3 - x^4*y^2 -    x^4*y - x^3*y^7 - 2*x^3*y^6 - 4*x^3*y^5 - 4*x^3*y^4 + 8*x^3*y^3 + 2*x^3*y^2     - x^3*y + x^2*y^7 - x^2*y^6 + 8*x^2*y^5 - 11*x^2*y^4 + 8*x^2*y^3 -     10*x^2*y^2 + 5*x^2*y - 2*x*y^6 + 5*x*y^5 - 10*x*y^4 + 14*x*y^3 - 8*x*y^2 +     x*y + y^5 - 3*y^4 + 4*y^3 - 4*y^2 + 3*y - 1;
f_29:=x^12*y^5 - x^12*y^4 - 6*x^11*y^6 + 4*x^11*y^5 + 2*x^11*y^4 + 15*x^10*y^7 -     3*x^10*y^6 - 10*x^10*y^5 - 3*x^10*y^4 + x^10*y^3 - 20*x^9*y^8 - 10*x^9*y^7 +    18*x^9*y^6 + 14*x^9*y^5 + 4*x^9*y^4 - 7*x^9*y^3 + 15*x^8*y^9 + 25*x^8*y^8 -     10*x^8*y^7 - 27*x^8*y^6 - 23*x^8*y^5 + 18*x^8*y^4 + 6*x^8*y^3 - 6*x^7*y^10 -    24*x^7*y^9 - 9*x^7*y^8 + 21*x^7*y^7 + 46*x^7*y^6 - 17*x^7*y^5 - 7*x^7*y^4 -     20*x^7*y^3 + 10*x^7*y^2 + x^6*y^11 + 11*x^6*y^10 + 15*x^6*y^9 + 4*x^6*y^8 -     51*x^6*y^7 + 8*x^6*y^6 - 15*x^6*y^5 + 54*x^6*y^4 - 18*x^6*y^3 - 5*x^6*y^2 -     2*x^5*y^11 - 7*x^5*y^10 - 15*x^5*y^9 + 26*x^5*y^8 + 39*x^5*y^6 - 63*x^5*y^5     + 14*x^5*y^4 + 12*x^5*y^2 - 5*x^5*y + x^4*y^11 + 6*x^4*y^10 + x^4*y^9 -     4*x^4*y^8 - 29*x^4*y^7 + 26*x^4*y^6 + 6*x^4*y^5 + x^4*y^4 - 12*x^4*y^3 +     2*x^4*y^2 + 2*x^4*y - 4*x^3*y^10 + 2*x^3*y^9 + 21*x^3*y^7 - 33*x^3*y^6 +     20*x^3*y^5 - 13*x^3*y^4 + 11*x^3*y^3 - 3*x^3*y^2 - 2*x^3*y + x^3 + 6*x^2*y^9    - 18*x^2*y^8 + 25*x^2*y^7 - 33*x^2*y^6 + 42*x^2*y^5 - 34*x^2*y^4 +     15*x^2*y^3 - 3*x^2*y^2 - 4*x*y^8 + 17*x*y^7 - 30*x*y^6 + 30*x*y^5 - 20*x*y^4    + 9*x*y^3 - 2*x*y^2 + y^7 - 5*y^6 + 10*y^5 - 10*y^4 + 5*y^3 - y^2;
f_30:=x^8*y^4 - x^8*y^3 - 4*x^7*y^5 + x^7*y^4 + 4*x^7*y^3 + 6*x^6*y^6 + 5*x^6*y^5 -     11*x^6*y^4 - 7*x^6*y^3 + 3*x^6*y^2 - 4*x^5*y^7 - 11*x^5*y^6 + 9*x^5*y^5 +     15*x^5*y^4 + 6*x^5*y^3 - 9*x^5*y^2 + x^4*y^8 + 8*x^4*y^7 - 9*x^4*y^5 -     20*x^4*y^4 + 6*x^4*y^3 + 13*x^4*y^2 - 3*x^4*y - 2*x^3*y^8 - 3*x^3*y^7 +     x^3*y^6 + 9*x^3*y^5 + 15*x^3*y^4 - 17*x^3*y^3 - 8*x^3*y^2 + 6*x^3*y +     x^2*y^8 + 3*x^2*y^6 - 14*x^2*y^5 + 5*x^2*y^4 + 6*x^2*y^3 + 5*x^2*y^2 -     7*x^2*y + x^2 - x*y^7 + 2*x*y^6 - x*y^5 + 5*x*y^4 - 10*x*y^3 + 4*x*y^2 +     2*x*y - x - y^3 + 3*y^2 - 3*y + 1;
f_31:=x^13*y^7 - 3*x^13*y^6 + 3*x^13*y^5 - x^13*y^4 - 6*x^12*y^8 + 15*x^12*y^7 -     10*x^12*y^6 + 15*x^11*y^9 - 27*x^11*y^8 + 12*x^11*y^6 + 12*x^11*y^5 -     8*x^11*y^4 + 2*x^11*y^3 - 20*x^10*y^10 + 15*x^10*y^9 + 42*x^10*y^8 -     23*x^10*y^7 - 45*x^10*y^6 + 12*x^10*y^5 + 2*x^10*y^4 + 2*x^10*y^3 +     15*x^9*y^11 + 15*x^9*y^10 - 70*x^9*y^9 + 6*x^9*y^8 + 49*x^9*y^7 + 42*x^9*y^6    - 15*x^9*y^5 - 28*x^9*y^4 + 7*x^9*y^3 - x^9*y^2 - 6*x^8*y^12 - 27*x^8*y^11 +    42*x^8*y^10 + 21*x^8*y^9 + 9*x^8*y^8 - 111*x^8*y^7 - 3*x^8*y^6 + 51*x^8*y^5     + 24*x^8*y^4 - 13*x^8*y^3 - 2*x^8*y^2 + x^7*y^13 + 15*x^7*y^12 - 20*x^7*y^10    - 45*x^7*y^9 + 60*x^7*y^8 + 71*x^7*y^7 - 16*x^7*y^6 - 96*x^7*y^5 +     13*x^7*y^4 + 26*x^7*y^3 - 3*x^7*y^2 - 3*x^6*y^13 - 10*x^6*y^12 + 3*x^6*y^11     + 14*x^6*y^10 + 50*x^6*y^9 - 111*x^6*y^8 + 3*x^6*y^7 + 47*x^6*y^6 +     47*x^6*y^5 - 14*x^6*y^4 - 44*x^6*y^3 + 17*x^6*y^2 + 3*x^5*y^13 + 3*x^5*y^12     + 12*x^5*y^11 - 58*x^5*y^10 + 64*x^5*y^9 - 42*x^5*y^8 + 87*x^5*y^7 -     97*x^5*y^6 - 32*x^5*y^5 + 87*x^5*y^4 - 22*x^5*y^3 - 5*x^5*y^2 - x^4*y^13 -     6*x^4*y^12 + 9*x^4*y^11 - 4*x^4*y^10 + 32*x^4*y^9 - 69*x^4*y^8 + 34*x^4*y^7     + 43*x^4*y^6 - 51*x^4*y^5 + 23*x^4*y^4 - 30*x^4*y^3 + 27*x^4*y^2 - 7*x^4*y +    4*x^3*y^12 - 6*x^3*y^11 + 4*x^3*y^10 - 24*x^3*y^9 + 59*x^3*y^8 - 70*x^3*y^7     + 60*x^3*y^6 - 59*x^3*y^5 + 59*x^3*y^4 - 34*x^3*y^3 + 6*x^3*y^2 + x^3*y -     6*x^2*y^11 + 24*x^2*y^10 - 46*x^2*y^9 + 70*x^2*y^8 - 96*x^2*y^7 +     100*x^2*y^6 - 70*x^2*y^5 + 31*x^2*y^4 - 10*x^2*y^3 + 6*x^2*y^2 - 4*x^2*y +     x^2 + 4*x*y^10 - 21*x*y^9 + 48*x*y^8 - 65*x*y^7 + 60*x*y^6 - 39*x*y^5 +     16*x*y^4 - 3*x*y^3 - y^9 + 6*y^8 - 15*y^7 + 20*y^6 - 15*y^5 + 6*y^4 - y^3;
f_37:=x^19*y^8 - 2*x^19*y^7 + x^19*y^6 - 10*x^18*y^9 + 17*x^18*y^8 - 4*x^18*y^7 -     3*x^18*y^6 + 45*x^17*y^10 - 60*x^17*y^9 - 10*x^17*y^8 + 18*x^17*y^7 +     9*x^17*y^6 - 2*x^17*y^5 - 120*x^16*y^11 + 105*x^16*y^10 + 100*x^16*y^9 -     24*x^16*y^8 - 61*x^16*y^7 - 13*x^16*y^6 + 14*x^16*y^5 + 210*x^15*y^12 -     60*x^15*y^11 - 285*x^15*y^10 - 100*x^15*y^9 + 171*x^15*y^8 + 129*x^15*y^7 -     48*x^15*y^6 - 26*x^15*y^5 + x^15*y^4 - 252*x^14*y^13 - 127*x^14*y^12 +     419*x^14*y^11 + 440*x^14*y^10 - 130*x^14*y^9 - 484*x^14*y^8 + 38*x^14*y^7 +     71*x^14*y^6 + 84*x^14*y^5 - 31*x^14*y^4 + 210*x^13*y^14 + 342*x^13*y^13 -     317*x^13*y^12 - 715*x^13*y^11 - 475*x^13*y^10 + 1010*x^13*y^9 + 156*x^13*y^8    + 27*x^13*y^7 - 392*x^13*y^6 + 53*x^13*y^5 + 45*x^13*y^4 - 120*x^12*y^15 -     405*x^12*y^14 + 39*x^12*y^13 + 520*x^12*y^12 + 1427*x^12*y^11 -     1036*x^12*y^10 - 575*x^12*y^9 - 569*x^12*y^8 + 877*x^12*y^7 + 50*x^12*y^6 -     46*x^12*y^5 - 127*x^12*y^4 + 35*x^12*y^3 + 45*x^11*y^16 + 290*x^11*y^15 +     170*x^11*y^14 - 37*x^11*y^13 - 1632*x^11*y^12 - x^11*y^11 + 837*x^11*y^10 +     1462*x^11*y^9 - 930*x^11*y^8 - 422*x^11*y^7 - 186*x^11*y^6 + 411*x^11*y^5 -     21*x^11*y^4 - 42*x^11*y^3 - 10*x^10*y^17 - 130*x^10*y^16 - 195*x^10*y^15 -     205*x^10*y^14 + 773*x^10*y^13 + 1202*x^10*y^12 - 541*x^10*y^11 -     1508*x^10*y^10 - 470*x^10*y^9 + 1085*x^10*y^8 + 634*x^10*y^7 - 561*x^10*y^6     - 140*x^10*y^5 + 31*x^10*y^4 + 84*x^10*y^3 - 21*x^10*y^2 + x^9*y^18 +     34*x^9*y^17 + 115*x^9*y^16 + 145*x^9*y^15 + 65*x^9*y^14 - 1261*x^9*y^13 +     31*x^9*y^12 + 130*x^9*y^11 + 2377*x^9*y^10 - 1173*x^9*y^9 - 819*x^9*y^8 -     189*x^9*y^7 + 695*x^9*y^6 - 25*x^9*y^5 - 145*x^9*y^4 - 10*x^9*y^3 +     21*x^9*y^2 - 4*x^8*y^18 - 39*x^8*y^17 - 52*x^8*y^16 - 210*x^8*y^15 +     505*x^8*y^14 + 189*x^8*y^13 + 883*x^8*y^12 - 2109*x^8*y^11 + 88*x^8*y^10 +     46*x^8*y^9 + 1928*x^8*y^8 - 1433*x^8*y^7 + 190*x^8*y^6 - 105*x^8*y^5 +     175*x^8*y^4 - 32*x^8*y^3 - 26*x^8*y^2 + 7*x^8*y + 6*x^7*y^18 + 17*x^7*y^17 +    69*x^7*y^16 - 12*x^7*y^15 - 165*x^7*y^14 - 476*x^7*y^13 + 193*x^7*y^12 +     890*x^7*y^11 + 700*x^7*y^10 - 2097*x^7*y^9 + 946*x^7*y^8 - 601*x^7*y^7 +     1090*x^7*y^6 - 728*x^7*y^5 + 165*x^7*y^4 + 5*x^7*y^3 + 2*x^7*y^2 - 4*x^7*y -    4*x^6*y^18 - 7*x^6*y^17 - 46*x^6*y^16 + 79*x^6*y^15 - 57*x^6*y^14 +     600*x^6*y^13 - 768*x^6*y^12 - 174*x^6*y^11 + 18*x^6*y^10 + 407*x^6*y^9 +     943*x^6*y^8 - 1700*x^6*y^7 + 868*x^6*y^6 - 212*x^6*y^5 + 85*x^6*y^4 -     40*x^6*y^3 + 6*x^6*y^2 + 3*x^6*y - x^6 + x^5*y^18 + 9*x^5*y^17 - 11*x^5*y^16    + 59*x^5*y^15 - 231*x^5*y^14 + 230*x^5*y^13 - 324*x^5*y^12 + 904*x^5*y^11 -     660*x^5*y^10 - 339*x^5*y^9 + 210*x^5*y^8 + 336*x^5*y^7 - 73*x^5*y^6 -     209*x^5*y^5 + 119*x^5*y^4 - 23*x^5*y^3 + x^5*y^2 + x^5*y - 4*x^4*y^17 +     4*x^4*y^16 - 6*x^4*y^15 + 24*x^4*y^14 + 64*x^4*y^13 - 174*x^4*y^12 +     78*x^4*y^11 - 320*x^4*y^10 + 1040*x^4*y^9 - 1154*x^4*y^8 + 658*x^4*y^7 -     453*x^4*y^6 + 401*x^4*y^5 - 194*x^4*y^4 + 40*x^4*y^3 - 5*x^4*y^2 + x^4*y +     6*x^3*y^16 - 26*x^3*y^15 + 64*x^3*y^14 - 137*x^3*y^13 + 159*x^3*y^12 +     48*x^3*y^11 - 366*x^3*y^10 + 621*x^3*y^9 - 997*x^3*y^8 + 1322*x^3*y^7 -     1095*x^3*y^6 + 527*x^3*y^5 - 160*x^3*y^4 + 44*x^3*y^3 - 11*x^3*y^2 + x^3*y -    4*x^2*y^15 + 24*x^2*y^14 - 67*x^2*y^13 + 122*x^2*y^12 - 129*x^2*y^11 -     52*x^2*y^10 + 444*x^2*y^9 - 767*x^2*y^8 + 795*x^2*y^7 - 647*x^2*y^6 +     466*x^2*y^5 - 263*x^2*y^4 + 94*x^2*y^3 - 17*x^2*y^2 + x^2*y + x*y^14 -     7*x*y^13 + 21*x*y^12 - 35*x*y^11 + 26*x*y^10 + 43*x*y^9 - 190*x*y^8 +     342*x*y^7 - 371*x*y^6 + 259*x*y^5 - 119*x*y^4 + 37*x*y^3 - 8*x*y^2 + x*y +     y^9 - 8*y^8 + 28*y^7 - 56*y^6 + 70*y^5 - 56*y^4 + 28*y^3 - 8*y^2 + y;
f_41:=x^23*y^7 + x^22*y^12 - 6*x^22*y^11 + 15*x^22*y^10 - 20*x^22*y^9 - 3*x^22*y^7 -     10*x^21*y^13 + 55*x^21*y^12 - 123*x^21*y^11 + 143*x^21*y^10 + 10*x^21*y^9 +     8*x^21*y^7 - 5*x^21*y^6 + 45*x^20*y^14 - 220*x^20*y^13 + 415*x^20*y^12 -     384*x^20*y^11 - 204*x^20*y^10 + 13*x^20*y^9 + 30*x^20*y^8 + 9*x^20*y^7 +     10*x^20*y^6 - 120*x^19*y^15 + 495*x^19*y^14 - 685*x^19*y^13 + 355*x^19*y^12     + 901*x^19*y^11 + 210*x^19*y^10 - 284*x^19*y^9 - 167*x^19*y^8 + 25*x^19*y^7     - 25*x^19*y^6 + 10*x^19*y^5 + 210*x^18*y^16 - 660*x^18*y^15 + 360*x^18*y^14     + 400*x^18*y^13 - 1887*x^18*y^12 - 1090*x^18*y^11 + 274*x^18*y^10 +     1299*x^18*y^9 - 130*x^18*y^8 - 8*x^18*y^7 - 45*x^18*y^6 - 10*x^18*y^5 -     252*x^17*y^17 + 462*x^17*y^16 + 690*x^17*y^15 - 1260*x^17*y^14 +     2140*x^17*y^13 + 2066*x^17*y^12 + 1608*x^17*y^11 - 3833*x^17*y^10 -     518*x^17*y^9 + 72*x^17*y^8 + 617*x^17*y^7 - 96*x^17*y^6 + 30*x^17*y^5 -     10*x^17*y^4 + 210*x^16*y^18 - 1554*x^16*y^16 + 864*x^16*y^15 -     1335*x^16*y^14 - 1620*x^16*y^13 - 5026*x^16*y^12 + 5108*x^16*y^11 +     2854*x^16*y^10 + 1494*x^16*y^9 - 2876*x^16*y^8 + 34*x^16*y^7 + 50*x^16*y^6 +    81*x^16*y^5 - 120*x^15*y^19 - 330*x^15*y^18 + 1350*x^15*y^17 + 678*x^15*y^16    + 723*x^15*y^15 + 84*x^15*y^14 + 5650*x^15*y^13 - 2108*x^15*y^12 -     4637*x^15*y^11 - 6325*x^15*y^10 + 4970*x^15*y^9 + 1985*x^15*y^8 +     246*x^15*y^7 - 1023*x^15*y^6 + 159*x^15*y^5 - 20*x^15*y^4 + 5*x^15*y^3 +     45*x^14*y^20 + 330*x^14*y^19 - 465*x^14*y^18 - 1620*x^14*y^17 -     1102*x^14*y^16 + 105*x^14*y^15 - 1647*x^14*y^14 - 1806*x^14*y^13 +     2730*x^14*y^12 + 9615*x^14*y^11 - 939*x^14*y^10 - 6205*x^14*y^9 -     2820*x^14*y^8 + 2859*x^14*y^7 + 425*x^14*y^6 - 159*x^14*y^5 - 66*x^14*y^4 +     5*x^14*y^3 - 10*x^13*y^21 - 165*x^13*y^20 - 135*x^13*y^19 + 1175*x^13*y^18 +    1506*x^13*y^17 + 1379*x^13*y^16 - 1829*x^13*y^15 + 1176*x^13*y^14 -     146*x^13*y^13 - 4479*x^13*y^12 - 8463*x^13*y^11 + 8466*x^13*y^10 +     5371*x^13*y^9 - 319*x^13*y^8 - 3794*x^13*y^7 - 230*x^13*y^6 + 908*x^13*y^5 -    134*x^13*y^4 + 10*x^13*y^3 - x^13*y^2 + x^12*y^22 + 44*x^12*y^21 +     195*x^12*y^20 - 320*x^12*y^19 - 1090*x^12*y^18 - 2157*x^12*y^17 +     935*x^12*y^16 + 1783*x^12*y^15 + 1548*x^12*y^14 - 3917*x^12*y^13 +     12434*x^12*y^12 - 7683*x^12*y^11 + 3*x^12*y^10 - 10042*x^12*y^9 +     7873*x^12*y^8 + 2083*x^12*y^7 - 1256*x^12*y^6 - 725*x^12*y^5 + 190*x^12*y^4     + 25*x^12*y^3 - 2*x^12*y^2 - 5*x^11*y^22 - 73*x^11*y^21 - 57*x^11*y^20 +     375*x^11*y^19 + 1355*x^11*y^18 + 1203*x^11*y^17 - 1902*x^11*y^16 -     3961*x^11*y^15 + 4746*x^11*y^14 - 7589*x^11*y^13 + 8104*x^11*y^12 -     10131*x^11*y^11 + 16906*x^11*y^10 - 7130*x^11*y^9 - 1905*x^11*y^8 -     2805*x^11*y^7 + 3155*x^11*y^6 + 135*x^11*y^5 - 455*x^11*y^4 + 50*x^11*y^3 -     3*x^11*y^2 + 10*x^10*y^22 + 56*x^10*y^21 - 19*x^10*y^20 - 352*x^10*y^19 -     1335*x^10*y^18 + 59*x^10*y^17 + 2922*x^10*y^16 + 31*x^10*y^15 +     2603*x^10*y^14 - 7955*x^10*y^13 + 9137*x^10*y^12 - 8423*x^10*y^11 +     1039*x^10*y^10 - 573*x^10*y^9 + 6595*x^10*y^8 - 3124*x^10*y^7 -     1079*x^10*y^6 - 94*x^10*y^5 + 640*x^10*y^4 - 135*x^10*y^3 - 4*x^10*y^2 -     10*x^9*y^22 - 24*x^9*y^21 - 5*x^9*y^20 + 441*x^9*y^19 + 638*x^9*y^18 -     500*x^9*y^17 - 1875*x^9*y^16 - 1516*x^9*y^15 + 2911*x^9*y^14 + 2718*x^9*y^13    - 5723*x^9*y^12 + 6944*x^9*y^11 - 4648*x^9*y^10 + 1439*x^9*y^9 -     3058*x^9*y^8 + 1604*x^9*y^7 + 2091*x^9*y^6 - 1538*x^9*y^5 - 14*x^9*y^4 +     130*x^9*y^3 - 5*x^9*y^2 + 5*x^8*y^22 + 16*x^8*y^21 - 15*x^8*y^20 -     280*x^8*y^19 - 304*x^8*y^18 + 567*x^8*y^17 + 1058*x^8*y^16 + 2029*x^8*y^15 -    8016*x^8*y^14 + 9710*x^8*y^13 - 12848*x^8*y^12 + 16752*x^8*y^11 -     15945*x^8*y^10 + 11762*x^8*y^9 - 4722*x^8*y^8 - 297*x^8*y^7 + 258*x^8*y^6 +     162*x^8*y^5 + 367*x^8*y^4 - 319*x^8*y^3 + 60*x^8*y^2 - x^7*y^22 -     13*x^7*y^21 + 25*x^7*y^20 + 105*x^7*y^19 + 180*x^7*y^18 - 211*x^7*y^17 -     1971*x^7*y^16 + 3627*x^7*y^15 - 4958*x^7*y^14 + 11322*x^7*y^13 -     17498*x^7*y^12 + 17311*x^7*y^11 - 14209*x^7*y^10 + 9998*x^7*y^9 -     5677*x^7*y^8 + 2696*x^7*y^7 - 265*x^7*y^6 - 936*x^7*y^5 + 537*x^7*y^4 -     43*x^7*y^3 - 19*x^7*y^2 + 4*x^6*y^21 + 2*x^6*y^20 - 70*x^6*y^19 -     75*x^6*y^18 + 322*x^6*y^17 + 21*x^6*y^16 + 868*x^6*y^15 - 3910*x^6*y^14 +     5210*x^6*y^13 - 4945*x^6*y^12 + 6395*x^6*y^11 - 6995*x^6*y^10 + 4855*x^6*y^9    - 2228*x^6*y^8 + 315*x^6*y^7 + 507*x^6*y^6 - 375*x^6*y^5 + 190*x^6*y^4 -     152*x^6*y^3 + 73*x^6*y^2 - 12*x^6*y - 6*x^5*y^20 + 22*x^5*y^19 + 65*x^5*y^18    - 213*x^5*y^17 + 136*x^5*y^16 - 628*x^5*y^15 + 2358*x^5*y^14 - 3465*x^5*y^13    + 3459*x^5*y^12 - 4401*x^5*y^11 + 5397*x^5*y^10 - 4475*x^5*y^9 +     2796*x^5*y^8 - 1672*x^5*y^7 + 958*x^5*y^6 - 513*x^5*y^5 + 255*x^5*y^4 -     81*x^5*y^3 + 6*x^5*y^2 + 2*x^5*y + 4*x^4*y^19 - 23*x^4*y^18 - 61*x^4*y^17 +     541*x^4*y^16 - 1433*x^4*y^15 + 2777*x^4*y^14 - 5327*x^4*y^13 + 8741*x^4*y^12    - 10719*x^4*y^11 + 10274*x^4*y^10 - 8543*x^4*y^9 + 6220*x^4*y^8 -     3625*x^4*y^7 + 1589*x^4*y^6 - 527*x^4*y^5 + 137*x^4*y^4 - 35*x^4*y^3 +     15*x^4*y^2 - 6*x^4*y + x^4 - x^3*y^18 + 7*x^3*y^17 + 63*x^3*y^16 -     553*x^3*y^15 + 1837*x^3*y^14 - 3778*x^3*y^13 + 5974*x^3*y^12 - 8100*x^3*y^11    + 9285*x^3*y^10 - 8477*x^3*y^9 + 5999*x^3*y^8 - 3321*x^3*y^7 + 1447*x^3*y^6     - 472*x^3*y^5 + 100*x^3*y^4 - 10*x^3*y^3 - 36*x^2*y^15 + 297*x^2*y^14 -     1108*x^2*y^13 + 2508*x^2*y^12 - 3942*x^2*y^11 + 4710*x^2*y^10 - 4536*x^2*y^9    + 3564*x^2*y^8 - 2208*x^2*y^7 + 1017*x^2*y^6 - 324*x^2*y^5 + 64*x^2*y^4 -     6*x^2*y^3 + 9*x*y^14 - 83*x*y^13 + 345*x*y^12 - 855*x*y^11 + 1410*x*y^10 -     1638*x*y^9 + 1386*x*y^8 - 870*x*y^7 + 405*x*y^6 - 135*x*y^5 + 29*x*y^4 -     3*x*y^3 - y^13 + 10*y^12 - 45*y^11 + 120*y^10 - 210*y^9 + 252*y^8 - 210*y^7     + 120*y^6 - 45*y^5 + 10*y^4 - y^3;
f_43:=x^26*y^9 - x^26*y^8 - 15*x^25*y^10 + 14*x^25*y^9 + x^25*y^8 + 105*x^24*y^11 -     90*x^24*y^10 - 8*x^24*y^9 - 14*x^24*y^8 + 7*x^24*y^7 + x^23*y^14 -     9*x^23*y^13 - 419*x^23*y^12 + 266*x^23*y^11 + 126*x^23*y^10 + 90*x^23*y^9 -     40*x^23*y^8 - 15*x^23*y^7 - 10*x^22*y^15 + 85*x^22*y^14 + 1044*x^22*y^13 -     196*x^22*y^12 - 776*x^22*y^11 - 441*x^22*y^10 + 175*x^22*y^9 + 77*x^22*y^8 +    63*x^22*y^7 - 21*x^22*y^6 + 45*x^21*y^16 - 355*x^21*y^15 - 1762*x^21*y^14 -     970*x^21*y^13 + 2140*x^21*y^12 + 1975*x^21*y^11 - 290*x^21*y^10 -     595*x^21*y^9 - 266*x^21*y^8 + 28*x^21*y^7 + 49*x^21*y^6 - 120*x^20*y^17 +     855*x^20*y^16 + 2330*x^20*y^15 + 3267*x^20*y^14 - 2524*x^20*y^13 -     5978*x^20*y^12 - 1390*x^20*y^11 + 2820*x^20*y^10 + 988*x^20*y^9 +     77*x^20*y^8 - 224*x^20*y^7 - 126*x^20*y^6 + 35*x^20*y^5 + 210*x^19*y^18 -     1290*x^19*y^17 - 3060*x^19*y^16 - 4850*x^19*y^15 - 684*x^19*y^14 +     11096*x^19*y^13 + 8126*x^19*y^12 - 5618*x^19*y^11 - 4470*x^19*y^10 -     1260*x^19*y^9 + 1412*x^19*y^8 + 406*x^19*y^7 + 7*x^19*y^6 - 70*x^19*y^5 -     252*x^18*y^19 + 1218*x^18*y^18 + 4233*x^18*y^17 + 4413*x^18*y^16 +     6178*x^18*y^15 - 12206*x^18*y^14 - 18638*x^18*y^13 + 1752*x^18*y^12 +     11620*x^18*y^11 + 8332*x^18*y^10 - 4833*x^18*y^9 - 1821*x^18*y^8 -     261*x^18*y^7 + 287*x^18*y^6 + 133*x^18*y^5 - 35*x^18*y^4 + 210*x^17*y^20 -     630*x^17*y^19 - 4963*x^17*y^18 - 3638*x^17*y^17 - 8718*x^17*y^16 +     6667*x^17*y^15 + 24875*x^17*y^14 + 11509*x^17*y^13 - 12830*x^17*y^12 -     25067*x^17*y^11 + 3669*x^17*y^10 + 8242*x^17*y^9 + 2544*x^17*y^8 -     1719*x^17*y^7 - 424*x^17*y^6 + 14*x^17*y^5 + 49*x^17*y^4 - 120*x^16*y^21 +     30*x^16*y^20 + 4101*x^16*y^19 + 4228*x^16*y^18 + 6680*x^16*y^17 +     1065*x^16*y^16 - 22845*x^16*y^15 - 20839*x^16*y^14 - 2906*x^16*y^13 +     39108*x^16*y^12 + 14454*x^16*y^11 - 15513*x^16*y^10 - 12860*x^16*y^9 +     2714*x^16*y^8 + 3369*x^16*y^7 - 194*x^16*y^6 - 164*x^16*y^5 - 77*x^16*y^4 +     21*x^16*y^3 + 45*x^15*y^22 + 195*x^15*y^21 - 2115*x^15*y^20 - 4746*x^15*y^19    - 3970*x^15*y^18 - 5494*x^15*y^17 + 17480*x^15*y^16 + 15935*x^15*y^15 +     23523*x^15*y^14 - 31710*x^15*y^13 - 38105*x^15*y^12 + 4316*x^15*y^11 +     27152*x^15*y^10 + 10144*x^15*y^9 - 12630*x^15*y^8 - 1599*x^15*y^7 +     1080*x^15*y^6 + 357*x^15*y^5 - 54*x^15*y^4 - 14*x^15*y^3 - 10*x^14*y^23 -     135*x^14*y^22 + 530*x^14*y^21 + 3490*x^14*y^20 + 3012*x^14*y^19 +     6075*x^14*y^18 - 11813*x^14*y^17 - 8034*x^14*y^16 - 26235*x^14*y^15 +     8962*x^14*y^14 + 38670*x^14*y^13 + 23070*x^14*y^12 - 20667*x^14*y^11 -     40151*x^14*y^10 + 15841*x^14*y^9 + 8672*x^14*y^8 + 2516*x^14*y^7 -     4388*x^14*y^6 + 696*x^14*y^5 + 2*x^14*y^4 + 24*x^14*y^3 - 7*x^14*y^2 +     x^13*y^24 + 41*x^13*y^23 + 36*x^13*y^22 - 1454*x^13*y^21 - 2404*x^13*y^20 -     4683*x^13*y^19 + 4736*x^13*y^18 + 7651*x^13*y^17 + 13335*x^13*y^16 +     7796*x^13*y^15 - 22718*x^13*y^14 - 28419*x^13*y^13 - 13064*x^13*y^12 +     55378*x^13*y^11 + 973*x^13*y^10 - 6941*x^13*y^9 - 22488*x^13*y^8 +     12293*x^13*y^7 + 420*x^13*y^6 - 359*x^13*y^5 - 214*x^13*y^4 + 40*x^13*y^3 -     x^13*y^2 - 5*x^12*y^24 - 56*x^12*y^23 + 259*x^12*y^22 + 1244*x^12*y^21 +     2624*x^12*y^20 + 1100*x^12*y^19 - 7935*x^12*y^18 - 3460*x^12*y^17 -     13504*x^12*y^16 + 17166*x^12*y^15 + 3761*x^12*y^14 + 40508*x^12*y^13 -     41397*x^12*y^12 - 10021*x^12*y^11 - 20668*x^12*y^10 + 43839*x^12*y^9 -     8137*x^12*y^8 - 3982*x^12*y^7 - 3954*x^12*y^6 + 3124*x^12*y^5 - 536*x^12*y^4    + 44*x^12*y^3 - 5*x^12*y^2 + x^12*y + 10*x^11*y^24 + 18*x^11*y^23 -     320*x^11*y^22 - 940*x^11*y^21 - 2390*x^11*y^20 + 3714*x^11*y^19 +     1247*x^11*y^18 + 12800*x^11*y^17 - 15895*x^11*y^16 + 11851*x^11*y^15 -     39111*x^11*y^14 + 27557*x^11*y^13 - 10786*x^11*y^12 + 47254*x^11*y^11 -     34500*x^11*y^10 - 8896*x^11*y^9 - 403*x^11*y^8 + 13887*x^11*y^7 -     4429*x^11*y^6 - 899*x^11*y^5 + 149*x^11*y^4 + 91*x^11*y^3 - 11*x^11*y^2 +     x^11*y - 10*x^10*y^24 + 18*x^10*y^23 + 172*x^10*y^22 + 1060*x^10*y^21 +     5*x^10*y^20 - 756*x^10*y^19 - 7267*x^10*y^18 + 5429*x^10*y^17 -     4624*x^10*y^16 + 21096*x^10*y^15 - 17894*x^10*y^14 + 19751*x^10*y^13 -     33986*x^10*y^12 + 4688*x^10*y^11 + 15678*x^10*y^10 + 6465*x^10*y^9 -     7386*x^10*y^8 - 7308*x^10*y^7 + 4110*x^10*y^6 + 1867*x^10*y^5 -     1276*x^10*y^4 + 184*x^10*y^3 - 17*x^10*y^2 + x^10*y + 5*x^9*y^24 -     7*x^9*y^23 - 145*x^9*y^22 - 553*x^9*y^21 + 65*x^9*y^20 + 1463*x^9*y^19 +     3148*x^9*y^18 - 3031*x^9*y^17 - 3640*x^9*y^16 - 2528*x^9*y^15 +     5071*x^9*y^14 - 4688*x^9*y^13 + 21557*x^9*y^12 - 23107*x^9*y^11 +     12572*x^9*y^10 - 22352*x^9*y^9 + 23779*x^9*y^8 - 6053*x^9*y^7 - 1756*x^9*y^6    - 639*x^9*y^5 + 993*x^9*y^4 - 132*x^9*y^3 - 23*x^9*y^2 + x^9*y - x^8*y^24 -     8*x^8*y^23 + 122*x^8*y^22 + 110*x^8*y^21 + 447*x^8*y^20 - 2604*x^8*y^19 +     2130*x^8*y^18 - 4195*x^8*y^17 + 14810*x^8*y^16 - 21381*x^8*y^15 +     27161*x^8*y^14 - 40768*x^8*y^13 + 46115*x^8*y^12 - 46077*x^8*y^11 +     47004*x^8*y^10 - 32761*x^8*y^9 + 13928*x^8*y^8 - 9223*x^8*y^7 + 7821*x^8*y^6    - 2540*x^8*y^5 - 360*x^8*y^4 + 298*x^8*y^3 - 29*x^8*y^2 + x^8*y + 4*x^7*y^23    - 28*x^7*y^22 - 178*x^7*y^21 + 280*x^7*y^20 - 153*x^7*y^19 + 2868*x^7*y^18 -    7799*x^7*y^17 + 11450*x^7*y^16 - 20871*x^7*y^15 + 37132*x^7*y^14 -     47503*x^7*y^13 + 50801*x^7*y^12 - 48458*x^7*y^11 + 36834*x^7*y^10 -     25174*x^7*y^9 + 18902*x^7*y^8 - 11029*x^7*y^7 + 3320*x^7*y^6 - 923*x^7*y^5 +    915*x^7*y^4 - 461*x^7*y^3 + 70*x^7*y^2 + x^7*y - 6*x^6*y^22 + 102*x^6*y^21 -    93*x^6*y^20 - 264*x^6*y^19 + 104*x^6*y^18 - 553*x^6*y^17 + 5165*x^6*y^16 -     11636*x^6*y^15 + 16058*x^6*y^14 - 21163*x^6*y^13 + 25518*x^6*y^12 -     23652*x^6*y^11 + 17982*x^6*y^10 - 12076*x^6*y^9 + 6419*x^6*y^8 -    3448*x^6*y^7 + 3084*x^6*y^6 - 2203*x^6*y^5 + 707*x^6*y^4 - 20*x^6*y^3 -     26*x^6*y^2 + x^6*y + 4*x^5*y^21 - 148*x^5*y^20 + 565*x^5*y^19 - 926*x^5*y^18    + 1535*x^5*y^17 - 3578*x^5*y^16 + 5680*x^5*y^15 - 5546*x^5*y^14 +     5335*x^5*y^13 - 7017*x^5*y^12 + 7965*x^5*y^11 - 6773*x^5*y^10 + 4679*x^5*y^9    - 2222*x^5*y^8 + 194*x^5*y^7 + 518*x^5*y^6 - 499*x^5*y^5 + 437*x^5*y^4 -     292*x^5*y^3 + 103*x^5*y^2 - 14*x^5*y - x^4*y^20 + 133*x^4*y^19 -     819*x^4*y^18 + 2357*x^4*y^17 - 4745*x^4*y^16 + 8692*x^4*y^15 -     14705*x^4*y^14 + 20527*x^4*y^13 - 23075*x^4*y^12 + 22036*x^4*y^11 -     18506*x^4*y^10 + 13206*x^4*y^9 - 7517*x^4*y^8 + 3134*x^4*y^7 - 667*x^4*y^6 -    235*x^4*y^5 + 266*x^4*y^4 - 91*x^4*y^3 + 9*x^4*y^2 + x^4*y - 84*x^3*y^18 +     672*x^3*y^17 - 2478*x^3*y^16 + 5815*x^3*y^15 - 10310*x^3*y^14 +     15307*x^3*y^13 - 19456*x^3*y^12 + 20558*x^3*y^11 - 17584*x^3*y^10 +     12110*x^3*y^9 - 6717*x^3*y^8 + 2931*x^3*y^7 - 922*x^3*y^6 + 143*x^3*y^5 +     50*x^3*y^4 - 56*x^3*y^3 + 28*x^3*y^2 - 8*x^3*y + x^3 + 36*x^2*y^17 -     333*x^2*y^16 + 1412*x^2*y^15 - 3680*x^2*y^14 + 6715*x^2*y^13 - 9312*x^2*y^12    + 10356*x^2*y^11 - 9444*x^2*y^10 + 6990*x^2*y^9 - 4065*x^2*y^8 +     1776*x^2*y^7 - 548*x^2*y^6 + 107*x^2*y^5 - 10*x^2*y^4 - 9*x*y^16 + 92*x*y^15    - 429*x*y^14 + 1210*x*y^13 - 2310*x*y^12 + 3168*x*y^11 - 3234*x*y^10 +     2508*x*y^9 - 1485*x*y^8 + 660*x*y^7 - 209*x*y^6 + 42*x*y^5 - 4*x*y^4 + y^15     - 11*y^14 + 55*y^13 - 165*y^12 + 330*y^11 - 462*y^10 + 462*y^9 - 330*y^8 +     165*y^7 - 55*y^6 + 11*y^5 - y^4;

//==================================== X_H(29), H=<2^2>  ========================================

N_X:=-(x^2*y-x*y+y-1)^3*y^15*x^15*(x*y-1)^12*(x*y-y+1)^3*(y-1)^19*(x-1)^6*(x^3*y-x^2*y^2-x^2*y+x*y^2-y+1)*(x^2*y-x^2-x*y^2+x*y-x+y-1)^9;
D_X:=x^23*(x*y-1)^15*(x*y-y+1)^2*(y-1)^22*(x-1)^2*y^10*(x-y+1)*(x^2*y-x*y^2+y-1)*(x-y)*(x^2*y-x*y^2-x*y+y^2-1)^10;

N_Y:=-(x^2*y-x*y+y-1)^69*y^367*x^395*(x*y-1)^313*(x*y-y+1)^66*(y-1)^474*(x-1)^132*(x^2*y-x^2-x*y^2+x*y-x+y-1)^210;
D_Y:=x^576*(x*y-1)^369*(x*y-y+1)^40*(y-1)^565*(x-1)^47*(x^4*y^2+6*x^3*y-6*x^3*y^2-x^3*y^3-4*x^2*y+6*x^2*y^3+x^2-3*x^2*y^2-3*y^3*x+x*y-2*x+4*x*y^2-y^3+1+3*y^2-3*y)^7*y^240*(x-y+1)^6*(x^2*y-x*y^2+y-1)^6*(x-y)^6*(x^3*y-x^2*y^2-x^2*y+x*y^2-y+1)^6*(x^2*y-x*y^2-x*y+y^2-1)^216;

X:=N_X/D_X;

Y:=N_Y/D_Y;

P_Xx:=-3*x*X^6+15*X^2*x^20-101*X^2*x^19+3217*X^3*x^12+331*X^3*x^11-2188*X^3*x^10+2172*X^3*x^9-1142*X^3*x^8+264*X^3*x^7+30*X^3*x^6-40*X^3*x^5+26*X^3*x^4-14*X^3*x^3-7693*X^3*x^15-7023*X^3*x^13+8891*X^3*x^14+4649*X^3*x^16-1929*X^3*x^17+524*X^3*x^18+6*X^3*x^20-84*X^3*x^19+7372*X^4*x^12-2366*X^4*x^11-189*X^4*x^10+536*X^4*x^9-166*X^4*x^8-192*X^4*x^7-84*x^12+126*x^11-126*x^10+84*x^9+X^10*x^12-X^10*x^11-8*X^10*x^10+16*X^10*x^9-8*X^10*x^8-X^10*x^7-36*x^8+9*x^7-x^6+736*X^7*x^12+732*X^7*x^11-2493*X^7*x^10+2728*X^7*x^9-1398*X^7*x^8+114*X^7*x^7+275*X^7*x^6-183*X^7*x^5+72*X^7*x^4-21*X^7*x^3-91*X^7*x^15-903*X^7*x^13+423*X^7*x^14+6*X^7*x^16+X^5-909*X*x^12+860*X*x^11-306*X*x^8+142*X*x^7-40*X*x^6+130*X*x^15+711*X*x^13-381*X*x^14-25*X*x^16+2*X*x^17-3*x*X^4+x^9*X^11-1606*X^2*x^12+2616*X^2*x^11-2396*X^2*x^10+1473*X^2*x^9-690*X^2*x^8+308*X^2*x^7-131*X^2*x^6+34*X^2*x^5-X^2*x^4-2278*X^2*x^15-171*X^2*x^13+1709*X^2*x^14+1866*X^2*x^16-1047*X^2*x^17-X^2*x^21+402*X^2*x^18+x^15+486*x^9*X-675*x^10*X+165*X^8*x^12+138*X^8*x^11-685*X^8*x^10+884*X^8*x^9-507*X^8*x^8+53*X^8*x^7+92*X^8*x^6-51*X^8*x^5+11*X^8*x^4-X^8*x^15-130*X^8*x^13+32*X^8*x^14+22*X^9*x^12+8*X^9*x^11-104*X^9*x^10+159*X^9*x^9-93*X^9*x^8+4*X^9*x^7+17*X^9*x^6-8*X^9*x^13+36*x^13-9*x^14-5*x^5*X^9+3*x^2*X^7-x^3*X^2-15*X^4*x^19+5242*X^5*x^12+405*X^5*x^11-3409*X^5*x^10+2448*X^5*x^9-356*X^5*x^8-602*X^5*x^7+593*X^5*x^6-373*X^5*x^5+188*X^5*x^4-70*X^5*x^3+21*X^5*x^2-3893*X^5*x^15-8608*X^5*x^13+7355*X^5*x^14+1289*X^5*x^16-245*X^5*x^17+20*X^5*x^18-6*X^5*x+2290*X^6*x^12+1589*X^6*x^11-4692*X^6*x^10+4256*X^6*x^9-1677*X^6*x^8-154*X^6*x^7+526*X^6*x^6-331*X^6*x^5+160*X^6*x^4-69*X^6*x^3+21*X^6*x^2-910*X^6*x^15-3587*X^6*x^13+2411*X^6*x^14+185*X^6*x^16-15*X^6*x^17+3*x^2*X^3+x^6*X^10+327*X^4*x^6-232*X^4*x^5+101*X^4*x^4-41*X^4*x^3+16*X^4*x^2-8164*X^4*x^15-11783*X^4*x^13+11973*X^4*x^14+3747*X^4*x^16-1116*X^4*x^17+195*X^4*x^18-x^3*X^8+5*x^5*X;
P_Xy:=-1-429*X^7*y^5+43*X^7*y^4+1964*X^7*y^6-5274*X^7*y^7+9368*X^7*y^8-11885*X^7*y^9+11584*X^7*y^10-9458*X^7*y^11+607*X^7*y^15+6840*X^7*y^12-4015*X^7*y^13+1233*X^7*y^14-1030*X^7*y^16+630*X^7*y^17-213*X^7*y^18+39*X^7*y^19-3*X^7*y^20+126*y^5-126*y^4-84*y^6+36*y^7-9*y^8+84*y^3+y^9-36*y^2+33*X^9*y^6-136*X^9*y^7+418*X^9*y^8-1145*X^9*y^9+2277*X^9*y^10-2882*X^9*y^11+240*X^9*y^15+2146*X^9*y^12-735*X^9*y^13-133*X^9*y^14-97*X^9*y^16+17*X^9*y^17-X^9*y^18-24*X^11*y^9+65*X^11*y^10-73*X^11*y^11+X^11*y^15+35*X^11*y^12-2*X^11*y^13-4*X^11*y^14-1415*X^3*y^5+329*X^3*y^4+3379*X^3*y^6-5218*X^3*y^7+5487*X^3*y^8-24*X^3*y^3-3618*X^3*y^9+341*X^3*y^10+2690*X^3*y^11+574*X^3*y^15-3901*X^3*y^12+3138*X^3*y^13-1646*X^3*y^14-129*X^3*y^16+17*X^3*y^17-X^3*y^18-373*X^2*y^5-33*X^2*y^4+1520*X^2*y^6-3355*X^2*y^7+4933*X^2*y^8+70*X^2*y^3-5054*X^2*y^9+3634*X^2*y^10-27*X^2*y^2-1814*X^2*y^11-X^2*y^15+612*X^2*y^12-133*X^2*y^13+17*X^2*y^14-2282*X^5*y^5+479*X^5*y^4+6768*X^5*y^6-14214*X^5*y^7+22381*X^5*y^8-26772*X^5*y^9+24037*X^5*y^10-15749*X^5*y^11+2445*X^5*y^15+6947*X^5*y^12-1026*X^5*y^13-1812*X^5*y^14-1781*X^5*y^16+831*X^5*y^17-244*X^5*y^18+41*X^5*y^19-3*X^5*y^20-1368*X^6*y^5+214*X^6*y^4+4908*X^6*y^6-11581*X^6*y^7+19560*X^6*y^8-24955*X^6*y^9+24592*X^6*y^10-18151*X^6*y^11+2216*X^6*y^15+8684*X^6*y^12-950*X^6*y^13-2324*X^6*y^14-1205*X^6*y^16+525*X^6*y^17-205*X^6*y^18+63*X^6*y^19-12*X^6*y^20+X^6*y^21-6*X^10*y^7+43*X^10*y^8-227*X^10*y^9+548*X^10*y^10-670*X^10*y^11-2924*X^4*y^5+634*X^4*y^4+8598*X^4*y^6-17489*X^4*y^7+25560*X^4*y^8-70*X^4*y^3-27306*X^4*y^9+21047*X^4*y^10-10344*X^4*y^11+3140*X^4*y^15+573*X^4*y^12+4669*X^4*y^13-5118*X^4*y^14-1241*X^4*y^16+313*X^4*y^17-46*X^4*y^18+3*X^4*y^19-46*y^3*X^5-y^3*X^7+y^2*X^4+2*y^8*X^11-y^9*X^12+3*y^4*X^8+4*y*X+4*y*X^2+y^6*X^10-3*y^2*X^3-3*y^5*X^9-12*y^3*X^6+748*X*y^5-467*X*y^4-770*X*y^6+490*X*y^7-158*X*y^8+183*X*y^3-8*X*y^9+27*X*y^10-41*X*y^2-9*X*y^11+X*y^12-60*X^8*y^5+378*X^8*y^6-1210*X^8*y^7+2495*X^8*y^8-3977*X^8*y^9+5428*X^8*y^10-6190*X^8*y^11+599*X^8*y^15+5304*X^8*y^12-2876*X^8*y^13+470*X^8*y^14-531*X^8*y^16+203*X^8*y^17-39*X^8*y^18+3*X^8*y^19+3*X^12*y^10-3*X^12*y^11+X^12*y^12+31*X^10*y^15+410*X^10*y^12-73*X^10*y^13-52*X^10*y^14-5*X^10*y^16+9*y;

f_29_2:=-(X^2-5*X-1)^7*Y^3+X^3*(4*X^2+9*X-4)*(34*X^6+621*X^5+389*X^4+917*X^3-389*X^2+621*X-34)*Y^2+X^5*(92*X^3+25*X^4+25-92*X+25*X^2)*Y+X^7;//used	

Total degree=17;
Degree(f_29_2,X)=14;
Degree(f_29_2,Y)=3;

//==================================== X_H(29), H=<2^2> smaller ========================================

N_X:=-(x^2*y-x*y+y-1)^3*y^15*x^15*(x*y-1)^12*(x*y-y+1)^3*(y-1)^19*(x-1)^6*(x^3*y-x^2*y^2-x^2*y+x*y^2-y+1)*(x^2*y-x^2-x*y^2+x*y-x+y-1)^9;
D_X:=x^23*(x*y-1)^15*(x*y-y+1)^2*(y-1)^22*(x-1)^2*y^10*(x-y+1)*(x^2*y-x*y^2+y-1)*(x-y)*(x^2*y-x*y^2-x*y+y^2-1)^10;

N_Y:=x^576*(x*y-1)^369*(x*y-y+1)^40*(y-1)^565*(x-1)^47*(x^4*y^2+6*x^3*y-6*x^3*y^2-x^3*y^3-4*x^2*y+6*x^2*y^3+x^2-3*x^2*y^2-3*y^3*x+x*y-2*x+4*x*y^2-y^3+1+3*y^2-3*y)^7*y^240*(x-y+1)^6*(x^2*y-x*y^2+y-1)^6*(x-y)^6*(x^3*y-x^2*y^2-x^2*y+x*y^2-y+1)^6*(x^2*y-x*y^2-x*y+y^2-1)^216;
D_Y:=-(x^2*y-x*y+y-1)^69*y^367*x^395*(x*y-1)^313*(x*y-y+1)^66*(y-1)^474*(x-1)^132*(x^2*y-x^2-x*y^2+x*y-x+y-1)^210;

X:=N_X/D_X;

Y:=N_Y/D_Y;


f_29_2:=Y^3*X^7+(92*X^8+25*X^5+25*X^9-92*X^6+25*X^7)*Y^2+(5141*X^7+7009*X^9+4685*X^8+136*X^3+136*X^11-4685*X^6+7009*X^5+2790*X^10-2790*X^4)*Y+1+4165*X^11+35*X+48650*X^9-X^14+19271*X^4+4165*X^3-27575*X^7-48965*X^8-19271*X^10-518*X^12+35*X^13+48965*X^6+48650*X^5+518*X^2;

Total degree=14;
Degree(f_29_2,X)=14;
Degree(f_29_2,Y)=3;
//==================================== X_H(29), H=<2^7>  ========================================

N_X:=y^4*(x-1)^2*(x^2*y - x*y + y - 1)^2*(x^2*y - x^2 - x*y^2 + x*y - x + y - 1)^6;
D_X:=(y-1)^2*x^4*(x-y)*(x - y + 1)*(x*y - 1)^2*(x^2*y - x*y^2 - x*y + y^2 - 1)^6;
X:=N_X/D_X;

N_Y:=y^3*(x-1)^2*(x - y + 1)*(x^2*y - x*y + y - 1)*(x^2*y - x^2 - x*y^2 + x*y - x + y - 1)^4;d_gx:=x^3*(x-y)*(x^2*y - x*y^2 - x*y + y^2 - 1)^4*(x^3*y^3 - x^2*y^3 - x^2*y^2 + x*y^3 - x*y - y^2 + 2*y - 1)^5*(x^4*y^4 - x^3*y^4 - x^3*y^3 + x^2*y^4 - x^2*y^2 - x*y^3 + 2*x*y^2 - x*y -y^2 +2*y - 1);
D_Y:=(y-1)^2*x^3*(x-y)*(x*y-1)*(x^2*y - x*y^2 - x*y + y^2 - 1)^4;
Y:=N_Y/D_Y;

P_Xx :=5*X^9+3*x^8*X-11*x^7*X-10*X^8-5*X^6-x^6+X^5+42*X^2*x^7-62*X^2*x^8-3*X^2*x^10-9*X^2*x^5+7*X^2*x^6+26*X^2*x^9+26*X^3*x^7+114*X^3*x^8+X^3*x^12-19*X^3*x^11+98*X^3*x^10-3*X^3*x^3+3*X^3*x^4+16*X^3*x^5-57*X^3*x^6-180*X^3*x^9-192*X^4*x^7+127*X^4*x^8-50*X^4*x^12+4*X^4*x^13+178*X^4*x^11-252*X^4*x^10+29*X^4*x^3-39*X^4*x^4-32*X^4*x^5+133*X^4*x^6-X^4*x^2+97*X^4*x^9+381*X^5*x^7-399*X^5*x^8+140*X^5*x^12-59*X^5*x^13-110*X^5*x^11+9*X^5*x^14-104*X^5*x^10+8*X^5*x-45*X^5*x^3+190*X^5*x^4-120*X^5*x^5-183*X^5*x^6-26*X^5*x^2+317*X^5*x^9-223*X^6*x^7+456*X^6*x^8+68*X^6*x^12+18*X^6*x^13-221*X^6*x^11-24*X^6*x^14+347*X^6*x^10-5*X^6*x-83*X^6*x^3-217*X^6*x^4+513*X^6*x^5-284*X^6*x^6+80*X^6*x^2-427*X^6*x^9-X^6*x^16+8*X^6*x^15-599*X^7*x^7+127*X^7*x^8-94*X^7*x^12+54*X^7*x^13+115*X^7*x^11-16*X^7*x^14-152*X^7*x^10-20*X^7*x+247*X^7*x^3-156*X^7*x^4-367*X^7*x^5+778*X^7*x^6-69*X^7*x^2+140*X^7*x^9+2*X^7*x^15+571*X^8*x^7-606*X^8*x^8-13*X^8*x^12+5*X^8*x^13+30*X^8*x^11-X^8*x^14-113*X^8*x^10+40*X^8*x-157*X^8*x^3+373*X^8*x^4-290*X^8*x^5-153*X^8*x^6-21*X^8*x^2+345*X^8*x^9+253*X^9*x^7+17*X^9*x^8+7*X^9*x^12-46*X^9*x^11+127*X^9*x^10-28*X^9*x-33*X^9*x^3-109*X^9*x^4+312*X^9*x^5-402*X^9*x^6+59*X^9*x^2-162*X^9*x^9-202*X^10*x^7+206*X^10*x^8-5*X^10*x^11+37*X^10*x^10+7*X^10*x+53*X^10*x^3-73*X^10*x^4+33*X^10*x^5+87*X^10*x^6-24*X^10*x^2-118*X^10*x^9-56*X^11*x^7+28*X^11*x^8+X^11*x^10-8*X^11*x^3+28*X^11*x^4-56*X^11*x^5+70*X^11*x^6-8*X^11*x^9+2*x^5*X+6*x^6*X-X^10+x^2*X^11+x^2*X^3-2*x*X^4-x^4*X^2+10*X^7;
P_Xy:=-13*X^11*y^4-X^11*y^6+11*X^11*y^3+2*X^11*y^2-2*X^12*y+X^12*y^2+X*y^11+X^12-75*X^10*y^4-3*X^10*y^6+39*X^10*y^3+2*X^10*y^8+5*X^11*y^5+2*X^5*y^14+39*X^5*y^13-2*X^5*y^15-168*X^5*y^12+94*X^5*y^6-1033*X^5*y^9+1205*X^5*y^8+57*X^6*y^10-1033*X^6*y^7-7*X^6*y^5+157*X^6*y^11-4*X^4*y^14+X^4*y^16+67*X^4*y^13-4*X^4*y^15-161*X^4*y^12+2*X^4*y^6-625*X^4*y^9+442*X^4*y^8+262*X^5*y^10-625*X^5*y^7+16*X^5*y^5+201*X^5*y^11+y^10+2*X*y^8+X*y^9-X*y^10+X^6*y^14+11*X^6*y^13-75*X^6*y^12+343*X^6*y^6-771*X^6*y^9+1340*X^6*y^8-13*X^7*y^10-771*X^7*y^7+61*X^7*y^5+46*X^7*y^11-13*X^7*y^12-46*X^7*y^4+262*X^7*y^6-304*X^7*y^9+769*X^7*y^8-168*X^9*y^4-13*X^9*y^6+67*X^9*y^3-5*X^9*y^9+31*X^9*y^8-5*X^10*y^7+46*X^10*y^5+2*X^2*y^10+X^2*y^7+16*X^2*y^11-X*y^12-13*y^4*X^6+4*y^3*X^7+31*y^3*X^8-7*y^2*X^9-4*y^2*X^10-4*y*X^11+y^6*X^2-y^6*X^3+y^5*X^4-y^4*X^5-3*X^8*y^10-304*X^8*y^7+201*X^8*y^5+5*X^8*y^11-161*X^8*y^4+57*X^8*y^6-61*X^8*y^9+236*X^8*y^8-X^9*y^10-61*X^9*y^7+157*X^9*y^5-2*X*y^7-2*y^9+y^8+4*X^2*y^13-13*X^2*y^12-16*X^2*y^9+5*X^2*y^8+94*X^3*y^10-16*X^3*y^7-7*X^3*y^11-7*X^3*y^14+31*X^3*y^13-46*X^3*y^12-118*X^3*y^9+69*X^3*y^8+343*X^4*y^10-118*X^4*y^7+61*X^4*y^11;
P_Yx := -Y^11-10*x^12*Y+x*Y^6+6*x*Y^7-x^7*Y^2+3*x^6*Y^3-5*x^5*Y^4-x^2*Y^5-x^12+x^13+5*x^11*Y+6*x^13*Y-Y*x^14-41*Y^2*x^12+18*Y^2*x^13-5*Y^2*x^9-5*Y^2*x^10+34*Y^2*x^11+3*Y^2*x^8-3*Y^2*x^14-87*Y^3*x^12+28*Y^3*x^13-38*Y^3*x^9-35*Y^3*x^10+109*Y^3*x^11-16*Y^3*x^7+39*Y^3*x^8-3*Y^3*x^14-102*Y^4*x^12+21*Y^4*x^13-104*Y^4*x^9-109*Y^4*x^10+192*Y^4*x^11+39*Y^4*x^6-121*Y^4*x^7+190*Y^4*x^8-Y^4*x^14-58*Y^5*x^12+5*Y^5*x^13+5*Y^5*x^3-130*Y^5*x^9-183*Y^5*x^10+184*Y^5*x^11-5*Y^5*x^4-38*Y^5*x^5+190*Y^5*x^6-415*Y^5*x^7+445*Y^5*x^8-10*Y^6*x^12+34*Y^6*x^3-50*Y^6*x^9-157*Y^6*x^10+80*Y^6*x^11-35*Y^6*x^4-104*Y^6*x^5+445*Y^6*x^6-717*Y^6*x^7+523*Y^6*x^8-10*Y^6*x^2+109*Y^7*x^3+18*Y^7*x^9-54*Y^7*x^10+10*Y^7*x^11-109*Y^7*x^4-130*Y^7*x^5+523*Y^7*x^6-623*Y^7*x^7+291*Y^7*x^8-41*Y^7*x^2+18*Y^8*x+192*Y^8*x^3+11*Y^8*x^9-5*Y^8*x^10-183*Y^8*x^4-50*Y^8*x^5+291*Y^8*x^6-255*Y^8*x^7+69*Y^8*x^8-87*Y^8*x^2+28*Y^9*x+184*Y^9*x^3+Y^9*x^9-157*Y^9*x^4+18*Y^9*x^5+69*Y^9*x^6-43*Y^9*x^7+5*Y^9*x^8-102*Y^9*x^2+21*Y^10*x+80*Y^10*x^3-54*Y^10*x^4+11*Y^10*x^5+5*Y^10*x^6-2*Y^10*x^7-58*Y^10*x^2+5*Y^11*x+10*Y^11*x^3-5*Y^11*x^4+Y^11*x^5-10*Y^11*x^2-Y^8-3*Y^9-3*Y^10;
P_Yy:=3*Y*y^12+199*Y*y^10-2352*Y*y^7-2124*Y*y^5-36*Y*y^11+1191*Y*y^4+2646*Y*y^6-444*Y*y^3-666*Y*y^9+1494*Y*y^8+99*Y*y^2+45*Y^2*y^12-3*Y^2*y^13+1309*Y^2*y^10-11254*Y^2*y^7-9684*Y^2*y^5-311*Y^2*y^11-25*Y^6*y^13+5829*Y^6*y^10-51854*Y^6*y^7-52126*Y^6*y^5-1491*Y^6*y^11+Y^6*y^14+32580*Y^6*y^4+60309*Y^6*y^6-548*Y^6*y-13995*Y^6*y^3-16260*Y^6*y^9+33516*Y^6*y^8+3775*Y^6*y^2+76*Y^7*y^12-5*Y^7*y^13+2516*Y^7*y^10-29368*Y^7*y^7-33273*Y^7*y^5-555*Y^7*y^11+21921*Y^7*y^4+36393*Y^7*y^6-470*Y^7*y-9958*Y^7*y^3-7837*Y^7*y^9+17637*Y^7*y^8+2888*Y^7*y^2+10*Y^8*y^12+670*Y^8*y^10-11290*Y^8*y^7-14876*Y^8*y^5-117*Y^8*y^11+10435*Y^8*y^4+15166*Y^8*y^6-280*Y^8*y-5034*Y^8*y^3-2435*Y^8*y^9+6163*Y^8*y^8+1567*Y^8*y^2+99*Y^9*y^10-2845*Y^9*y^7-4457*Y^9*y^5-10*Y^9*y^11+10*y^10-210*y^7-210*y^5-y^11+206*Y^3*y^12-22*Y^3*y^13+4196*Y^3*y^10-30729*Y^3*y^7-26210*Y^3*y^5-1137*Y^3*y^11+Y^3*y^14+14804*Y^3*y^4+33084*Y^3*y^6-135*Y^3*y-5624*Y^3*y^3-11023*Y^3*y^9+21303*Y^3*y^8+1285*Y^3*y^2-10*y*Y-46*y*Y^2-2*y*Y^11+y^2*Y^12+120*y^4+252*y^6+35*Y^6-y+3369*Y^9*y^4+4186*Y^9*y^6-108*Y^9*y-1744*Y^9*y^3-470*Y^9*y^9+1392*Y^9*y^8+581*Y^9*y^2+5*Y^10*y^10-460*Y^10*y^7-845*Y^10*y^5+672*Y^10*y^4+751*Y^10*y^6-22*Y^10*y-369*Y^10*y^3-44*Y^10*y^9+184*Y^10*y^8+127*Y^10*y^2-33*Y^11*y^7-113*Y^11*y^5+98*Y^11*y^4+79*Y^11*y^6-51*Y^11*y^3-Y^11*y^9+8*Y^11*y^8+15*Y^11*y^2-4*Y^12*y^5+6*Y^12*y^4+Y^12*y^6-4*Y^12*y^3+5413*Y^2*y^4+12247*Y^2*y^6-2025*Y^2*y^3-3733*Y^2*y^9+7588*Y^2*y^8+454*Y^2*y^2+427*Y^4*y^12-52*Y^4*y^13+7645*Y^4*y^10-53628*Y^4*y^7-46883*Y^4*y^5-2176*Y^4*y^11+3*Y^4*y^14+27104*Y^4*y^4+58215*Y^4*y^6-287*Y^4*y-10601*Y^4*y^3-19521*Y^4*y^9+37231*Y^4*y^8+2516*Y^4*y^2+454*Y^5*y^12-54*Y^5*y^13+8451*Y^5*y^10-63350*Y^5*y^7-58503*Y^5*y^5-2359*Y^5*y^11+3*Y^5*y^14+34998*Y^5*y^4+70561*Y^5*y^6-460*Y^5*y-14277*Y^5*y^3-22031*Y^5*y^9+42956*Y^5*y^8+3589*Y^5*y^2+254*Y^6*y^12-45*y^3-45*y^9+120*y^8+35*Y^7+21*Y^8+7*Y^9+Y^10+10*y^2+21*Y^5+Y^3+7*Y^4;

f_29_7:=10*X^4-5*X^5+5*X^2+4*Y^5+Y^6-40*X*Y^4-28*X*Y^5-12*X*Y^6-5*X*Y-16*X*Y^2-33*X*Y^3-2*X*Y^7+26*X^2*Y+71*X^2*Y^2+110*X^2*Y^3-49*X^3*Y-107*X^3*Y^2-114*X^3*Y^3-60*X^3*Y^4-30*X^3*Y^5+92*X^2*Y^4+41*X^2*Y^5+11*X^2*Y^6+4*X^2*Y^7+X^2*Y^8-19*X^3*Y^6-2*X^3*Y^7+41*X^4*Y+63*X^4*Y^2+44*X^4*Y^3+37*X^4*Y^4+6*Y^4+4*Y^3+Y^2+33*X^4*Y^5+X^4*Y^6-14*X^5*Y-14*X^5*Y^2-20*X^5*Y^3-10*X^3+X^6+4*X^6*Y^2+9*X^6*Y^3-26*X^5*Y^4+X^6*Y-X^7*Y^2-X;//used

Total degree=10;
Degree(f_29_7,X)=7;
Degree(f_29_7,Y)=8;
//==================================== X_H(31), H=<3^3>  ========================================

N_X:=-(x^2*y-x^2-x*y^2+x*y-x+y-1)^2*(x^3*y-x^2*y^2-x^2*y+x*y^2-y+1)*(x^2*y-x*y^2+y-1)*(x-y+1)*(x-1)^2*y^2;
D_X:=x^2*(x^2*y^2-2*x^2*y-x*y^3+2*x*y^2-y+1)^2*(x^2*y-x*y^2-x*y+y^2-1)*(x-y)*(y-1)*(x*y-1)*(x*y-y+1);
X :=N_X/D_X;

N_Y:=(x*y-1)*(x*y-y+1)^2*(x^2*y^2-2*x^2*y-x*y^3+2*x*y^2-y+1)^4;
D_Y:=y^2*(x^2*y-x^2-x*y^2+x*y-x+y-1)^3*(x^2*y-x*y^2-x*y+y^2-1)*(x-y)*(y-1)^2*(x-1)*(x^2*y-x*y+y-1)^2;
Y :=N_Y/D_Y;

P_Xx:=x^30*X^5 - 14*x^29*X^5 + x^28*X^8 - 4*x^28*X^7 - x^28*X^6 + 90*x^28*X^5+ 3*x^28*X^4 + 2*x^27*X^9 - 15*x^27*X^8 + 51*x^27*X^7 + 16*x^27*X^6 -374*x^27*X^5 - 31*x^27*X^4 + x^26*X^10 - 22*x^26*X^9 + 110*x^26*X^8 -287*x^26*X^7 - 148*x^26*X^6 + 1216*x^26*X^5 + 138*x^26*X^4 + 3*x^26*X^3- 11*x^25*X^10 + 122*x^25*X^9 - 497*x^25*X^8 + 943*x^25*X^7 +917*x^25*X^6 - 3427*x^25*X^5 - 385*x^25*X^4 - 21*x^25*X^3 - x^24*X^11 +59*x^24*X^10 - 445*x^24*X^9 + 1513*x^24*X^8 - 1890*x^24*X^7 -3919*x^24*X^6 + 8393*x^24*X^5 + 975*x^24*X^4 + 52*x^24*X^3 + x^24*X^2 +7*x^23*X^11 - 191*x^23*X^10 + 1131*x^23*X^9 - 3157*x^23*X^8 +1697*x^23*X^7 + 12073*x^23*X^6 - 17025*x^23*X^5 - 2810*x^23*X^4 -67*x^23*X^3 - 3*x^23*X^2 - x^22*X^12 - 14*x^22*X^11 + 377*x^22*X^10 -1937*x^22*X^9 + 4228*x^22*X^8 + 2728*x^22*X^7 - 27671*x^22*X^6 +27195*x^22*X^5 + 7708*x^22*X^4 + 335*x^22*X^3 - 18*x^22*X^2 +8*x^21*X^12 - 23*x^21*X^11 - 371*x^21*X^10 + 1967*x^21*X^9 -2670*x^21*X^8 - 13393*x^21*X^7 + 47262*x^21*X^6 - 31849*x^21*X^5 -16933*x^21*X^4 - 2135*x^21*X^3 + 109*x^21*X^2 + 2*x^21*X + x^20*X^13 -32*x^20*X^12 + 177*x^20*X^11 - 81*x^20*X^10 - 755*x^20*X^9 -1022*x^20*X^8 + 25455*x^20*X^7 - 58027*x^20*X^6 + 22163*x^20*X^5 +28290*x^20*X^4 + 7654*x^20*X^3 - 152*x^20*X^2 - 17*x^20*X - 4*x^19*X^13+ 72*x^19*X^12 - 392*x^19*X^11 + 551*x^19*X^10 + 87*x^19*X^9 +1507*x^19*X^8 - 28031*x^19*X^7 + 46835*x^19*X^6 + 1641*x^19*X^5 -33811*x^19*X^4 - 18095*x^19*X^3 - 369*x^19*X^2 + 51*x^19*X + 6*x^18*X^13- 89*x^18*X^12 + 414*x^18*X^11 - 81*x^18*X^10 - 2248*x^18*X^9 +4407*x^18*X^8 + 18981*x^18*X^7 - 19612*x^18*X^6 - 21659*x^18*X^5 +22644*x^18*X^4 + 31380*x^18*X^3 + 1970*x^18*X^2 - 7*x^18*X + x^18 -4*x^17*X^13 + 57*x^17*X^12 - 167*x^17*X^11 - 1126*x^17*X^10 +5276*x^17*X^9 - 9485*x^17*X^8 - 12325*x^17*X^7 - 42*x^17*X^6 +16497*x^17*X^5 + 6072*x^17*X^4 - 41371*x^17*X^3 - 4235*x^17*X^2 -436*x^17*X - 12*x^17 + x^16*X^13 - 19*x^16*X^12 - 32*x^16*X^11 +1565*x^16*X^10 - 4873*x^16*X^9 + 5651*x^16*X^8 + 16767*x^16*X^7 +2695*x^16*X^6 + 9188*x^16*X^5 - 32061*x^16*X^4 + 40303*x^16*X^3 +5694*x^16*X^2 + 1695*x^16*X + 66*x^16 + 10*x^15*X^12 + 11*x^15*X^11 -917*x^15*X^10 + 1786*x^15*X^9 + 1660*x^15*X^8 - 19686*x^15*X^7 -4699*x^15*X^6 - 25880*x^15*X^5 + 29771*x^15*X^4 - 26375*x^15*X^3 -4545*x^15*X^2 - 3883*x^15*X - 220*x^15 - 10*x^14*X^12 + 35*x^14*X^11 +365*x^14*X^10 - 251*x^14*X^9 - 2860*x^14*X^8 + 10127*x^14*X^7 +15920*x^14*X^6 + 18618*x^14*X^5 - 1497*x^14*X^4 + 10227*x^14*X^3 -935*x^14*X^2 + 6636*x^14*X + 495*x^14 + 5*x^13*X^12 - 7*x^13*X^11 -326*x^13*X^10 + 710*x^13*X^9 - 239*x^13*X^8 + 1718*x^13*X^7 -22642*x^13*X^6 - 4150*x^13*X^5 - 21989*x^13*X^4 - 6574*x^13*X^3 +11017*x^13*X^2 - 9336*x^13*X - 792*x^13 - x^12*X^12 - 17*x^12*X^11 +298*x^12*X^10 - 836*x^12*X^9 + 980*x^12*X^8 - 3620*x^12*X^7 +14553*x^12*X^6 + 737*x^12*X^5 + 20512*x^12*X^4 + 16141*x^12*X^3 -21745*x^12*X^2 + 11212*x^12*X + 924*x^12 + 11*x^11*X^11 - 132*x^11*X^10+ 218*x^11*X^9 + 680*x^11*X^8 - 683*x^11*X^7 - 2093*x^11*X^6 -4461*x^11*X^5 - 5741*x^11*X^4 - 24208*x^11*X^3 + 25991*x^11*X^2 -11371*x^11*X - 792*x^11 - 2*x^10*X^11 + 16*x^10*X^10 + 173*x^10*X^9 -1404*x^10*X^8 + 2475*x^10*X^7 - 2240*x^10*X^6 + 4087*x^10*X^5 -2185*x^10*X^4 + 19916*x^10*X^3 - 20385*x^10*X^2 + 9417*x^10*X + 495*x^10+ 5*x^9*X^10 - 131*x^9*X^9 + 758*x^9*X^8 - 970*x^9*X^7 - 143*x^9*X^6 +439*x^9*X^5 + 199*x^9*X^4 - 8012*x^9*X^3 + 9475*x^9*X^2 - 6140*x^9*X -220*x^9 - x^8*X^10 + 28*x^8*X^9 - 135*x^8*X^8 - 345*x^8*X^7 +2079*x^8*X^6 - 2901*x^8*X^5 + 2773*x^8*X^4 - 854*x^8*X^3 - 757*x^8*X^2 +3043*x^8*X + 66*x^8 - x^7*X^9 - 18*x^7*X^8 + 403*x^7*X^7 - 1540*x^7*X^6+ 1849*x^7*X^5 - 2043*x^7*X^4 + 2905*x^7*X^3 - 2520*x^7*X^2 - 1101*x^7*X- 12*x^7 + 7*x^6*X^8 - 122*x^6*X^7 + 465*x^6*X^6 - 164*x^6*X^5 -92*x^6*X^4 - 1380*x^6*X^3 + 2141*x^6*X^2 + 274*x^6*X + x^6 + 10*x^5*X^7- 20*x^5*X^6 - 394*x^5*X^5 + 984*x^5*X^4 - 50*x^5*X^3 - 958*x^5*X^2 -42*x^5*X + x^4*X^7 - 22*x^4*X^6 + 238*x^4*X^5 - 696*x^4*X^4 +403*x^4*X^3 + 263*x^4*X^2 + 3*x^4*X + 4*x^3*X^6 - 60*x^3*X^5 +249*x^3*X^4 - 240*x^3*X^3 - 42*x^3*X^2 + 6*x^2*X^5 - 48*x^2*X^4 +75*x^2*X^3 + 3*x^2*X^2 + 4*x*X^4 - 13*x*X^3 + X^3;
P_Yx:=x^30*Y^11 - 9*x^29*Y^11 + 2*x^29*Y^10 + 41*x^28*Y^11 - 18*x^28*Y^10 +x^28*Y^9 + x^28*Y^8 - 2*x^27*Y^12 - 130*x^27*Y^11 + 78*x^27*Y^10 -11*x^27*Y^9 - 10*x^27*Y^8 + 2*x^27*Y^7 + 16*x^26*Y^12 + 329*x^26*Y^11 -231*x^26*Y^10 + 50*x^26*Y^9 + 41*x^26*Y^8 - 20*x^26*Y^7 + x^26*Y^6 -62*x^25*Y^12 - 692*x^25*Y^11 + 546*x^25*Y^10 - 142*x^25*Y^9 -102*x^25*Y^8 + 85*x^25*Y^7 - 9*x^25*Y^6 + x^24*Y^13 + 153*x^24*Y^12 +1213*x^24*Y^11 - 1078*x^24*Y^10 + 304*x^24*Y^9 + 194*x^24*Y^8 -226*x^24*Y^7 + 31*x^24*Y^6 + x^24*Y^5 - 6*x^23*Y^13 - 268*x^23*Y^12 -1808*x^23*Y^11 + 1769*x^23*Y^10 - 506*x^23*Y^9 - 294*x^23*Y^8 +474*x^23*Y^7 - 53*x^23*Y^6 - 13*x^23*Y^5 - x^23*Y^4 + 15*x^22*Y^13 +359*x^22*Y^12 + 2392*x^22*Y^11 - 2424*x^22*Y^10 + 542*x^22*Y^9 +291*x^22*Y^8 - 863*x^22*Y^7 + 51*x^22*Y^6 + 76*x^22*Y^5 + 6*x^22*Y^4 -x^22*Y^3 - 20*x^21*Y^13 - 395*x^21*Y^12 - 2893*x^21*Y^11 +2860*x^21*Y^10 - 5*x^21*Y^9 - 49*x^21*Y^8 + 1362*x^21*Y^7 - 26*x^21*Y^6- 251*x^21*Y^5 - 12*x^21*Y^4 + 10*x^21*Y^3 + 15*x^20*Y^13 +376*x^20*Y^12 + 3167*x^20*Y^11 - 2992*x^20*Y^10 - 1380*x^20*Y^9 -431*x^20*Y^8 - 1844*x^20*Y^7 + 15*x^20*Y^6 + 594*x^20*Y^5 + 8*x^20*Y^4 -44*x^20*Y^3 + 2*x^20*Y^2 - 6*x^19*Y^13 - 311*x^19*Y^12 - 3052*x^19*Y^11+ 2739*x^19*Y^10 + 3490*x^19*Y^9 + 1105*x^19*Y^8 + 2085*x^19*Y^7 -190*x^19*Y^6 - 1200*x^19*Y^5 + 13*x^19*Y^4 + 113*x^19*Y^3 - 15*x^19*Y^2+ x^18*Y^13 + 220*x^18*Y^12 + 2556*x^18*Y^11 - 2075*x^18*Y^10 -5986*x^18*Y^9 - 2021*x^18*Y^8 - 1750*x^18*Y^7 + 908*x^18*Y^6 +2148*x^18*Y^5 - 66*x^18*Y^4 - 209*x^18*Y^3 + 49*x^18*Y^2 - x^18*Y -138*x^17*Y^12 - 1877*x^17*Y^11 + 1193*x^17*Y^10 + 8359*x^17*Y^9 +3205*x^17*Y^8 + 670*x^17*Y^7 - 2357*x^17*Y^6 - 3243*x^17*Y^5 +226*x^17*Y^4 + 343*x^17*Y^3 - 104*x^17*Y^2 + 7*x^17*Y + 84*x^16*Y^12 +1235*x^16*Y^11 - 370*x^16*Y^10 - 9798*x^16*Y^9 - 4574*x^16*Y^8 +886*x^16*Y^7 + 4262*x^16*Y^6 + 4027*x^16*Y^5 - 599*x^16*Y^4 -509*x^16*Y^3 + 178*x^16*Y^2 - 21*x^16*Y - 49*x^15*Y^12 - 749*x^15*Y^11 -246*x^15*Y^10 + 9593*x^15*Y^9 + 5860*x^15*Y^8 - 2628*x^15*Y^7 -6384*x^15*Y^6 - 4373*x^15*Y^5 + 1049*x^15*Y^4 + 578*x^15*Y^3 -266*x^15*Y^2 + 38*x^15*Y + 23*x^14*Y^12 + 425*x^14*Y^11 + 593*x^14*Y^10- 7775*x^14*Y^9 - 6597*x^14*Y^8 + 4619*x^14*Y^7 + 8983*x^14*Y^6 +4866*x^14*Y^5 - 1081*x^14*Y^4 - 375*x^14*Y^3 + 360*x^14*Y^2 - 52*x^14*Y+ x^14 - 7*x^13*Y^12 - 215*x^13*Y^11 - 648*x^13*Y^10 + 5155*x^13*Y^9 +6461*x^13*Y^8 - 6669*x^13*Y^7 - 12085*x^13*Y^6 - 6113*x^13*Y^5 +341*x^13*Y^4 - 129*x^13*Y^3 - 451*x^13*Y^2 + 61*x^13*Y - 4*x^13 +x^12*Y^12 + 86*x^12*Y^11 + 488*x^12*Y^10 - 2725*x^12*Y^9 - 5578*x^12*Y^8+ 7874*x^12*Y^7 + 14751*x^12*Y^6 + 7884*x^12*Y^5 + 914*x^12*Y^4 +736*x^12*Y^3 + 486*x^12*Y^2 - 60*x^12*Y + 6*x^12 - 23*x^11*Y^11 -267*x^11*Y^10 + 1081*x^11*Y^9 + 4296*x^11*Y^8 - 7432*x^11*Y^7 -15735*x^11*Y^6 - 9311*x^11*Y^5 - 2021*x^11*Y^4 - 1099*x^11*Y^3 -399*x^11*Y^2 + 52*x^11*Y - 4*x^11 + 3*x^10*Y^11 + 104*x^10*Y^10 -272*x^10*Y^9 - 2887*x^10*Y^8 + 5515*x^10*Y^7 + 14537*x^10*Y^6 +9612*x^10*Y^5 + 2410*x^10*Y^4 + 983*x^10*Y^3 + 216*x^10*Y^2 - 49*x^10*Y+ x^10 - 26*x^9*Y^10 + 12*x^9*Y^9 + 1599*x^9*Y^8 - 3087*x^9*Y^7 -11622*x^9*Y^6 - 8528*x^9*Y^5 - 1991*x^9*Y^4 - 491*x^9*Y^3 - 44*x^9*Y^2 +46*x^9*Y + 3*x^8*Y^10 + 21*x^8*Y^9 - 680*x^8*Y^8 + 1158*x^8*Y^7 +7985*x^8*Y^6 + 6469*x^8*Y^5 + 1189*x^8*Y^4 - 30*x^8*Y^3 - 26*x^8*Y^2 -31*x^8*Y - 8*x^7*Y^9 + 205*x^7*Y^8 - 172*x^7*Y^7 - 4625*x^7*Y^6 -4231*x^7*Y^5 - 502*x^7*Y^4 + 296*x^7*Y^3 - 4*x^7*Y^2 + 12*x^7*Y +x^6*Y^9 - 38*x^6*Y^8 - 86*x^6*Y^7 + 2172*x^6*Y^6 + 2423*x^6*Y^5 +123*x^6*Y^4 - 280*x^6*Y^3 + 50*x^6*Y^2 - 2*x^6*Y + 3*x^5*Y^8 +62*x^5*Y^7 - 773*x^5*Y^6 - 1228*x^5*Y^5 + 5*x^5*Y^4 + 144*x^5*Y^3 -53*x^5*Y^2 - 17*x^4*Y^7 + 187*x^4*Y^6 + 548*x^4*Y^5 - 14*x^4*Y^4 -41*x^4*Y^3 + 28*x^4*Y^2 + 2*x^3*Y^7 - 25*x^3*Y^6 - 206*x^3*Y^5 +3*x^3*Y^4 + 5*x^3*Y^3 - 8*x^3*Y^2 + x^2*Y^6 + 59*x^2*Y^5 + x^2*Y^2 -11*x*Y^5 + Y^5;
P_Xy:=-y^30*X^9 - 2*y^29*X^10 + 20*y^29*X^9 - y^28*X^11 + 36*y^28*X^10 -184*y^28*X^9 - 9*y^28*X^8 + 14*y^27*X^11 - 294*y^27*X^10 + 1007*y^27*X^9+ 160*y^27*X^8 - 2*y^26*X^12 - 78*y^26*X^11 + 1412*y^26*X^10 -3526*y^26*X^9 - 1290*y^26*X^8 - 36*y^26*X^7 + 32*y^25*X^12 +164*y^25*X^11 - 4280*y^25*X^10 + 7716*y^25*X^9 + 6093*y^25*X^8 +567*y^25*X^7 - y^24*X^13 - 235*y^24*X^12 + 404*y^24*X^11 +7870*y^24*X^10 - 8264*y^24*X^9 - 17964*y^24*X^8 - 3993*y^24*X^7 -84*y^24*X^6 + 16*y^23*X^13 + 1042*y^23*X^12 - 3915*y^23*X^11 -5972*y^23*X^10 - 5422*y^23*X^9 + 30997*y^23*X^8 + 16137*y^23*X^7 +1168*y^23*X^6 - 120*y^22*X^13 - 3080*y^22*X^12 + 13405*y^22*X^11 -9433*y^22*X^10 + 32263*y^22*X^9 - 16321*y^22*X^8 - 39116*y^22*X^7 -7161*y^22*X^6 - 126*y^22*X^5 + 560*y^21*X^13 + 6289*y^21*X^12 -27166*y^21*X^11 + 33246*y^21*X^10 - 37903*y^21*X^9 - 59559*y^21*X^8 +48894*y^21*X^7 + 24626*y^21*X^6 + 1541*y^21*X^5 - 1820*y^20*X^13 -8776*y^20*X^12 + 32992*y^20*X^11 - 40469*y^20*X^10 - 20447*y^20*X^9 +166312*y^20*X^8 + 9363*y^20*X^7 - 48293*y^20*X^6 - 8202*y^20*X^5 -126*y^20*X^4 + 4368*y^19*X^13 + 7656*y^19*X^12 - 14606*y^19*X^11 +15378*y^19*X^10 + 119133*y^19*X^9 - 187800*y^19*X^8 - 147298*y^19*X^7 +39084*y^19*X^6 + 23917*y^19*X^5 + 1350*y^19*X^4 - 8008*y^18*X^13 -2638*y^18*X^12 - 29154*y^18*X^11 + 11261*y^18*X^10 - 162501*y^18*X^9 +63821*y^18*X^8 + 240149*y^18*X^7 + 48050*y^18*X^6 - 37410*y^18*X^5 -6228*y^18*X^4 - 84*y^18*X^3 + 11440*y^17*X^13 - 1949*y^17*X^12 +76561*y^17*X^11 + 11734*y^17*X^10 + 114982*y^17*X^9 + 61077*y^17*X^8 -127777*y^17*X^7 - 164328*y^17*X^6 + 15070*y^17*X^5 + 15419*y^17*X^4 +785*y^17*X^3 - 12870*y^16*X^13 + 1210*y^16*X^12 - 103131*y^16*X^11 -81490*y^16*X^10 - 81870*y^16*X^9 + 3252*y^16*X^8 - 110816*y^16*X^7 +151901*y^16*X^6 + 55617*y^16*X^5 - 19208*y^16*X^4 - 3140*y^16*X^3 -36*y^16*X^2 + 11440*y^15*X^13 + 4226*y^15*X^12 + 104724*y^15*X^11 +133993*y^15*X^10 + 159844*y^15*X^9 - 177066*y^15*X^8 + 165616*y^15*X^7 +45527*y^15*X^6 - 107226*y^15*X^5 + 1118*y^15*X^4 + 6672*y^15*X^3 +292*y^15*X^2 - 8008*y^14*X^13 - 8722*y^14*X^12 - 92606*y^14*X^11 -127412*y^14*X^10 - 272585*y^14*X^9 + 186577*y^14*X^8 + 66681*y^14*X^7 -218516*y^14*X^6 + 48375*y^14*X^5 + 34097*y^14*X^4 - 6910*y^14*X^3 -1014*y^14*X^2 - 9*y^14*X + 4368*y^13*X^13 + 8375*y^13*X^12 +74277*y^13*X^11 + 87900*y^13*X^10 + 277957*y^13*X^9 + 19833*y^13*X^8 -284324*y^13*X^7 + 138810*y^13*X^6 + 87638*y^13*X^5 - 48223*y^13*X^4 -599*y^13*X^3 + 1890*y^13*X^2 + 63*y^13*X - 1820*y^12*X^13 -4672*y^12*X^12 - 50918*y^12*X^11 - 57471*y^12*X^10 - 172503*y^12*X^9 -200279*y^12*X^8 + 217162*y^12*X^7 + 96567*y^12*X^6 - 150964*y^12*X^5 +15717*y^12*X^4 + 11476*y^12*X^3 - 1826*y^12*X^2 - 189*y^12*X - y^12 +560*y^11*X^13 + 1276*y^11*X^12 + 26912*y^11*X^11 + 42242*y^11*X^10 +67797*y^11*X^9 + 190009*y^11*X^8 + 5594*y^11*X^7 - 207913*y^11*X^6 +79897*y^11*X^5 + 31997*y^11*X^4 - 14748*y^11*X^3 + 305*y^11*X^2 +312*y^11*X + 6*y^11 - 120*y^10*X^13 + 168*y^10*X^12 - 9660*y^10*X^11 -28715*y^10*X^10 - 25573*y^10*X^9 - 80504*y^10*X^8 - 119459*y^10*X^7 +128476*y^10*X^6 + 22428*y^10*X^5 - 46177*y^10*X^4 + 7389*y^10*X^3 +1487*y^10*X^2 - 304*y^10*X - 15*y^10 + 16*y^9*X^13 - 299*y^9*X^12 +1759*y^9*X^11 + 14270*y^9*X^10 + 19728*y^9*X^9 + 11109*y^9*X^8 +86539*y^9*X^7 - 16321*y^9*X^6 - 54397*y^9*X^5 + 25280*y^9*X^4 +1758*y^9*X^3 - 2079*y^9*X^2 + 177*y^9*X + 20*y^9 - y^8*X^13 +121*y^8*X^12 + 143*y^8*X^11 - 4634*y^8*X^10 - 15300*y^8*X^9 -119*y^8*X^8 - 26829*y^8*X^7 - 22280*y^8*X^6 + 30879*y^8*X^5 -2835*y^8*X^4 - 4879*y^8*X^3 + 1485*y^8*X^2 - 65*y^8*X - 15*y^8 -24*y^7*X^12 - 137*y^7*X^11 + 1009*y^7*X^10 + 7642*y^7*X^9 + 4142*y^7*X^8+ 3253*y^7*X^7 + 13920*y^7*X^6 - 7470*y^7*X^5 - 4185*y^7*X^4 +3177*y^7*X^3 - 657*y^7*X^2 + 21*y^7*X + 6*y^7 + 2*y^6*X^12 + 13*y^6*X^11- 265*y^6*X^10 - 2583*y^6*X^9 - 3501*y^6*X^8 - 868*y^6*X^7 -4066*y^6*X^6 + 143*y^6*X^5 + 2778*y^6*X^4 - 1100*y^6*X^3 + 169*y^6*X^2 -7*y^6*X - y^6 + 5*y^5*X^11 + 116*y^5*X^10 + 756*y^5*X^9 + 1295*y^5*X^8 +714*y^5*X^7 + 1146*y^5*X^6 + 518*y^5*X^5 - 1002*y^5*X^4 + 239*y^5*X^3 -16*y^5*X^2 - y^4*X^11 - 34*y^4*X^10 - 232*y^4*X^9 - 357*y^4*X^8 -134*y^4*X^7 - 347*y^4*X^6 - 342*y^4*X^5 + 262*y^4*X^4 - 36*y^4*X^3 +4*y^3*X^10 + 55*y^3*X^9 + 122*y^3*X^8 - 18*y^3*X^7 + 8*y^3*X^6 +136*y^3*X^5 - 34*y^3*X^4 - 6*y^2*X^9 - 34*y^2*X^8 - 7*y^2*X^7 +33*y^2*X^6 - 22*y^2*X^5 + 4*y*X^8 + 7*y*X^7 - 7*y*X^6 - X^7;
P_Yy:=y^30*Y^13 - 18*y^29*Y^13 + 2*y^29*Y^12 + 153*y^28*Y^13 - 31*y^28*Y^12 -3*y^28*Y^11 + 3*y^28*Y^10 - 816*y^27*Y^13 + 220*y^27*Y^12 + 48*y^27*Y^11- 55*y^27*Y^10 + 4*y^27*Y^9 + 3060*y^26*Y^13 - 943*y^26*Y^12 -370*y^26*Y^11 + 460*y^26*Y^10 - 58*y^26*Y^9 - 6*y^26*Y^8 + 3*y^26*Y^7 -8568*y^25*Y^13 + 2702*y^25*Y^12 + 1849*y^25*Y^11 - 2343*y^25*Y^10 +399*y^25*Y^9 + 84*y^25*Y^8 - 52*y^25*Y^7 + 2*y^25*Y^6 + 18564*y^24*Y^13- 5373*y^24*Y^12 - 6756*y^24*Y^11 + 8160*y^24*Y^10 - 1690*y^24*Y^9 -553*y^24*Y^8 + 419*y^24*Y^7 - 29*y^24*Y^6 - 3*y^24*Y^5 + y^24*Y^4 -31824*y^23*Y^13 + 7339*y^23*Y^12 + 19117*y^23*Y^11 - 20670*y^23*Y^10 +4698*y^23*Y^9 + 2257*y^23*Y^8 - 2095*y^23*Y^7 + 207*y^23*Y^6 +36*y^23*Y^5 - 15*y^23*Y^4 + 43758*y^22*Y^13 - 6267*y^22*Y^12 -42928*y^22*Y^11 + 39646*y^22*Y^10 - 7982*y^22*Y^9 - 6330*y^22*Y^8 +7294*y^22*Y^7 - 948*y^22*Y^6 - 199*y^22*Y^5 + 108*y^22*Y^4 - 2*y^22*Y^3- 48620*y^21*Y^13 + 1990*y^21*Y^12 + 76864*y^21*Y^11 - 59666*y^21*Y^10 +3763*y^21*Y^9 + 12789*y^21*Y^8 - 18682*y^21*Y^7 + 3068*y^21*Y^6 +675*y^21*Y^5 - 484*y^21*Y^4 + 28*y^21*Y^3 + 43758*y^20*Y^13 +1769*y^20*Y^12 - 108744*y^20*Y^11 + 73907*y^20*Y^10 + 21889*y^20*Y^9 -19135*y^20*Y^8 + 35913*y^20*Y^7 - 7373*y^20*Y^6 - 1583*y^20*Y^5 +1470*y^20*Y^4 - 179*y^20*Y^3 + y^20*Y^2 - 31824*y^19*Y^13 -363*y^19*Y^12 + 118424*y^19*Y^11 - 81386*y^19*Y^10 - 75992*y^19*Y^9 +22118*y^19*Y^8 - 51284*y^19*Y^7 + 13553*y^19*Y^6 + 2709*y^19*Y^5 -3103*y^19*Y^4 + 685*y^19*Y^3 - 14*y^19*Y^2 + 18564*y^18*Y^13 -6525*y^18*Y^12 - 92803*y^18*Y^11 + 87446*y^18*Y^10 + 139117*y^18*Y^9 -22111*y^18*Y^8 + 51768*y^18*Y^7 - 19206*y^18*Y^6 - 3235*y^18*Y^5 +4487*y^18*Y^4 - 1723*y^18*Y^3 + 91*y^18*Y^2 - 8568*y^17*Y^13 +13924*y^17*Y^12 + 40482*y^17*Y^11 - 94870*y^17*Y^10 - 166781*y^17*Y^9 +22328*y^17*Y^8 - 32818*y^17*Y^7 + 20056*y^17*Y^6 + 1465*y^17*Y^5 -4136*y^17*Y^4 + 2916*y^17*Y^3 - 360*y^17*Y^2 + 3060*y^16*Y^13 -16511*y^16*Y^12 + 12008*y^16*Y^11 + 97672*y^16*Y^10 + 125820*y^16*Y^9 -20011*y^16*Y^8 + 12843*y^16*Y^7 - 12004*y^16*Y^6 + 4881*y^16*Y^5 +1895*y^16*Y^4 - 3182*y^16*Y^3 + 954*y^16*Y^2 - 2*y^16*Y - 816*y^15*Y^13+ 13461*y^15*Y^12 - 41254*y^15*Y^11 - 87276*y^15*Y^10 - 31627*y^15*Y^9 +3702*y^15*Y^8 - 24716*y^15*Y^7 - 4495*y^15*Y^6 - 16567*y^15*Y^5 +28*y^15*Y^4 + 1850*y^15*Y^3 - 1748*y^15*Y^2 + 24*y^15*Y + 153*y^14*Y^13- 7993*y^14*Y^12 + 43295*y^14*Y^11 + 63259*y^14*Y^10 - 61128*y^14*Y^9 +31881*y^14*Y^8 + 82588*y^14*Y^7 + 20603*y^14*Y^6 + 30063*y^14*Y^5 +510*y^14*Y^4 - 226*y^14*Y^3 + 2176*y^14*Y^2 - 131*y^14*Y - 18*y^13*Y^13+ 3492*y^13*Y^12 - 30248*y^13*Y^11 - 34912*y^13*Y^10 + 106752*y^13*Y^9 -71558*y^13*Y^8 - 160713*y^13*Y^7 - 23878*y^13*Y^6 - 38916*y^13*Y^5 -2793*y^13*Y^4 + 929*y^13*Y^3 - 1660*y^13*Y^2 + 427*y^13*Y + y^12*Y^13 -1102*y^12*Y^12 + 15863*y^12*Y^11 + 12884*y^12*Y^10 - 100785*y^12*Y^9 +91118*y^12*Y^8 + 214400*y^12*Y^7 + 12074*y^12*Y^6 + 40564*y^12*Y^5 +5018*y^12*Y^4 - 4466*y^12*Y^3 + 500*y^12*Y^2 - 916*y^12*Y + y^12 +239*y^11*Y^12 - 6528*y^11*Y^11 - 1439*y^11*Y^10 + 68572*y^11*Y^9 -82342*y^11*Y^8 - 219590*y^11*Y^7 + 1329*y^11*Y^6 - 40009*y^11*Y^5 -7803*y^11*Y^4 + 7379*y^11*Y^3 - 10*y^11*Y^2 + 1335*y^11*Y - 10*y^11 -32*y^10*Y^12 + 2149*y^10*Y^11 - 1840*y^10*Y^10 - 35969*y^10*Y^9 +58107*y^10*Y^8 + 185457*y^10*Y^7 - 1788*y^10*Y^6 + 42888*y^10*Y^5 +12727*y^10*Y^4 - 5748*y^10*Y^3 + 1202*y^10*Y^2 - 1290*y^10*Y + 45*y^10 +2*y^9*Y^12 - 563*y^9*Y^11 + 1517*y^9*Y^10 + 14508*y^9*Y^9 -34887*y^9*Y^8 - 135167*y^9*Y^7 - 9402*y^9*Y^6 - 46675*y^9*Y^5 -17987*y^9*Y^4 + 164*y^9*Y^3 - 3397*y^9*Y^2 + 702*y^9*Y - 120*y^9 +112*y^8*Y^11 - 642*y^8*Y^10 - 4120*y^8*Y^9 + 19156*y^8*Y^8 +86245*y^8*Y^7 + 19049*y^8*Y^6 + 43793*y^8*Y^5 + 19187*y^8*Y^4 +4822*y^8*Y^3 + 4742*y^8*Y^2 + 16*y^8*Y + 210*y^8 - 15*y^7*Y^11 +170*y^7*Y^10 + 539*y^7*Y^9 - 9648*y^7*Y^8 - 47302*y^7*Y^7 -18949*y^7*Y^6 - 32227*y^7*Y^5 - 14833*y^7*Y^4 - 5969*y^7*Y^3 -4211*y^7*Y^2 - 382*y^7*Y - 252*y^7 + y^6*Y^11 - 27*y^6*Y^10 +148*y^6*Y^9 + 4125*y^6*Y^8 + 21487*y^6*Y^7 + 12174*y^6*Y^6 +17922*y^6*Y^5 + 8161*y^6*Y^4 + 4101*y^6*Y^3 + 2527*y^6*Y^2 + 327*y^6*Y +210*y^6 + 2*y^5*Y^10 - 97*y^5*Y^9 - 1348*y^5*Y^8 - 7783*y^5*Y^7 -5430*y^5*Y^6 - 7389*y^5*Y^5 - 3110*y^5*Y^4 - 1824*y^5*Y^3 - 1019*y^5*Y^2- 129*y^5*Y - 120*y^5 + 22*y^4*Y^9 + 301*y^4*Y^8 + 2189*y^4*Y^7 +1721*y^4*Y^6 + 2215*y^4*Y^5 + 782*y^4*Y^4 + 537*y^4*Y^3 + 262*y^4*Y^2 +14*y^4*Y + 45*y^4 - 2*y^3*Y^9 - 39*y^3*Y^8 - 475*y^3*Y^7 - 391*y^3*Y^6 -469*y^3*Y^5 - 118*y^3*Y^4 - 104*y^3*Y^3 - 39*y^3*Y^2 + 7*y^3*Y - 10*y^3+ 2*y^2*Y^8 + 81*y^2*Y^7 + 63*y^2*Y^6 + 66*y^2*Y^5 + 8*y^2*Y^4 +13*y^2*Y^3 + 3*y^2*Y^2 - 2*y^2*Y + y^2 - 11*y*Y^7 - 6*y*Y^6 - 5*y*Y^5 +Y^7;

f_31_3 := Y^6-3*X*Y^5-X*(-9*X+2*X^2-4)*Y^4+X*(X-1)*(4*X^2+3*X+2)*Y^3+X^2*(X^4+9*X^2-3*X^3+9-X)*Y^2-X^2*(2*X^2-4*X+3)*Y+X^2 ;//used	   

Total degree=8;
Degree(f_31_3,X)=6;
Degree(f_31_3,Y)=6;

//==================================== X_H(31), H=<3^5>  ========================================

N_X:=-(y-1)*(x^2*y - x*y^2 - x*y + y^2 - 1)*(x^2*y^2 - 2*x^2*y - x*y^3 + 2*x*y^2 - y + 1);
D_X:=y*(x-y)*(x-y+1)*(x^2*y - x*y^2 + y - 1)*(x^2*y - x^2 - x*y^2 + x*y - x + y - 1);
X :=N_X/D_X;

N_Y:=(y-1)*(x^2*y - x*y^2 + y - 1)^2*(x^2*y - x^2 - x*y^2 + x*y - x + y - 1)^2;
D_Y:=(x-y)*(x-y+1)*(x*y-1)*(x^2*y^2 - 2*x^2*y - x*y^3 + 2*x*y^2 - y + 1)^2;
Y :=N_Y/D_Y;

P_Xx:=-8*x^8+33*X*x^2+28*x^3+101*X*x^10-295*X*x^9+579*X*x^8-795*X*x^7+70*x^5+28*x^7-56*x^6-56*x^4-2179*X^2*x^6+7034*X^3*x^8-10103*X^4*x^10-21*X*x^11+102*X^2*x^13-2377*X^2*x^10+3498*X^2*x^9-3873*X^2*x^8+3285*X^2*x^7+1188*X^2*x^11+2*X*x^12-15*X^2*x^14-423*X^2*x^12-213*X^3*x^15+820*X^3*x^14-2271*X^3*x^13+4710*X^3*x^12-7434*X^3*x^11+9076*X^3*x^10-8814*X^3*x^9-3*X^12*x^21+2*X^12*x^19-X^12*x^18+4*X^12*x^17-2*X^12*x^16+X^13*x^20+X^2*x^15-3*X^3*x^17+36*X^3*x^16+202*X^4*x^17-758*X^4*x^16-4422*X^4*x^14+7526*X^4*x^13-10231*X^4*x^12+11152*X^4*x^11+2076*X^4*x^15-4084*X^6*x^14+6907*X^5*x^12+3*X^4*x^19-35*X^4*x^18-5726*X^5*x^11-70*X^5*x^19+270*X^5*x^18-773*X^5*x^17+1737*X^5*x^16-3230*X^5*x^15+5131*X^5*x^14-6723*X^5*x^13+352*X^4*x^5+7930*X^4*x^9-5312*X^4*x^8-2576*X^5*x^9+1245*X^5*x^8-496*X^5*x^7+169*X^5*x^6-33*X^5*x^5+X^5*x^4+36*X^6*x^7-223*X^6*x^9+70*X^6*x^8+56*X^6*x^10-16*X^6*x^6-5*X^7*x^8-446*X^7*x^10+175*X^7*x^9+551*X^7*x^11-8*X^7*x^7+1405*X^7*x^14-1925*X^7*x^15+701*X^7*x^18-1234*X^7*x^17-244*X^7*x^13+174*X^2*x^3+4*X^2*x-510*X^2*x^4-39*X^2*x^2-1129*X^3*x^5+360*X^3*x^4-71*X^3*x^3+6*X^3*x^2+1164*X^2*x^5-4691*X^3*x^7+2584*X^3*x^6+2859*X^4*x^7-1180*X^4*x^6-63*X^4*x^4+4*X^4*x^3+429*X^8*x^15-295*X^8*x^18+192*X^8*x^19-9*X^8*x^9-13*X^9*x^12+61*X^9*x^20-16*X^9*x^21+6*X^9*x^22-X^9*x^23+78*X^9*x^13+X^9*x^10+32*X^9*x^16-96*X^9*x^17-193*X^9*x^14+146*X^9*x^15+144*X^9*x^18-149*X^9*x^19+12*X^5*x^20+3614*X^6*x^13+956*X^6*x^17+131*X^6*x^19-385*X^6*x^18+9*X^6*x^21-40*X^6*x^20-1945*X^6*x^12-X^6*x^22-1903*X^6*x^16+3140*X^6*x^15+1682*X^7*x^16-278*X^7*x^19-2*X^8*x^8+200*X^8*x^12-98*X^8*x^20+48*X^8*x^21-15*X^8*x^22+2*X^8*x^23-183*X^8*x^11-199*X^8*x^13+87*X^8*x^10-449*X^8*x^16+327*X^8*x^17-35*X^8*x^14+4156*X^5*x^10+585*X^6*x^11-440*X^7*x^12+X^11*x^12-8*X^11*x^20+3*X^11*x^21-3*X^11*x^22-4*X^11*x^13+5*X^11*x^16+6*X^11*x^17+4*X^11*x^14-3*X^11*x^15-18*X^11*x^18+17*X^11*x^19+X-17*X^10*x^12-12*X^10*x^20+12*X^10*x^21-13*X^10*x^22+6*X^10*x^23-X^10*x^24+4*X^10*x^11+18*X^10*x^13+79*X^10*x^16-58*X^10*x^17+22*X^10*x^14-76*X^10*x^15+54*X^10*x^18-18*X^10*x^19-8*x^2+82*X^7*x^20-18*X^7*x^21+2*X^7*x^22+x^9-X^5*x^21+x+270*X*x^4-8*X*x+774*X*x^6-537*X*x^5-104*X*x^3;
P_Xy:=2*y^6*X-25*y^7*X+1708*X*y^14-744*X*y^15+217*X*y^16-38*X*y^17+3*X*y^18+153*X*y^8-587*X*y^9+1494*X*y^10-2600*X*y^11+3171*X*y^12-2754*X*y^13-21726*X^2*y^14+13140*X^2*y^15-5810*X^2*y^16+1835*X^2*y^17-393*X^2*y^18+51*X^2*y^19+587*X^2*y^7-3*X^2*y^20+26*X^2*y^5-156*X^2*y^6-1647*X^2*y^8+3976*X^2*y^9-8724*X^2*y^10+16325*X^2*y^11-23983*X^2*y^12+26504*X^2*y^13+82449*X^3*y^14-67605*X^3*y^15+41825*X^3*y^16-19260*X^3*y^17+6497*X^3*y^18-1559*X^3*y^19-24*X^3*y^21+X^3*y^22-3481*X^3*y^7+251*X^3*y^20-327*X^3*y^5+1190*X^3*y^6+8350*X^3*y^8+63*X^3*y^4-16296*X^3*y^9+26942*X^3*y^10-41069*X^3*y^11+59791*X^3*y^12-77732*X^3*y^13-60701*X^4*y^14+56020*X^4*y^15-44564*X^4*y^16+28247*X^4*y^17-13561*X^4*y^18+4777*X^4*y^19+203*X^4*y^21-21*X^4*y^22+X^4*y^23-36*y^14+9*y^15-y^16+X^11-2*y^4*X^2-6*y^3*X^3+y*X^4+10*y*X^8+7*y*X^9-7*y*X^10-2*y^2*X^12+y^4*X^13+y^7-9*y^8+36*y^9-84*y^10+126*y^11-126*y^12+84*y^13-6754*X^7*y^7+564*X^7*y^20-549*X^7*y^5+1860*X^7*y^6+16351*X^7*y^8+205*X^7*y^4-21208*X^7*y^9-83*X^7*y^3+3609*X^7*y^10+39002*X^7*y^11+36*X^7*y^2-78106*X^7*y^12+78573*X^7*y^13-12738*X^8*y^14+12638*X^8*y^15-5865*X^8*y^16+1015*X^8*y^17+261*X^8*y^18-153*X^8*y^19+343*X^8*y^7+21*X^8*y^20+18*X^8*y^5+X^8*y^6+180*X^8*y^8-141*X^8*y^4-5435*X^8*y^9+159*X^8*y^3+16485*X^8*y^10-24421*X^8*y^11-75*X^8*y^2+17932*X^8*y^12-236*X^8*y^13+1670*X^9*y^14+1002*X^9*y^15-1315*X^9*y^16+598*X^9*y^17-116*X^9*y^18+X^9*y^19+2785*X^9*y^7+2*X^9*y^20+188*X^9*y^5-1409*X^9*y^6-2020*X^9*y^8+68*X^9*y^4-1374*X^9*y^9+3*X^9*y^3+5274*X^9*y^10-7849*X^9*y^11-20*X^9*y^2+8180*X^9*y^12-5675*X^9*y^13+778*X^10*y^14-620*X^10*y^15+257*X^10*y^16-56*X^10*y^17+5*X^10*y^18+197*X^10*y^7-155*X^10*y^5+293*X^10*y^6-1670*X^10*y^8+44*X^10*y^4+3215*X^10*y^9-41*X^10*y^3-3645*X^10*y^10+12*y^2*X^5-6*y*X^6-6*y*X^7+2779*X^10*y^11+28*X^10*y^2-1226*X^10*y^12-176*X^10*y^13-117*X^11*y^14+28*X^11*y^15-3*X^11*y^16-5*X^11*y-438*X^11*y^7+161*X^11*y^6+576*X^11*y^8-22*X^11*y^4-340*X^11*y^9-129*X^11*y^10+456*X^11*y^11+9*X^11*y^2-468*X^11*y^12+291*X^11*y^13-34*X^12*y^14+9*X^12*y^15-X^12*y^16-364*X^12*y^7-14*X^12*y^5+155*X^12*y^6+506*X^12*y^8-23*X^12*y^4-474*X^12*y^9+12*X^12*y^3+289*X^12*y^10-75*X^12*y^11-50*X^12*y^12+66*X^12*y^13-56*X^13*y^7-8*X^13*y^5+28*X^13*y^6+70*X^13*y^8-56*X^13*y^9+28*X^13*y^10-8*X^13*y^11+X^13*y^12+8781*X^4*y^7-1197*X^4*y^20+1107*X^4*y^5-3746*X^4*y^6-15753*X^4*y^8-230*X^4*y^4+24555*X^4*y^9+45*X^4*y^3-35863*X^4*y^10+48198*X^4*y^11-9*X^4*y^2-57313*X^4*y^12+61023*X^4*y^13+9132*X^5*y^14-28292*X^5*y^15+30214*X^5*y^16-20895*X^5*y^17+10487*X^5*y^18-3908*X^5*y^19-193*X^5*y^21+21*X^5*y^22-X^5*y^23-9418*X^5*y^7+1055*X^5*y^20-674*X^5*y^5+2717*X^5*y^6+20190*X^5*y^8+281*X^5*y^4-25535*X^5*y^9-96*X^5*y^3+14312*X^5*y^10+9716*X^5*y^11-25374*X^5*y^12+16249*X^5*y^13+54311*X^6*y^14-27254*X^6*y^15-1444*X^6*y^16+16175*X^6*y^17-15842*X^6*y^18+9195*X^6*y^19+990*X^6*y^21-181*X^6*y^22+20*X^6*y^23-X^6*y^24+8067*X^6*y^7-3626*X^6*y^20+531*X^6*y^5-2839*X^6*y^6-15801*X^6*y^8+186*X^6*y^4+19926*X^6*y^9-197*X^6*y^3-10784*X^6*y^10-14287*X^6*y^11+60*X^6*y^2+44393*X^6*y^12-61592*X^6*y^13-39714*X^7*y^14-3980*X^7*y^15+23417*X^7*y^16-19714*X^7*y^17+9447*X^7*y^18-2887*X^7*y^19-67*X^7*y^21+4*X^7*y^22;
P_Yx:=-Y^8-7*Y*x^19+23*Y*x^20-46*Y*x^21+62*Y*x^22-56*Y*x^23+24*Y*x^24-2*Y*x^25+3*Y*x^26-5*Y*x^27-469*Y^2*x^19+467*Y^2*x^20-205*Y^2*x^21-93*Y^2*x^22+143*Y^2*x^23-38*Y^2*x^24-6*Y^2*x^25-9*Y^2*x^26+10*Y^2*x^27+29*Y^2*x^16-123*Y^2*x^17+300*Y^2*x^18-18*Y^3*x^13+7411*Y^3*x^19-6329*Y^3*x^20+3549*Y^3*x^21-1284*Y^3*x^22+382*Y^3*x^23-170*Y^3*x^24+60*Y^3*x^25+6*Y^3*x^26-10*Y^3*x^27-1190*Y^3*x^16+3262*Y^3*x^17-5906*Y^3*x^18+20*Y^3*x^14+213*Y^3*x^15+15*Y^4*x^11-147*Y^4*x^12+363*Y^4*x^13+3*Y^4*x^10-3*x^15*Y^2+3*x^12*Y^3-x^2*Y^11-x^4*Y^12+x^8*Y^13+x^18*Y+3*x*Y^9+5*x^2*Y^10-x^9*Y^4+x^7*Y^5-x^5*Y^6+8*x^3*Y^7-32434*Y^4*x^19+22664*Y^4*x^20-11700*Y^4*x^21+4731*Y^4*x^22-1685*Y^4*x^23+552*Y^4*x^24-129*Y^4*x^25+6*Y^4*x^26+5*Y^4*x^27+12632*Y^4*x^16-24805*Y^4*x^17+33592*Y^4*x^18+277*Y^4*x^14-3939*Y^4*x^15-7*Y^5*x^8-4*Y^5*x^11+540*Y^5*x^12+59*Y^5*x^13-147*Y^5*x^10+59193*Y^5*x^19-35336*Y^5*x^20+16718*Y^5*x^21-6568*Y^5*x^22+2217*Y^5*x^23-616*Y^5*x^24+118*Y^5*x^25-9*Y^5*x^26-Y^5*x^27-50431*Y^5*x^16+72844*Y^5*x^17-75998*Y^5*x^18-6325*Y^5*x^14+23698*Y^5*x^15+54*Y^5*x^9+24*Y^6*x^8-1759*Y^6*x^11+2110*Y^6*x^12+63*Y^6*x^7-15*Y^6*x^6-6705*Y^6*x^13+1287*Y^6*x^10-54104*Y^6*x^19+28629*Y^6*x^20-12421*Y^6*x^21+4494*Y^6*x^22-1339*Y^6*x^23+310*Y^6*x^24-48*Y^6*x^25+3*Y^6*x^26+84660*Y^6*x^16-95733*Y^6*x^17+81638*Y^6*x^18+23590*Y^6*x^14-54177*Y^6*x^15-506*Y^6*x^9-345*Y^7*x^8+5784*Y^7*x^11-6136*Y^7*x^12-5*Y^7*x^5-264*Y^7*x^7+167*Y^7*x^6-29*Y^7*x^4+12751*Y^7*x^13-4825*Y^7*x^10+28681*Y^7*x^19-13523*Y^7*x^20+5219*Y^7*x^21-1631*Y^7*x^22+395*Y^7*x^23-70*Y^7*x^24+8*Y^7*x^25-70811*Y^7*x^16+67185*Y^7*x^17-49268*Y^7*x^18-31267*Y^7*x^14+55671*Y^7*x^15+2305*Y^7*x^9+760*Y^8*x^8-2202*Y^8*x^11+1147*Y^8*x^12-55*Y^8*x^3-4*Y^8*x^5+304*Y^8*x^7-267*Y^8*x^6+91*Y^8*x^4-6418*Y^8*x^13+12*Y^8*x^2+3802*Y^8*x^10-9224*Y^8*x^19+3762*Y^8*x^20-1234*Y^8*x^21+320*Y^8*x^22-61*Y^8*x^23+8*Y^8*x^24-Y^8*x^25+34287*Y^8*x^16-28369*Y^8*x^17+18161*Y^8*x^18+18686*Y^8*x^14-30680*Y^8*x^15-2826*Y^8*x^9+2*Y^8*x+134*Y^9*x^8-2294*Y^9*x^11+2864*Y^9*x^12+117*Y^9*x^3+181*Y^9*x^5-448*Y^9*x^7+157*Y^9*x^6-229*Y^9*x^4+362*Y^9*x^13-30*Y^9*x^2+323*Y^9*x^10+1772*Y^9*x^19-605*Y^9*x^20+158*Y^9*x^21-31*Y^9*x^22+4*Y^9*x^23-10131*Y^9*x^16+7347*Y^9*x^17-4071*Y^9*x^18-5985*Y^9*x^14+10020*Y^9*x^15+382*Y^9*x^9-271*Y^10*x^8+2275*Y^10*x^11-2375*Y^10*x^12-31*Y^10*x^3+3*Y^10*x^5+358*Y^10*x^7-211*Y^10*x^6+62*Y^10*x^4+971*Y^10*x^13-1160*Y^10*x^10-180*Y^10*x^19+44*Y^10*x^20-6*Y^10*x^21+1806*Y^10*x^16-1139*Y^10*x^17+525*Y^10*x^18+895*Y^10*x^14-1918*Y^10*x^15+347*Y^10*x^9+104*Y^11*x^8-932*Y^11*x^11+862*Y^11*x^12+7*Y^11*x^3-6*Y^11*x^5-105*Y^11*x^7+65*Y^11*x^6-14*Y^11*x^4-425*Y^11*x^13+591*Y^11*x^10+4*Y^11*x^19-168*Y^11*x^16+84*Y^11*x^17-26*Y^11*x^18-5*Y^11*x^14+190*Y^11*x^15-225*Y^11*x^9-19*Y^12*x^8+196*Y^12*x^11-168*Y^12*x^12+6*Y^12*x^5+19*Y^12*x^7-15*Y^12*x^6+84*Y^12*x^13-133*Y^12*x^10+4*Y^12*x^16-Y^12*x^17-20*Y^12*x^14-3*Y^12*x^15+51*Y^12*x^9-20*Y^13*x^11+15*Y^13*x^12-6*Y^13*x^13+15*Y^13*x^10+Y^13*x^14-6*Y^13*x^9+x^27;
P_Yy:=-1-23880*Y^7*y^19+100515*Y^8*y^14-465337*Y^8*y^15+439776*Y^8*y^16+9635*Y^8*y^21-242373*Y^8*y^17+73774*Y^8*y^18-16242*Y^8*y^20-3328*Y^8*y^22-2824*Y^11*y^16+Y^11*y^21+1353*Y^11*y^17-440*Y^11*y^18+13573*Y^10*y^7+323*Y^10*y^5-2815*Y^10*y^6-42062*Y^10*y^8+89915*Y^10*y^9-136849*Y^10*y^10+148435*Y^10*y^11-109270*Y^10*y^12+24405*Y^10*y^16+65*Y^10*y^21-11962*Y^10*y^17+3635*Y^10*y^18+45*Y^13*y^14+1388*Y^9*y^19+10435*Y^10*y^14-30073*Y^10*y^15-1783852*Y^7*y^13+153070*Y^2*y^5-392943*Y^2*y^6-1351140*Y^2*y^8-46132*Y^2*y^4+1876923*Y^2*y^9+10258*Y^2*y^3-2176022*Y^2*y^10+2104580*Y^2*y^11-1564*Y^2*y^2-1682361*Y^2*y^12+1086959*Y^2*y^13+y^4*Y^11-16*y^3*Y^8+144*Y^2*y+806094*Y^2*y^7+Y^13*y^16-208701*Y^7*y^7+788*Y^7*y^5+30127*Y^7*y^6+757374*Y^7*y^8-10*Y^13*y^15-1033*Y^7*y^4-1817629*Y^7*y^9+126*Y^7*y^3+3103092*Y^7*y^10-3844110*Y^7*y^11+3361148*Y^7*y^12-3060*y^14+816*y^15-153*y^16-6*y*Y^5-487*Y^10*y^19-457*Y^11*y^14+3511*Y^11*y^15+60791*Y^7*y^20-895*Y^12*y^8+2101*Y^12*y^9-3335*Y^12*y^10+3669*Y*y^17-1416*Y*y^18+70064*Y^6*y^19+36495*Y^7*y^14+970776*Y^7*y^15-1041071*Y^7*y^16+65451*Y^9*y^17-20218*Y^9*y^18+2215*Y^9*y^20+476*Y^9*y^22-107*Y^9*y^23-82*Y*y-36868*Y^7*y^21+609560*Y^7*y^17-183933*Y^7*y^18-49839*Y^9*y^14+146360*Y^9*y^15-126001*Y^9*y^16-1388*Y^9*y^21-133212*Y^5*y^19-745339*Y^6*y^14-1226509*Y^6*y^15+1624638*Y^6*y^16+85847*Y^6*y^21-1025930*Y^6*y^17+309704*Y^6*y^18-138969*Y^6*y^20+306378*Y^6*y^7+242*Y^12*y^7-36*Y^12*y^6-2622*Y^6*y^5-40686*Y^6*y^6-1149158*Y^6*y^8+1804*Y^6*y^4+2839613*Y^6*y^9-201*Y^6*y^3-5018128*Y^6*y^10+6505892*Y^6*y^11-6088159*Y^6*y^12+3717555*Y^6*y^13-8029397*Y^5*y^11+136*Y^5*y^2+7877083*Y^5*y^12-5361776*Y^5*y^13+117312*Y^5*y^6+1504441*Y^5*y^8+5261*Y^5*y^4-3486461*Y^5*y^9-1082*Y^5*y^3+6084543*Y^5*y^10+46987*Y*y^14-5776*Y*y^15-4637*Y*y^16+2558*Y^8*y^19-Y^12*y^19-483601*Y^5*y^7-24189*Y^5*y^5+2*y^2*Y^6+3*Y*y^21-47*Y*y^20+680*Y^2*y^21-666*Y^2*y^20-230*Y^2*y^22+40*Y^2*y^23-3*Y^2*y^24+19540*Y*y^4-4701*Y*y^3+788*Y*y^2+18*y^17-y^18+1029732*Y^5*y^17-278979*Y^5*y^18+190700*Y^5*y^20+135554*Y^4*y^19+1861885*Y^5*y^14+724000*Y^5*y^15-1517852*Y^5*y^16-18044*Y^2*y^17+12033*Y^2*y^18+182709*Y^2*y^15-20896*Y^2*y^16+18*y-32989*Y^6*y^22+8445*Y^6*y^23-1355*Y^6*y^24+101*Y^6*y^25+4*Y^6*y^26-Y^6*y^27+13745*Y^7*y^22-3471*Y^7*y^23+587*Y^7*y^24-61*Y^7*y^25+3*Y^7*y^26+737*Y^8*y^23-98*Y^8*y^24+6*Y^8*y^25+15*Y^9*y^24-Y^9*y^25+336*Y*y^19-6*Y^2-540838*Y^2*y^14-8445*Y^3*y^21+29406*Y^3*y^20-663*Y^3*y^22+1618*Y^3*y^23-688*Y^3*y^24+155*Y^3*y^25-19*Y^3*y^26+Y^3*y^27+637926*Y^8*y^13+890447*Y^8*y^9-1450010*Y^8*y^10+1705051*Y^8*y^11-1389273*Y^8*y^12-713*Y^4*y^2-6936698*Y^4*y^12+5018180*Y^4*y^13+5611*Y^4*y^3-5613579*Y^4*y^10+7075178*Y^4*y^11-576784*Y^9*y^11+441882*Y^9*y^12-180275*Y^9*y^13+62142*Y^4*y^21-130917*Y^4*y^20-16258*Y^4*y^22+1109*Y^4*y^23+794*Y^4*y^24-305*Y^4*y^25+48*Y^4*y^26-3*Y^4*y^27-109773*Y^5*y^21-1859918*Y^4*y^8-28100*Y^4*y^4+3566083*Y^4*y^9+38695*Y^5*y^22-8273*Y^5*y^23+740*Y^5*y^24+105*Y^5*y^25-36*Y^5*y^26+3*Y^5*y^27+46*Y^4*y+819912*Y^4*y^7+103756*Y^4*y^5-313579*Y^4*y^6+1876*Y^8*y^5-22180*Y^8*y^6-391981*Y^8*y^8+67*Y^8*y^4-10*Y^13*y^7+45*Y^13*y^8+118470*Y^8*y^7-252*Y^13*y^11+210*Y^13*y^10-120*Y^13*y^9+10183*Y^9*y^6+151442*Y^9*y^8-329230*Y^9*y^9+514176*Y^9*y^10-48589*Y^9*y^7-1213*Y^9*y^5+210*Y^13*y^12-120*Y^13*y^13+31824*y^7-14*y^4*Y^10+8568*y^5-18564*y^6-43758*y^8-3060*y^4+48620*y^9+816*y^3-43758*y^10+31824*y^11-153*y^2-18564*y^12+4*Y+8568*y^13-3*y^2*Y^7-2311460*Y^4*y^14+209342*Y^4*y^15+604251*Y^4*y^16-455969*Y^4*y^17+65494*Y^4*y^18+y^6*Y^13-46282*Y^3*y^19-Y^4+2*y^5*Y^12-3095445*Y^3*y^9-10795*Y^3*y^3+4113454*Y^3*y^10-4574035*Y^3*y^11+1507*Y^3*y^2+4162883*Y^3*y^12-2994483*Y^3*y^13+3656*Y^12*y^11-2718*Y^12*y^12+1239*Y^12*y^13+98*Y^11*y^19+42862*Y^10*y^13+515686*Y*y^10-422493*Y*y^11+276039*Y*y^12-137935*Y*y^13-177*Y^12*y^15-104*Y^10*y^20-13*Y^10*y^22+Y^10*y^23-180*Y^12*y^14-120*Y^3*y-1068127*Y^3*y^7-178824*Y^3*y^5+484304*Y^3*y^6+1973878*Y^3*y^8+51412*Y^3*y^4+57*y^4*Y^9+145*Y^12*y^16-2420*Y^11*y^7-41*Y^11*y^5+449*Y^11*y^6+7922*Y^11*y^8-17307*Y^11*y^9+26345*Y^11*y^10-28194*Y^11*y^11+20470*Y^11*y^12-8453*Y^11*y^13-510763*Y*y^9+143659*Y*y^6+412677*Y*y^8-60292*Y*y^5-271246*Y*y^7-54*Y^12*y^17+59755*Y^3*y^16+22244*Y^3*y^17+24952*Y^3*y^18+11*Y^12*y^18+4*Y^3+1599063*Y^3*y^14-546710*Y^3*y^15-14*Y^11*y^20-2645*Y^2*y^19;

f_31_5:=-1+5*Y^7*X^5-100*Y^4*X^2-Y^6+6*Y^5-2*Y^6*X^8-68*Y^2*X^2-53*Y^6*X^6-15*Y^2-16*Y^5*X^5+9*Y^5*X^8+Y^7*X^4+14*Y*X-8*Y^7*X^7-77*Y^4*X^6+96*Y^4*X^5+17*Y^5*X^2+8*Y^2*X^4-68*Y^4*X-123*Y^3*X^4+7*Y^3*X^6+Y*X^2-58*Y^5*X^3+203*Y^4*X^4+39*Y^3*X^3+92*Y^3*X-21*Y^6*X^5+22*Y^5*X+17*Y^3*X^5+6*Y-111*Y^5*X^4+54*Y^4*X^3-6*Y^4*X^8+Y^8*X^7-58*Y^2*X+16*Y^6*X^3-2*Y^6*X+15*Y^6*X^4-15*Y^4+20*Y^3-Y^7*X^3+21*Y^6*X^7+7*Y^7*X^6+26*Y^4*X^7+122*Y^5*X^6+150*Y^3*X^2+Y^4*X^9-26*Y^5*X^7+14*X^3*Y^2;//used

Total degree=15;
Degree(f_31_5,X)=9;
Degree(f_31_5,Y)=8;

//==================================== X_H(31), H=<3^5>  smaller ========================================

N_X:=(x^2*y-x*y+y-1)^9*x^94*y^72*(x*y-1)^52*(x*y-y+1)^21*(x*y-y+1-x)^41*(1-x^5*y^2-38*x^4*y^3+34*x^2*y^5+13*x^3*y-36*x^3*y^2+2*x^3*y^4-14*x^2*y-x^3+13*x*y+3*x^5*y^3-3*x^5*y^4+24*x^4*y^4-3*x-6*y-20*x*y^2+15*y^2+25*x^4*y^2+y^6+33*x^3*y^3+17*x^2*y^2+12*x^2*y^3+5*x*y^4-20*y^3-6*x^4*y-7*x*y^5+10*x*y^3-6*y^5+2*x*y^6+3*x^2+x^5*y^5-4*x^4*y^5+7*x^3*y^6-18*x^3*y^5-x^4*y^6-9*x^2*y^6-43*x^2*y^4+15*y^4)*(y-1)^27*(-2*y+1+y^2)^5*(x-y+1)*(x^2*y-x*y^2+y-1)*(x-y)*(x^2*y-x*y^2-x*y+y^2-1)*(x^2*y-x^2-x*y^2+x*y-x+y-1)^27;
D_X:=(x*y-1)^58*(x*y-y+1)^31*(x*y-y+1-x)^31*x^105*y^56*(-2*y+1+y^2)^21*(x^2*y^2-2*x^2*y-x*y^3+2*x*y^2-y+1)^27;
X :=N_X/D_X;

N_Y:=(x^2*y-x*y+y-1)^13*x^130*y^100*(x*y-1)^73*(x*y-y+1)^29*(x*y-y+1-x)^57*(1-x^5*y^2-38*x^4*y^3+34*x^2*y^5+13*x^3*y-36*x^3*y^2+2*x^3*y^4-14*x^2*y-x^3+13*x*y+3*x^5*y^3-3*x^5*y^4+24*x^4*y^4-3*x-6*y-20*x*y^2+15*y^2+25*x^4*y^2+y^6+33*x^3*y^3+17*x^2*y^2+12*x^2*y^3+5*x*y^4-20*y^3-6*x^4*y-7*x*y^5+10*x*y^3-6*y^5+2*x*y^6+3*x^2+x^5*y^5-4*x^4*y^5+7*x^3*y^6-18*x^3*y^5-x^4*y^6-9*x^2*y^6-43*x^2*y^4+15*y^4)*(y-1)^36*(-2*y+1+y^2)^9*(x-y+1)*(x^2*y-x*y^2+y-1)*(x-y)*(x^3*y-x^2*y^2-x^2*y+x*y^2-y+1)*(x^2*y-x*y^2-x*y+y^2-1)*(x^2*y-x^2-x*y^2+x*y-x+y-1)^39;
D_Y:=(x*y-1)^82*(x*y-y+1)^43*(x*y-y+1-x)^43*x^146*y^77*(-2*y+1+y^2)^30*(x^2*y^2-2*x^2*y-x*y^3+2*x*y^2-y+1)^38;

Y :=N_Y/D_Y;

f_31_5:=(-6*X^2-X^4-4*X^3-1-4*X)*Y^6+(-X^5+1+20*X^2+14*X+9*X^3)*Y^5+(-14*X^2+4*X^5+9*X^4-11*X+7*X^3)*Y^4+(5*X^2-5*X^5-13*X^3-6*X^4)*Y^3+(20*X^3+6*X^5+7*X^4)*Y^2+(9*X^4+X^6+2*X^5)*Y+X^5;

Total degree=10;
Degree(f_31_5,X)=6;
Degree(f_31_5,Y)=6;

//==================================== X_H(37), H=<2^2>  ========================================

N_X:=-y^4*(x*y - 1)^4*(x^2*y - x*y + y - 1)^5*(x^2*y - x*y^2 - x*y + y^2 - 1)*(x^2*y - x^2 - x*y^2 + x*y - x + y - 1)*(x^3*y - x^2*y^2 - x^2*y + x*y^2 - y + 1)*(x^4*y - 3*x^3*y^2 + x^3*y + 2*x^2*y^3 + x^2*y^2 - 2*x^2*y - 2*x*y^3 + 2*x*y^2 + y^2 - 2*y + 1)^16*(x^4*y - x^3*y^3 - x^3*y + x^2*y^4 + x^2*y - x^2 - x*y^4 + x*y^3 - x*y^2 + x*y + y^3 - 2*y^2 + y);
D_X:=(y-1)*x^5*(x-1)^3*(x-y)*(x-y+1)*(x*y - y + 1)^3*(x^2*y - x*y^2 + y - 1)*(x^2*y^2 - 2*x^2*y - x*y^3 + 2*x*y^2 - y + 1)*(x^5*y^2 - 3*x^4*y^3 + 3*x^3*y^4 + 2*x^3*y^2 - 2*x^3*y - x^2*y^5 - x^2*y^4 - x^2*y^3 + x^2*y^2 + x^2*y + x*y^5 - x*y^4 + 2*x*y^3 - 2*x*y^2 - x*y + x - y^4 + 2*y^3 - y^2)^15;
X:=N_X/D_X;

N_Y:=-(x^2*y-x*y+y-1)^117*y^69*(x*y-1)^90*(x-y+1)^6*(x^2*y-x*y^2+y-1)^6*(x-y)^6*(x^3*y-x^2*y^2-x^2*y+x*y^2-y+1)^6*(x^2*y-x*y^2-x*y+y^2-1)^6*(x^2*y-x^2-x*y^2+x*y-x+y-1)^6*(x^2*y^2-2*x^2*y-x*y^3+2*x*y^2-y+1)^6*(x^4*y-x^3*y^3-x^3*y+x^2*y^4+x^2*y-x^2-x*y^4+x*y^3-x*y^2+x*y+y^3-2*y^2+y)^6*(x^4*y-3*x^3*y^2+x^3*y+2*x^2*y^3+x^2*y^2-2*x^2*y-2*x*y^3+2*x*y^2+y^2-2*y+1)^348*(-y^3-x^3*y^3+6*x^2*y^3-3*x*y^3+4*x*y^2-3*x^2*y^2+3*y^2-6*x^3*y^2+x^4*y^2-3*y+x*y+6*x^3*y-4*x^2*y+x^2-2*x+1)^9;
D_Y:=x^99*(x^5*y^2-3*x^4*y^3+3*x^3*y^4+2*x^3*y^2-2*x^3*y-x^2*y^5-x^2*y^4-x^2*y^3+x^2*y^2+x^2*y+x*y^5-x*y^4+2*x*y^3-2*x*y^2-x*y+x-y^4+2*y^3-y^2)^342*(y-1)^51*(x-1)^69*(x*y-y+1)^42;
Y:=N_Y/D_Y;

P_Xx:=x^20*(x-1)^10*X^18+x^15*(1+x^15+15*x^2+107*x^9-6*x+31*x^13-52*x^12-56*x^10-9*x^14+49*x^11-62*x^5+24*x^7-21*x^3+31*x^4-119*x^8+65*x^6)*(x-1)^5*X^17+x^14*(-9+198*x^15-71*x^2-73*x^9+45*x+451*x^13-194*x^12-277*x^10-427*x^14+125*x^11+22*x^5-605*x^7+x^3+67*x^4+710*x^8-45*x^16+4*x^17+87*x^6)*(x-1)^5*X^16-x^12*(-3-640*x^19-477*x^15+1529*x^18+3*x^22+192*x^20-284*x^2-1631*x^9+62*x+1945*x^13-2723*x^12-1639*x^10-1595*x^14+3895*x^11-150*x^5+968*x^7+490*x^3-189*x^4+945*x^8+2512*x^16-2570*x^17-36*x^21-602*x^6)*(x-1)^4*X^15+x^10*(1+4581*x^19-10093*x^15-1043*x^24+2307*x^18-4115*x^22+2702*x^23-4934*x^20-294*x^2-10797*x^9+18*x-612*x^13-4974*x^12+16935*x^10+8266*x^14-6222*x^11+626*x^5-2913*x^7+1281*x^3-24*x^26+x^27-2225*x^4+2734*x^8+223*x^25+13532*x^16-12119*x^17+4374*x^21+2777*x^6)*(x-1)^3*X^14+x^9*(-9-7719*x^19-23065*x^15-8251*x^24-7987*x^18-1954*x^22+6287*x^23+10204*x^20+816*x^2+3766*x^9-31*x-38901*x^13+70127*x^12-8226*x^10+11082*x^14-36437*x^11+1647*x^5+3339*x^7-3390*x^3+4*x^29-2493*x^26+596*x^27+4817*x^4+8172*x^8-76*x^28+5982*x^25+17366*x^16+8102*x^17-3486*x^21-10258*x^6)*(x-1)^3*X^13+x^8*(-36-41*x^19+325026*x^15+11319*x^24-130234*x^18-45217*x^22+21766*x^23+66453*x^20+1338*x^2-26232*x^9+88*x-3937*x^13+87934*x^12-40338*x^10-243630*x^14+17451*x^11-3415*x^5+37353*x^7-8076*x^3-4047*x^29+15035*x^26-14041*x^27+16175*x^4+6*x^32-123*x^31+978*x^30+16854*x^8+9646*x^28-17095*x^25-233465*x^16+182522*x^17-6368*x^21-33671*x^6)*(x-1)^2*X^12+x^7*(x-1)*(-86-609399*x^19+337605*x^15-73503*x^24+785719*x^18+286511*x^22-61198*x^23+423681*x^20+188*x^2-198645*x^9+550*x-147320*x^13-48776*x^12+184313*x^10-484*x^14+51447*x^11-31481*x^5+134195*x^7-10463*x^3+13052*x^29-41394*x^26+28430*x^27+33893*x^4+11*x^35-160*x^34+992*x^33-3401*x^32+7095*x^31-10060*x^30-27193*x^8-19873*x^28+72091*x^25-154681*x^16-473327*x^17-397239*x^21-51102*x^6)*X^11-x^5*(1-204878*x^19+1148665*x^15-2098844*x^24-407073*x^18+x^40-1344110*x^22+2251072*x^23+437382*x^20-1186*x^2+1111*x^36-17*x^39+124*x^38-494*x^37+156949*x^9+119*x+339545*x^13+357590*x^12+197129*x^10-895415*x^14-575684*x^11-38374*x^5-47623*x^7+3534*x^3-235977*x^29-285739*x^26-195932*x^27+2280*x^4-1195*x^35-70*x^34+175*x^33+10130*x^32-46801*x^31+125240*x^30-121927*x^8+308405*x^28+1184422*x^25-1214496*x^16+974483*x^17+128847*x^21+88632*x^6)*X^10+x^4*(x-1)*(-5+874979*x^19-407081*x^15-1289730*x^24-1060456*x^18-559111*x^22+1177127*x^23-160243*x^20+1046*x^2-160*x^36+12*x^37-29862*x^9-71*x-835122*x^13+495617*x^12-104469*x^10+666677*x^14+119*x^11+16090*x^5+35287*x^7-4205*x^3-84484*x^29-624352*x^26+298886*x^27+4187*x^4+788*x^35-1259*x^34-4232*x^33+28288*x^32-75280*x^31+114562*x^30+42876*x^8-56029*x^28+1003809*x^25+172356*x^16+436795*x^17-22578*x^21-50782*x^6)*X^9+x^3*(-10-26363*x^19+639511*x^15+430919*x^24-280883*x^18+1079287*x^22-825518*x^23+473515*x^20+394*x^2-68*x^36+5*x^37-14073*x^9+29*x-322424*x^13+319102*x^12-50911*x^10-152137*x^14-48128*x^11+2260*x^5+8151*x^7-2564*x^3-39851*x^29+205316*x^26-207925*x^27+4843*x^4+424*x^35-1652*x^34+4665*x^33-10243*x^32+16005*x^31-8102*x^30+30572*x^8+132228*x^28-216472*x^25-718934*x^16+523300*x^17-926450*x^21-17863*x^6)*(x-1)^2*X^8+x^2*(-10-366103*x^19+104148*x^15-358868*x^24+428935*x^18-731631*x^22+618004*x^23+12993*x^20-64*x^2+x^36+7144*x^9+73*x+3304*x^13+46069*x^12-40593*x^10-130333*x^14+15196*x^11-1130*x^5+1463*x^7-793*x^3+1841*x^29-71917*x^26+22955*x^27+2498*x^4-11*x^35+41*x^34+7*x^33-499*x^32+1591*x^31-2286*x^30+8767*x^8-4592*x^28+170398*x^25+101811*x^16-310371*x^17+476114*x^21-4272*x^6)*(x-1)^3*X^7+x*(-5+117952*x^19-1281*x^15+178072*x^24-66620*x^18+144160*x^22-186068*x^23-51125*x^20-103*x^2+7262*x^9+43*x-19606*x^13+31485*x^12-16951*x^10-19839*x^14-103*x^11-395*x^5+199*x^7-87*x^3+2385*x^29+62252*x^26-20985*x^27+645*x^4+x^35-15*x^34+103*x^33-424*x^32+1141*x^31-2143*x^30+981*x^8+2365*x^28-124060*x^25+58605*x^16-35168*x^17-61896*x^21-987*x^6)*(x-1)^4*X^6-(1+17529*x^19-14937*x^15+26137*x^24-4038*x^18+10569*x^22-24391*x^23-26074*x^20+25*x^2-1462*x^9-9*x+1472*x^13-8812*x^12+2627*x^10+13572*x^14+2631*x^11-30*x^5+542*x^7-9*x^3-1208*x^29+15438*x^26-8344*x^27-41*x^4+2*x^32-36*x^31+271*x^30-611*x^8+3636*x^28-22410*x^25+7157*x^16-2918*x^17+13937*x^21+36*x^6)*(x-1)^5*X^5+x^2*(3-3726*x^19-1612*x^15-345*x^24+3700*x^18-1280*x^22+743*x^23+1451*x^20+36*x^2+2593*x^9-21*x+5396*x^13+1972*x^12-173*x^10-6112*x^14-4494*x^11+204*x^5-1175*x^7+76*x^3-20*x^26+x^27-321*x^4-454*x^8+114*x^25+7660*x^16-6045*x^17+974*x^21+645*x^6)*(x-1)^6*X^4+x^6*(7+4*x^19-282*x^15+3*x^18-71*x^2-354*x^9-4*x-1495*x^13+580*x^12+234*x^10+815*x^14+268*x^11-383*x^5+545*x^7+69*x^3+228*x^4-292*x^8+196*x^16-86*x^17-102*x^6)*(x-1)^7*X^3-x^5*(-1-55*x^15+5*x^2+69*x^9+2*x-20*x^13+160*x^12-117*x^10+46*x^14-64*x^11+23*x^5-28*x^7-11*x^3-7*x^4+24*x^8+13*x^16+x^17+5*x^6)*(x-1)^8*X^2+x^11*(6*x^7-12*x^6-4*x^5-5*x^4+3*x^3+7*x^2-3*x-2)*(x-1)^9*X-x^15*(x-1)^10;
P_Xy:=(y-1)^20*X^19+y*(3*y^9-22*y^8+72*y^7-129*y^6+116*y^5-16*y^4-55*y^3+35*y^2-5)*(y-1)^15*X^18+y^2*(7-562*y^12+1084*y^11-35*y^14-105*y-1192*y^10+125*y^9-3936*y^7+345*y^2-2668*y^5+3*y^15+183*y^13+3995*y^6+1418*y^4+2070*y^8-734*y^3)*(y-1)^13*X^17+y^2*(19-14952*y^12+67377*y^11+30534*y^14+1583*y^17-60*y-99665*y^10+y^23+89852*y^9+26496*y^7-353*y^2+12524*y^5-19494*y^15+5802*y^16-2831*y^18+130*y^21-17*y^22-584*y^20+1659*y^19-22411*y^13-16018*y^6-7616*y^4-54658*y^8+2681*y^3)*(y-1)^10*X^16-y^3*(6+213774*y^12-473914*y^11-147748*y^14+11240*y^17+y^24+352*y+526417*y^10-14*y^23-335461*y^9+89713*y^7-1817*y^2+60621*y^5+115166*y^15-49882*y^16+515*y^18-328*y^21+87*y^22+873*y^20-1621*y^19+45091*y^13-107373*y^6-21740*y^4+69838*y^8+6200*y^3)*(y-1)^9*X^15-y^3*(11+2364780*y^12+636*y^26-1238307*y^11+2393146*y^14-3713*y^25+700651*y^17+14289*y^24-91*y+138720*y^10-37203*y^23+540238*y^9+595083*y^7-276*y^2+130320*y^5-1166756*y^15-57637*y^16-710164*y^18-39138*y^21+61589*y^22-106847*y^20+402969*y^19-2882189*y^13-333289*y^6+3*y^28-34520*y^4-65*y^27-737863*y^8+5620*y^3)*(y-1)^7*X^14+y^4*(-27-4373164*y^12-9310*y^26+y^31+10663052*y^11-20*y^30+20741048*y^14+2424*y^25+675053*y^17+188*y^29+65746*y^24-375*y-8992271*y^10-245913*y^23+4582849*y^9+383885*y^7+5282*y^2-50011*y^5-21277798*y^15+11139858*y^16-6370274*y^18+201810*y^21+378138*y^22-2343192*y^20+5516252*y^19-9121160*y^13-50279*y^6-1090*y^28+54429*y^4+4148*y^27-1554839*y^8-24441*y^3)*(y-1)^5*X^13-y^4*(-4-33802457*y^12+469167*y^26-166*y^31+20274692*y^11+2491*y^30+3042823*y^14-576942*y^25-39457328*y^17-17590*y^29+96560*y^24-17*y+y^33-3849856*y^10+1469705*y^23-4434423*y^9-2831213*y^7+844*y^2-354584*y^5-38573497*y^15+53030307*y^16+13973562*y^18+8110945*y^21-4365872*y^22-10093046*y^20+4421606*y^19+27431947*y^13-4*y^32+1127293*y^6+77607*y^28+87845*y^4-231577*y^27+4984993*y^8-13816*y^3)*(y-1)^4*X^12+y^5*(-18+42102054*y^12-1204280*y^26-9173*y^31-3752678*y^11+42906*y^30+69903225*y^14+3662625*y^25+121921941*y^17-134947*y^29-4379263*y^24+184*y-118*y^33-16560435*y^10-3281763*y^23+18555533*y^9+5036880*y^7+737*y^2+188215*y^5-6944012*y^15-77967595*y^16-93847705*y^18-40351857*y^21+22433783*y^22+29601143*y^20+24388744*y^19-76364874*y^13+1321*y^32-1346953*y^6+250406*y^28-3450*y^4+5*y^34-51976*y^27-11885039*y^8-3572*y^3)*(y-1)^3*X^11+y^5*(1+59982357*y^12+2797711*y^26+3*y^36-148271*y^31-94*y^35-52896967*y^11+268246*y^30-130195575*y^14-9278352*y^25-121866609*y^17-127355*y^29+5688663*y^24-23*y-9742*y^33+24612752*y^10+27053059*y^23-5859232*y^9+2229189*y^7-123*y^2+408155*y^5+203302247*y^15-102523393*y^16+267773368*y^18+74045195*y^21-76465080*y^22+41579152*y^20-211537333*y^19+3569872*y^13+47484*y^32-1291549*y^6-525473*y^28-67801*y^4+1264*y^34+615290*y^27-1186282*y^8+5252*y^3)*(y-1)^2*X^10-y^6*(-1+185963883*y^12-1462806*y^26-3758*y^36-31*y^38+253895*y^31+21576*y^35-48403388*y^11+919211*y^30+39192843*y^14+19145418*y^25+147166882*y^17-3221410*y^29-59778553*y^24+70*y+240159*y^33-30989671*y^10+113230090*y^23+39614866*y^9+10063344*y^7-994*y^2+847497*y^5+305953364*y^15-438080324*y^16+317481552*y^18-62510367*y^21-105920315*y^22+358234655*y^20-525348076*y^19-235832227*y^13-421782*y^32-3412269*y^6+5235100*y^28-132039*y^4-86466*y^34-4534715*y^27+y^39-23437414*y^8+11762*y^3+439*y^37)*X^9-y^7*(y-1)*(-5+109302463*y^12+5928615*y^26+47788*y^31+6*y^35-30270764*y^11-125524*y^30-38018415*y^14-6603571*y^25-46699775*y^17+128118*y^29-4408404*y^24+132*y+1678*y^33-31821190*y^10+31963724*y^23+37478269*y^9+4720174*y^7-1140*y^2+133664*y^5+165591626*y^15-128605379*y^16+181912397*y^18+40364906*y^21-58534262*y^22+50922840*y^20-164595180*y^19-97807247*y^13-11195*y^32-695592*y^6+454827*y^28-48102*y^4-149*y^34-2510103*y^27-18204961*y^8+9732*y^3)*X^8-y^8*(-2+40688602*y^12+142643*y^26+4*y^31-20096063*y^11-54*y^30-20974475*y^14-402851*y^25-24988639*y^17+110*y^29+514772*y^24-8*y-9882082*y^10+673610*y^23+18739669*y^9+938535*y^7+118*y^2-730214*y^5+35346432*y^15-7824513*y^16+29106184*y^18+8659947*y^21-4420155*y^22-5629765*y^20-10583179*y^19-20955897*y^13+1416974*y^6+2726*y^28+140929*y^4-28767*y^27-9845778*y^8-8818*y^3)*(y-1)^2*X^7-y^9*(7+7580538*y^12+693*y^26-6965699*y^11-3730039*y^14-4679*y^25-2960762*y^17+18593*y^24-204*y-95279*y^10-38258*y^23+4782588*y^9+163788*y^7+2348*y^2-785850*y^5+1647667*y^15+2384450*y^16+893591*y^18+263302*y^21-5069*y^22-703891*y^20+626377*y^19-1012546*y^13+1156700*y^6+2*y^28+242532*y^4-57*y^27-3425017*y^8-35824*y^3)*(y-1)^3*X^6-y^10*(19+144987*y^12-944634*y^11-174912*y^14-30222*y^17+6*y^24-227*y+729520*y^10-87*y^23+286110*y^9+122118*y^7+4838*y^2-371242*y^5-177855*y^15+181512*y^16-37072*y^18-345*y^21+438*y^22-5550*y^20+24905*y^19+407978*y^13+376324*y^6+167683*y^4-663199*y^8-41082*y^3)*(y-1)^4*X^5+y^10*(1-7063*y^12-79440*y^11-5491*y^14+263*y^17-8*y+91816*y^10+1891*y^9-35642*y^7+355*y^2-63136*y^5-12795*y^15+7007*y^16-1395*y^18+5*y^21-84*y^20+526*y^19+35438*y^13+88745*y^6+22638*y^4-39218*y^8-4403*y^3)*(y-1)^5*X^4-y^12*(-14+1579*y^12-3457*y^11-387*y^14-12*y^17+302*y-1653*y^10+11137*y^9+1356*y^7-2298*y^2+17484*y^5+23*y^15+41*y^16+y^18+396*y^13-4790*y^6-18688*y^4-10246*y^8+9225*y^3)*(y-1)^5*X^3-y^13*(11+2*y^12-5*y^11-117*y-27*y^10+100*y^9-280*y^7+564*y^2-44*y^5+263*y^6+451*y^4-12*y^8-909*y^3)*(y-1)^7*X^2+y^14*(y^7-2*y^6-4*y^5+6*y^4+3*y^3+14*y^2-27*y+4)*(y-1)^9*X+y^15*(y-1)^10;

f_37_2:=-X^9*Y^5+X^8*(42*X^2-547*X-42)*Y^4+X^6*(895*X^6+30696*X^4-8403*X-128697*X^3-895-30696*X^2-8403*X^5)*Y^3-X^4*(61239*X^9-408+408*X^10+61239*X-5203230*X^6+2938638*X^7-684189*X^8+5203230*X^4+2938638*X^3+684189*X^2+13223411*X^5)*Y^2+X^2*(-391135275*X^9+242823585*X^8+39*X^14-28269*X^13+1694238*X^12-22865208*X^11+136215400*X^10-247869536*X^7-391135275*X^5-28269*X-39-242823585*X^6-1694238*X^2-136215400*X^4-22865208*X^3)*Y-(X^2+12*X-1)^9;  

Total degree=18;
Degree(f_37_2,X)=18;
Degree(f_37_2,Y)=5;

//==================================== X_H(37), H=<2^2>  smaller ========================================
N_X:=-x^230*(x*y-1)^85*(x*y-y+1)^17*(x*y-y+1-x)^29*y^150*(-2*y+1+y^2)^86*(x^5*y^2-3*x^4*y^3+3*x^3*y^4+2*x^3*y^2-2*x^3*y-x^2*y^5-x^2*y^4-x^2*y^3+x^2*y^2+x^2*y+x*y^5-x*y^4+2*x*y^3-2*x*y^2-x*y+x-y^4+2*y^3-y^2)^114;
D_X:=(x^2*y-x*y+y-1)^39*y^173*x^197*(x*y-1)^115*(x*y-y+1)^3*(x*y-y+1-x)^3*(1-x^5*y^2-38*x^4*y^3+34*x^2*y^5+13*x^3*y-36*x^3*y^2+2*x^3*y^4-14*x^2*y-x^3+13*x*y+3*x^5*y^3-3*x^5*y^4+24*x^4*y^4-3*x-6*y-20*x*y^2+15*y^2+25*x^4*y^2+y^6+33*x^3*y^3+17*x^2*y^2+12*x^2*y^3+5*x*y^4-20*y^3-6*x^4*y-7*x*y^5+10*x*y^3-6*y^5+2*x*y^6+3*x^2+x^5*y^5-4*x^4*y^5+7*x^3*y^6-18*x^3*y^5-x^4*y^6-9*x^2*y^6-43*x^2*y^4+15*y^4)^3*(y-1)^104*(-2*y+1+y^2)^34*(x-y+1)^2*(x^2*y-x*y^2+y-1)^2*(x-y)^2*(x^3*y-x^2*y^2-x^2*y+x*y^2-y+1)^2*(x^2*y-x*y^2-x*y+y^2-1)^2*(x^2*y-x^2-x*y^2+x*y-x+y-1)^2*(x^2*y^2-2*x^2*y-x*y^3+2*x*y^2-y+1)^2*(x^4*y-x^3*y^3-x^3*y+x^2*y^4+x^2*y-x^2-x*y^4+x*y^3-x*y^2+x*y+y^3-2*y^2+y)^2*(x^4*y-3*x^3*y^2+x^3*y+2*x^2*y^3+x^2*y^2-2*x^2*y-2*x*y^3+2*x*y^2+y^2-2*y+1)^116;

X:=N_X/D_X;

N_Y:=-(x^2*y-x*y+y-1)^5*y^25*x^25*(x*y-1)^16*(y-1)^14*(-2*y+1+y^2)^7*(x^3*y-x^2*y^2-x^2*y+x*y^2-y+1)*(x^2*y-x*y^2-x*y+y^2-1)*(x^2*y-x^2-x*y^2+x*y-x+y-1)*(x^4*y-x^3*y^3-x^3*y+x^2*y^4+x^2*y-x^2-x*y^4+x*y^3-x*y^2+x*y+y^3-2*y^2+y)*(x^4*y-3*x^3*y^2+x^3*y+2*x^2*y^3+x^2*y^2-2*x^2*y-2*x*y^3+2*x*y^2+y^2-2*y+1)^16;
D_Y:=x^30*(x*y-1)^12*(x*y-y+1)^3*(x*y-y+1-x)^3*y^21*(-2*y+1+y^2)^13*(x-y+1)*(x^2*y-x*y^2+y-1)*(x-y)*(x^2*y^2-2*x^2*y-x*y^3+2*x*y^2-y+1)*(x^5*y^2-3*x^4*y^3+3*x^3*y^4+2*x^3*y^2-2*x^3*y-x^2*y^5-x^2*y^4-x^2*y^3+x^2*y^2+x^2*y+x*y^5-x*y^4+2*x*y^3-2*x*y^2-x*y+x-y^4+2*y^3-y^2)^15;
Y:=N_Y/D_Y;

f_37_2:=X^5*Y^6+(36*X^5+33*X^4)*Y^5+(-466*X^4+429*X^5+51*X^3-13*X^2)*Y^4+(542*X^4+1656*X^5+63*X^2-91*X^3-5*X+1)*Y^3+(13*X^2+466*X^4-429*X^5-51*X^3)*Y^2+(36*X^5+33*X^4)*Y-X^5;

Total degree=11;
Degree(f_37_2,X)=5;
Degree(f_37_2,Y)=6;
//==================================== X_H(37), H=<2^3>  ========================================

N_X:=-y*(x^2*y - x*y + y - 1)*(x^3*y - x^2*y^2 - x^2*y + x*y^2 - y + 1)*(x^4*y - 3*x^3*y^2 + x^3*y + 2*x^2*y^3 + x^2*y^2 - 2*x^2*y - 2*x*y^3 + 2*x*y^2 + y^2 - 2*y + 1)^3;
D_X:=(y-1)*(x-1)*(x - y + 1)*(x^2*y - x*y^2 + y - 1)*(x^2*y - x*y^2 - x*y + y^2 - 1)*(x^5*y^2 - 3*x^4*y^3 + 3*x^3*y^4 + 2*x^3*y^2 - 2*x^3*y - x^2*y^5 - x^2*y^4 - x^2*y^3 + x^2*y^2 + x^2*y + x*y^5 - x*y^4 + 2*x*y^3 - 2*x*y^2 - x*y + x - y^4 + 2*y^3 - y^2)^2;
X:=N_X/D_X;

N_Y:=-y^2*(x-y)*(x*y - 1)^3*(x^2*y - x*y + y - 1)^4*(x^2*y - x^2 - x*y^2 + x*y - x + y - 1)*(x^2*y^2 - 2*x^2*y - x*y^3 + 2*x*y^2 - y + 1)*(x^4*y - 3*x^3*y^2 + x^3*y + 2*x^2*y^3 + x^2*y^2 - 2*x^2*y - 2*x*y^3 + 2*x*y^2 + y^2 - 2*y + 1)^10*(x^4*y - x^3*y^3 - x^3*y + x^2*y^4 + x^2*y - x^2 - x*y^4 + x*y^3 - x*y^2 + x*y + y^3 - 2*y^2 + y);
D_Y:=(y - 1)^2*x^3*(x - 1)^2*(x*y - y + 1)*(x^3*y - x^2*y^2 - x^2*y + x*y^2 - y + 1)*(x^5*y^2 - 3*x^4*y^3 + 3*x^3*y^4 + 2*x^3*y^2 - 2*x^3*y - x^2*y^5 - x^2*y^4 - x^2*y^3 + x^2*y^2 + x^2*y + x*y^5 - x*y^4 + 2*x*y^3 - 2*x*y^2 - x*y + x - y^4 + 2*y^3 - y^2)^11;
Y:=N_Y/D_Y;


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P_Yy:=124*y^3*Y^10+6*y^2*Y^10-13*y*Y^10-8575162*y^7*Y^10+1680064*y^6*Y^10-203627*y^5*Y^10+11478*y^4*Y^10+30022366*y^8*Y^10-76040021*y^9*Y^10+143604998*y^10*Y^10-177847006*y^13*Y^10+222375136*y^12*Y^10-205334342*y^11*Y^10+94642289*y^14*Y^10+86330*y^24*Y^10-331257*y^23*Y^10+764782*y^22*Y^10-638372*y^21*Y^10-2377842*y^20*Y^10+11349312*y^19*Y^10-25983245*y^18*Y^10+37547855*y^17*Y^10-28888318*y^16*Y^10-15852666*y^15*Y^10+y^28*Y^10-69*y^27*Y^10+1394*y^26*Y^10-14196*y^25*Y^10+4*y^2*Y^3-86*y^3*Y^3+840*y^4*Y^3-5018*y^5*Y^3+20886*y^6*Y^3-64544*y^7*Y^3+152811*y^8*Y^3-280874*y^9*Y^3+401072*y^10*Y^3-440086*y^11*Y^3+361116*y^12*Y^3-207944*y^13*Y^3-6*y^3*Y^2+87*y^4*Y^2-630*y^5*Y^2+2894*y^6*Y^2-9265*y^7*Y^2-y*Y^4+43*y^2*Y^4-615*y^3*Y^4+4957*y^4*Y^4-26757*y^5*Y^4+105347*y^6*Y^4-318284*y^7*Y^4+758913*y^8*Y^4-1443626*y^9*Y^4+2186496*y^10*Y^4-2604709*y^11*Y^4+2381888*y^12*Y^4-9*y^4*Y^16+106*y^5*Y^16-579*y^6*Y^16+1963*y^7*Y^16-4098*y^8*Y^16-280*y^9*Y^16+48676*y^10*Y^16-246262*y^11*Y^16+751256*y^12*Y^16-4563663*y^11*Y^15+9042509*y^12*Y^15-14238326*y^13*Y^15+17972924*y^14*Y^15-18142213*y^15*Y^15+14398821*y^16*Y^15-8554393*y^17*Y^15+3186991*y^18*Y^15+126293*y^19*Y^15-1356967*y^20*Y^15+1334871*y^21*Y^15-882759*y^22*Y^15+454470*y^23*Y^15-187242*y^24*Y^15+61086*y^25*Y^15-15328*y^26*Y^15+2831*y^27*Y^15-360*y^28*Y^15+28*y^29*Y^15-y^30*Y^15+9*y^6+Y^10-7*y*Y^5-2583*y^3*Y^5+206*y^2*Y^5+19439*y^4*Y^5-1176964*y^7*Y^5+391100*y^6*Y^5+194207*y^24*Y^11-37591*y^25*Y^11+4731*y^26*Y^11-346*y^27*Y^11+11*y^28*Y^11-101078*y^5*Y^5+8668824*y^10*Y^5-5503636*y^9*Y^5+2829356*y^8*Y^5-10946891*y^11*Y^5+10850694*y^12*Y^5-19*y^3*Y^15+146*y^4*Y^15-323*y^5*Y^15+424*y^6*Y^15-10563*y^7*Y^15+101669*y^8*Y^15-519999*y^9*Y^15+1789093*y^10*Y^15-8113928*y^13*Y^5-1592598*y^13*Y^4+685408*y^14*Y^4-87101*y^15*Y^4-114969*y^16*Y^4+96968*y^17*Y^4-39751*y^18*Y^4+9613*y^19*Y^4-1293*y^20*Y^4+70*y^21*Y^4+y^22*Y^4-1035318*y^15*Y^5+4180930*y^14*Y^5+1718*y^21*Y^5-17619*y^20*Y^5+92936*y^19*Y^5-295449*y^18*Y^5+558538*y^17*Y^5-400234*y^16*Y^5+5*y^4*Y^17-84*y^5*Y^17+622*y^6*Y^17-2527*y^7*Y^17+5002*y^8*Y^17+4030*y^9*Y^17-21*y*Y^6+543*y^2*Y^6-6703*y^3*Y^6+51244*y^4*Y^6-272734*y^5*Y^6+1080953*y^6*Y^6-3325461*y^7*Y^6+8150805*y^8*Y^6-16164823*y^9*Y^6+26099421*y^10*Y^6-34182800*y^11*Y^6+35771836*y^12*Y^6-28963858*y^13*Y^6+16905155*y^14*Y^6-5659176*y^15*Y^6-629928*y^16*Y^6+2124576*y^17*Y^6-1406453*y^18*Y^6+539037*y^19*Y^6-127480*y^20*Y^6+16422*y^21*Y^6-409*y^22*Y^6-162*y^23*Y^6+15*y^24*Y^6-6*y^23*Y^5-28*y^22*Y^5-82*y^3*Y^14+704*y^4*Y^14-1529*y^5*Y^14-8867*y^6*Y^14+82518*y^7*Y^14-344766*y^8*Y^14+953481*y^9*Y^14-1902691*y^10*Y^14+2760672*y^11*Y^14-2655167*y^12*Y^14-84*y^11+15*y^6*Y^19-105*y^7*Y^19+455*y^8*Y^19-1365*y^9*Y^19+3003*y^10*Y^19-5005*y^11*Y^19+6435*y^12*Y^19-6435*y^13*Y^19+5005*y^14*Y^19-3003*y^15*Y^19+1365*y^16*Y^19-455*y^17*Y^19+105*y^18*Y^19-15*y^19*Y^19+y^20*Y^19-7116474*y^7*Y^7+18164535*y^8*Y^7-37024247*y^9*Y^7+60984836*y^10*Y^7-81524855*y^11*Y^7+87880482*y^12*Y^7-74617283*y^13*Y^7+47087635*y^14*Y^7-18522566*y^15*Y^7+207177*y^16*Y^7+5760139*y^17*Y^7-4593623*y^18*Y^7+2041878*y^19*Y^7-558513*y^20*Y^7+80857*y^21*Y^7+411*y^22*Y^7-2361*y^23*Y^7+375*y^24*Y^7-20*y^25*Y^7-y^5*Y^19+68534*y^14*Y^3+3536*y^15*Y^3-17791*y^16*Y^3+10128*y^17*Y^3-3052*y^18*Y^3+504*y^19*Y^3-36*y^20*Y^3-9*y^13+36*y^12+126*y^10-29*y*Y^7+787*y^2*Y^7-10501*y^3*Y^7+88121*y^4*Y^7-512197*y^5*Y^7+2185436*y^6*Y^7+97626*y^24*Y^13-22577*y^25*Y^13+4180*y^26*Y^13-567*y^27*Y^13+49*y^28*Y^13-2*y^29*Y^13+15*y^26*Y^8-9*y*Y^11+114*y^2*Y^11-570*y^3*Y^11+3925*y^4*Y^11-56486*y^5*Y^11+563508*y^6*Y^11-3454161*y^7*Y^11+14015693*y^8*Y^11-39788172*y^9*Y^11+81529055*y^10*Y^11-121749833*y^11*Y^11+129898003*y^12*Y^11-89939075*y^13*Y^11+21299856*y^14*Y^11+36260650*y^15*Y^11-57672198*y^16*Y^11+47473287*y^17*Y^11-25639669*y^18*Y^11+8032769*y^19*Y^11+499457*y^20*Y^11-2394344*y^21*Y^11+1641563*y^22*Y^11-684375*y^23*Y^11+4*y^4*Y-45*y^5*Y+245*y^6*Y-834*y^7*Y+1937*y^8*Y-3186*y^9*Y+3763*y^10*Y-3174*y^11*Y+1844*y^12*Y-651*y^13*Y+57*y^14*Y+72*y^15*Y-41*y^16*Y+10*y^17*Y-y^18*Y+84*y^8-12*y*Y^8+510*y^2*Y^8-8870*y^3*Y^8+91971*y^4*Y^8-635324*y^5*Y^8+3103077*y^6*Y^8-11175193*y^7*Y^8+30616377*y^8*Y^8-65329994*y^9*Y^8+110483488*y^10*Y^8-149736727*y^11*Y^8+162954267*y^12*Y^8-140388664*y^13*Y^8+91169285*y^14*Y^8-37947367*y^15*Y^8+1421627*y^16*Y^8+12257423*y^17*Y^8-10818176*y^18*Y^8+5273104*y^19*Y^8-1554368*y^20*Y^8+209979*y^21*Y^8+29799*y^22*Y^8-19858*y^23*Y^8+4022*y^24*Y^8-391*y^25*Y^8-126*y^9+18*y^2*Y^13-282*y^3*Y^13+1405*y^4*Y^13+1230*y^5*Y^13-55367*y^6*Y^13+365303*y^7*Y^13-1443585*y^8*Y^13+4101403*y^9*Y^13-9164719*y^10*Y^13+2023702*y^22*Y^12-818120*y^23*Y^12+246929*y^24*Y^12-54566*y^25*Y^12+8438*y^26*Y^12-844*y^27*Y^12+47*y^28*Y^12-y^29*Y^12+50022*y^10*Y^2-49176*y^11*Y^2+34941*y^12*Y^2-16420*y^13*Y^2+3473*y^14*Y^2+1308*y^15*Y^2-1393*y^16*Y^2+539*y^17*Y^2-107*y^18*Y^2+9*y^19*Y^2+21683*y^8*Y^2-37959*y^9*Y^2-21424*y^16*Y^18+31785*y^17*Y^18-30830*y^18*Y^18+21217*y^19*Y^18-10668*y^20*Y^18+3922*y^21*Y^18-1031*y^22*Y^18+184*y^23*Y^18-20*y^24*Y^18+y^25*Y^18-36*y^7+7*y^5*Y^18-105*y^6*Y^18+723*y^7*Y^18-3012*y^8*Y^18+8402*y^9*Y^18-16330*y^10*Y^18+22107*y^11*Y^18-19852*y^12*Y^18+10283*y^13*Y^18-3224*y^14*Y^18+7865*y^15*Y^18+36*y^2*Y^12-320*y^3*Y^12+1323*y^4*Y^12-3957*y^5*Y^12+32247*y^6*Y^12-315523*y^7*Y^12+1808233*y^8*Y^12-6360088*y^9*Y^12+14455526*y^10*Y^12-20749704*y^11*Y^12+14382421*y^12*Y^12+10238775*y^13*Y^12-42487459*y^14*Y^12+61727627*y^15*Y^12-56843223*y^16*Y^12+35427653*y^17*Y^12-13295620*y^18*Y^12+77926*y^19*Y^12+4158200*y^20*Y^12-3659658*y^21*Y^12-y^5+7*y*Y^9-21*y^2*Y^9-2529*y^3*Y^9+49390*y^4*Y^9-477620*y^5*Y^9+2905301*y^6*Y^9-12187306*y^7*Y^9+37163253*y^8*Y^9-85263769*y^9*Y^9+150663427*y^10*Y^9-208128140*y^11*Y^9+226037353*y^12*Y^9-190994186*y^13*Y^9+119405064*y^14*Y^9-44874293*y^15*Y^9-4967446*y^16*Y^9+22779166*y^17*Y^9-19134879*y^18*Y^9+9412121*y^19*Y^9-2686694*y^20*Y^9+171894*y^21*Y^9+210704*y^22*Y^9-101678*y^23*Y^9+23841*y^24*Y^9-3177*y^25*Y^9+223*y^26*Y^9-6*y^27*Y^9+730326*y^13*Y^14+3123742*y^14*Y^14-7803976*y^15*Y^14+11310302*y^16*Y^14-11925930*y^17*Y^14+9490680*y^18*Y^14-5545131*y^19*Y^14+2084882*y^20*Y^14-160412*y^21*Y^14-409687*y^22*Y^14+336224*y^23*Y^14-154196*y^24*Y^14+47819*y^25*Y^14-10265*y^26*Y^14+1471*y^27*Y^14-127*y^28*Y^14+5*y^29*Y^14+17080969*y^11*Y^13-62700*y^10*Y^17+229915*y^11*Y^17-527409*y^12*Y^17+857290*y^13*Y^17-1008618*y^14*Y^17+817947*y^15*Y^17-347373*y^16*Y^17-138936*y^17*Y^17+399704*y^18*Y^17-396459*y^19*Y^17+257132*y^20*Y^17-119922*y^21*Y^17+40872*y^22*Y^17-9996*y^23*Y^17+1667*y^24*Y^17-170*y^25*Y^17+8*y^26*Y^17+y^14+37023487*y^13*Y^13-27283018*y^12*Y^13-1609804*y^13*Y^16+2518178*y^14*Y^16-2857323*y^15*Y^16+2188207*y^16*Y^16-762644*y^17*Y^16-609283*y^18*Y^16+1261685*y^19*Y^16-1158701*y^20*Y^16+714538*y^21*Y^16-318917*y^22*Y^16+104160*y^23*Y^16-24399*y^24*Y^16+3892*y^25*Y^16-379*y^26*Y^16+17*y^27*Y^16-41180111*y^14*Y^13-21313162*y^16*Y^13+35489183*y^15*Y^13+5775135*y^17*Y^13+5102153*y^20*Y^13-6752731*y^19*Y^13+4124996*y^18*Y^13-354255*y^23*Y^13+1080159*y^22*Y^13-2676920*y^21*Y^13;

f_37_3:=-X^5*Y^5+(5*X^4-9*X^2-3*X^3-5*X-1)*Y^4-X*(9*X^2-2*X-3)*Y^3+3*X*(X+3)*Y^2+5*X*Y+X;//used

Total degree=10;
Degree(f_37_2,X)=5;
Degree(f_37_2,Y)=5;

//==================================== X_H(37), H=<2^3>  smaller ========================================
N_X:=x^86*(x*y-1)^32*(x*y-y+1)^6*(x*y-y+1-x)^11*y^55*(-2*y+1+y^2)^32*(x^5*y^2-3*x^4*y^3+3*x^3*y^4+2*x^3*y^2-2*x^3*y-x^2*y^5-x^2*y^4-x^2*y^3+x^2*y^2+x^2*y+x*y^5-x*y^4+2*x*y^3-2*x*y^2-x*y+x-y^4+2*y^3-y^2)^43;
D_X:=(x^2*y-x*y+y-1)^15*y^64*x^74*(x*y-1)^43*(x*y-y+1)*(x*y-y+1-x)*(1-20*y^3+y^6-7*x*y^5+15*y^2+15*y^4+10*x*y^3-14*x^2*y+3*x^5*y^3-3*x^5*y^4+24*x^4*y^4-3*x-6*y-6*y^5+25*x^4*y^2+33*x^3*y^3-9*x^2*y^6-18*x^3*y^5+x^5*y^5+7*x^3*y^6-4*x^4*y^5-x^4*y^6+17*x^2*y^2-6*x^4*y+13*x*y+5*x*y^4-20*x*y^2-x^3+12*x^2*y^3+3*x^2+13*x^3*y-36*x^3*y^2-43*x^2*y^4-x^5*y^2-38*x^4*y^3+2*x^3*y^4+34*x^2*y^5+2*x*y^6)*(y-1)^38*(-2*y+1+y^2)^13*(x-y)*(x^3*y-x^2*y^2-x^2*y+x*y^2-y+1)*(x^2*y-x^2-x*y^2+x*y-x+y-1)*(x^2*y^2-2*x^2*y-x*y^3+2*x*y^2-y+1)*(x^4*y-x^3*y^3-x^3*y+x^2*y^4+x^2*y-x^2-x*y^4+x*y^3-x*y^2+x*y+y^3-2*y^2+y)*(x^4*y-3*x^3*y^2+x^3*y+2*x^2*y^3+x^2*y^2-2*x^2*y-2*x*y^3+2*x*y^2+y^2-2*y+1)^44;

X:=N_X/D_X;

N_Y:=-x^82*(x*y-1)^30*(x*y-y+1)^6*(x*y-y+1-x)^10*y^54*(-2*y+1+y^2)^31*(x^5*y^2-3*x^4*y^3+3*x^3*y^4+2*x^3*y^2-2*x^3*y-x^2*y^5-x^2*y^4-x^2*y^3+x^2*y^2+x^2*y+x*y^5-x*y^4+2*x*y^3-2*x*y^2-x*y+x-y^4+2*y^3-y^2)^41;
D_Y:=(x^2*y-x*y+y-1)^14*y^62*x^70*(x*y-1)^41*(x*y-y+1)*(x*y-y+1-x)*(1-20*y^3+y^6-7*x*y^5+15*y^2+15*y^4+10*x*y^3-14*x^2*y+3*x^5*y^3-3*x^5*y^4+24*x^4*y^4-3*x-6*y-6*y^5+25*x^4*y^2+33*x^3*y^3-9*x^2*y^6-18*x^3*y^5+x^5*y^5+7*x^3*y^6-4*x^4*y^5-x^4*y^6+17*x^2*y^2-6*x^4*y+13*x*y+5*x*y^4-20*x*y^2-x^3+12*x^2*y^3+3*x^2+13*x^3*y-36*x^3*y^2-43*x^2*y^4-x^5*y^2-38*x^4*y^3+2*x^3*y^4+34*x^2*y^5+2*x*y^6)*(y-1)^38*(-2*y+1+y^2)^12*(x-y+1)*(x^2*y-x*y^2+y-1)*(x-y)*(x^2*y-x*y^2-x*y+y^2-1)*(x^2*y-x^2-x*y^2+x*y-x+y-1)*(x^2*y^2-2*x^2*y-x*y^3+2*x*y^2-y+1)*(x^4*y-x^3*y^3-x^3*y+x^2*y^4+x^2*y-x^2-x*y^4+x*y^3-x*y^2+x*y+y^3-2*y^2+y)*(x^4*y-3*x^3*y^2+x^3*y+2*x^2*y^3+x^2*y^2-2*x^2*y-2*x*y^3+2*x*y^2+y^2-2*y+1)^41;

Y:=N_Y/D_Y;


f_37_3:=X^2*Y^5+(4*X^3+7*X^2)*Y^4+(-7*X^4-6*X^3-5*X-2*X^2)*Y^3+(X^5-4*X^4+2*X^3+4*X^2+1)*Y^2+(-2*X^4+2*X^2+3*X^3)*Y+X^3;

Total degree=7;
Degree(f_37_2,X)=5;
Degree(f_37_2,Y)=5;

//==================================== X_H(37), H=<2^9>  ========================================

N_X:=x^2*y - x*y^2 + y - 1;
D_X:=x^3*y - x^2*y^2 - x^2*y + x*y^2 - y + 1;
X:=N_X/D_X;

N_Y:=x*(x-y)*(x^5*y^2 - 3*x^4*y^3 + 3*x^3*y^4 + 2*x^3*y^2 - 2*x^3*y - x^2*y^5 - x^2*y^4 - x^2*y^3 + x^2*y^2 + x^2*y + x*y^5 - x*y^4 + 2*x*y^3 - 2*x*y^2 - x*y + x - y^4 + 2*y^3 - y^2);
D_Y:=(x^3*y - x^2*y^2 - x^2*y + x*y^2 - y + 1)*(x^4*y - 3*x^3*y^2 + x^3*y + 2*x^2*y^3 + x^2*y^2 - 2*x^2*y - 2*x*y^3 + 2*x*y^2 + y^2 - 2*y + 1);        
Y:=N_Y/D_Y;

P_Xx:=-2*x^4+x^3+15*X*x^3-197*X^16*x^11+90*X^16*x^14+265*X^16*x^12+3*X^16*x^16-24*X^16*x^15-198*X^16*x^13-345*X^12*x^8-129*X^13*x^9-406*X^15*x^10+1118*X^14*x^11-239*X^14*x^14-967*X^14*x^12-7*X^14*x^16+60*X^14*x^15+585*X^14*x^13+1312*X^13*x^11-20*X^6+15*X^4*x^11-39*X^4*x^10-112*X^4*x^9+617*X^4*x^8-148*X^6*x^12-20*X^5*x^12-6*X^4-1742*X^10*x^7+4218*X^10*x^6-2887*X^10*x^5-8165*X^9*x^7+9615*X^9*x^6+185*X^12*x^6+905*X^10*x^4-77*X^10*x^3-23*X^10*x^2+4*X^10*x+20*X^13*x^4-2*X^13*x^3-5107*X^6*x^4+2869*x^3*X^5-202*X^12*x^5-905*X^11*x^5+81*X^12*x^4+348*X^11*x^4-15*X^12*x^3-59*X^11*x^3+X^12*x^2+3*X^11*x^2+397*X^15*x^9-231*X^15*x^8+76*X^15*x^7-11*X^15*x^6+77*X^16*x^9-80*X^16*x^8+37*X^16*x^7-9*X^16*x^6+X^16*x^5+136*X^12*x^7+910*X^11*x^6-1300*X^6*x^2+189*X^5*x+3596*X^6*x^3-1013*X^5*x^2+245*X^6*x+1415*X^8*x^3-1097*X^7*x^2+652*X^11*x^7-42*X^14*x^7+60*X^14*x^6-25*X^14*x^5+4*X^14*x^4-590*X^8*x^2+203*X^7*x+105*X^8*x-1492*X^7*x^5-3381*X^7*x^4+2927*X^7*x^3+12527*X^8*x^6-4927*X^8*x^5-557*X^8*x^4+1010*X^9*x^4+278*X^9*x^3-184*X^9*x^2+31*X^9*x+25*X^3*x-519*X^4*x^2+91*X^4*x+14*X^9*x^15-88*X^9*x^14+403*X^9*x^13+63*X^10*x^15-217*X^10*x^14+513*X^10*x^13-1122*X^10*x^12+2738*X^10*x^11-5509*X^10*x^10-1504*X^9*x^12+4077*X^9*x^11-7166*X^9*x^10-10*X^10*x^16-120*X^17*x^11+x^5-15*X^7+6*X^13*x^17-736*X^13*x^14-1744*X^13*x^12-54*X^13*x^16+251*X^13*x^15+1409*X^13*x^13+21*X^17*x^14+114*X^17*x^12-3*X^17*x^15-65*X^17*x^13+2011*X^6*x^5+2846*X^5*x^5-X^3+3063*X^11*x^9+218*X^15*x^11-909*X^14*x^10-2749*X^11*x^8+21*X^12*x^9+10*X^12*x^17+542*X^12*x^11-857*X^12*x^14-1403*X^12*x^12-72*X^12*x^16+316*X^12*x^15+1447*X^12*x^13-6*X^3*x^10-9*X^3*x^9+111*X^3*x^8-181*X^3*x^7-95*X^3*x^6+633*X^3*x^5-839*X^3*x^4+532*X^3*x^3-170*X^3*x^2+6827*X^10*x^9+6656*X^9*x^9-457*X^13*x^10-X^9-1703*X^11*x^10-2*X*x^7-2*X*x^6+19*X*x^5-27*x^4*X-736*X^6*x^10-X^12*x^18-13165*X^7*x^7-13681*X^8*x^7-3*X*x^2+785*X^11*x^11-538*X^11*x^14-843*X^11*x^12-41*X^11*x^16+192*X^11*x^15+880*X^11*x^13-3681*X^10*x^8-33*X^2*x^2+X^2*x^9+10*X^2*x^8-26*X^2*x^7-25*X^2*x^6+143*X^2*x^5-190*x^4*X^2+117*X^2*x^3-929*X^6*x^9-466*X^5*x^9+5221*X^6*x^8+2217*X^5*x^8-8106*X^6*x^7-3315*X^5*x^7+4725*X^6*x^6+1141*X^5*x^6+183*X^9*x^8+496*X^14*x^9+X^8*x^15-6*X^7*x^14-36*X^8*x^14+96*X^7*x^13+259*X^8*x^13-534*X^7*x^12-1165*X^8*x^12+5*X^11*x^17-174*X^5*x^10+533*X^6*x^11+120*X^5*x^11+15*X^6*x^13-17*X^17*x^9-249*X^13*x^7+169*X^13*x^6-78*X^13*x^5-134*X^14*x^8+15*X^18*x^12-20*X^18*x^11+72*X^17*x^10+5*X^17*x^7-X^17*x^6+X^18*x^14+15*X^18*x^10-6*X^18*x^13-5159*X^9*x^5-6*X^18*x^9+X^18*x^8-6*X^17*x^8-15*X^5+9938*X^7*x^6+1627*X^7*x^11-2413*X^7*x^10-302*X^7*x^9+7615*X^7*x^8+3290*X^8*x^11-5266*X^8*x^10+2818*X^8*x^9+5813*X^8*x^8-6*X^8+156*X^12*x^10+35*X^16*x^10-X^15*x^17+89*X^15*x^14+6*X^15*x^12+9*X^15*x^16-38*X^15*x^15-108*X^15*x^13-4379*X^5*x^4+3*X^2*x-920*X^4*x^7-17*X^4*x^6+1749*X^4*x^5-2382*X^4*x^4+1523*X^4*x^3+282*X^13*x^8;
P_Xy:=3*X^10*y-y^14+20*X^16+X^13-7*y^8+3*X^7*y^2+X^4*y^3+21*X^13*y^13-2410*X^2*y^12+509*X*y^11+83449*X^6*y^7-12431*X^6*y^14-274120*X^6*y^10+208346*X^6*y^11+2270*X^6*y^15+260481*X^6*y^9-114610*X^6*y^12+45177*X^6*y^13-176554*X^6*y^8-219411*X^7*y^8+973*X^7*y^15+220127*X^7*y^11-106418*X^7*y^12-53*X^7*y^16-318133*X^7*y^10+35273*X^7*y^13-7640*X^7*y^14+320396*X^7*y^9+244762*X^8*y^9+25*X^8*y^16-51485*X^8*y^12+11916*X^8*y^13-X^8*y^17+133960*X^8*y^11-1270*X^8*y^14-54*X^8*y^15-225101*X^8*y^10-59907*X^9*y^10-2841*X^9*y^13+1122*X^9*y^14-540*X^9*y^12-182*X^9*y^15+10*X^9*y^16+22171*X^9*y^11-28557*X^10*y^11+624*X^10*y^14-41*X^10*y^15-3890*X^10*y^13+13388*X^10*y^12+X^11*y^15+78*X^11*y^14-1112*X^11*y^13-7*X^12*y^14-1642*X^3*y^14+5066*X^3*y^13+1073*X^2*y^13-324*X*y^12+38*X^8*y^2+9*X^5*y^3+645*X^4*y^5-35115*X^4*y^12-35789*X^4*y^8+58135*X^4*y^9+15976*X^4*y^13+15118*X^4*y^7-67286*X^4*y^10+56696*X^4*y^11-4113*X^4*y^6-13506*X^5*y^6+33682*X^5*y^13+145921*X^5*y^9-160985*X^5*y^10-10574*X^5*y^14-95454*X^5*y^8+130067*X^5*y^11-77334*X^5*y^12+43853*X^5*y^7-196*X^4*y^16+1238*X^4*y^15-5281*X^4*y^14+365*X^3*y^15-324*X^2*y^14+135*X*y^13+32*X^6*y^3-4*X^3*y^4-47*X^4*y^4+6*X^18+4*X^3*y^17-6*X^2*y^16+13*X^6*y^17-332*X^5*y^16+2314*X^5*y^15-52*X^3*y^16+62*X^2*y^15-34*X*y^14+19*X^4*y^17-X^5*y^18+28*X^5*y^17-250*X^6*y^16+4*X*y^15-X^4*y^18+316*X^13*y^11-214*X^13*y^10+373*X^13*y^9-139*X^13*y^12-3750*X^13*y^8+12379*X^13*y^7+318*X^10*y^2-4644*X^10*y^3-2481*X^11*y^3+13937*X^11*y^4+37*X^11*y^2-6139*X^12*y^4+91*X^12*y+5224*X^12*y^5-865*X^12*y^2+3229*X^12*y^3+22838*X^13*y^5+141*X^13*y-1503*X^13*y^2-21473*X^13*y^6+6479*X^13*y^3-15469*X^13*y^4-14457*X^14*y^6-934*X^14*y^2+4008*X^14*y^3+11366*X^14*y^7+69*X^14*y-9319*X^14*y^4+13855*X^14*y^5+3783*X^15*y^7-101*X^15*y^3-699*X^15*y^4-2613*X^15*y^8+223*X^15*y^2+2205*X^15*y^5-3607*X^15*y^6-97*X^15*y+1155*X^15*y^9+35*X^15*y^11-299*X^15*y^10-26584*X^6*y^6+96564*X^7*y^7-159999*X^8*y^8+6206*X^8*y^4+17025*X^8*y^6-18695*X^8*y^5-853*X^8*y^3+43527*X^8*y^7+2568*X^5*y^5-639*X^6*y^4-21*X^16*y^10+309*X^14*y^11-35*X^14*y^12+3516*X^14*y^9-7086*X^14*y^8-1298*X^14*y^10-129*X^17*y-444*X^16*y^8+1924*X^16*y^4-1233*X^16*y^5+152*X^16*y^9-1545*X^16*y^3+44*X^16*y^6+569*X^16*y^7+717*X^16*y^2-183*X^16*y+7*X^17*y^9-658*X^17*y^5+186*X^17*y^6+1020*X^17*y^4+30*X^17*y^7-35*X^17*y^8-898*X^17*y^3+462*X^17*y^2+79068*X^11*y^8-77918*X^11*y^7+63274*X^11*y^6-37617*X^11*y^5-67497*X^11*y^9+44937*X^11*y^10+5420*X^6*y^5+253*X^7*y^4-24064*X^7*y^6+2187*X^7*y^5+865*X^12*y^12-4926*X^12*y^11+28303*X^12*y^8-18262*X^12*y^7+3682*X^12*y^6+14504*X^12*y^10-25664*X^12*y^9-21176*X^11*y^11+17771*X^9*y^4-2924*X^9*y^3-51842*X^9*y^7+79666*X^9*y^6-23190*X^9*y^8-52149*X^9*y^5+72664*X^9*y^9-105939*X^10*y^7+104155*X^10*y^6-65650*X^10*y^5+78384*X^10*y^8+24373*X^10*y^4+42263*X^10*y^10-54787*X^10*y^9+6*X^14+7*y^13-21*y^12-35*y^10+35*y^11+X^19-6*X^19*y^5+15*X^19*y^4+15*X^19*y^2+6442*X^11*y^12+21*y^9-6*X^19*y-20*X^19*y^3+134*X^18*y^2+28*X^18*y^6-112*X^18*y^5-X^18*y^8+209*X^18*y^4-220*X^18*y^3+15*X^15+X^19*y^6-35*X^12*y^13+369*X*y^9-4*X*y^6-534*X*y^10+39*X*y^7-160*X*y^8-4118*X^2*y^10-86*X^2*y^6+495*X^2*y^7+3767*X^2*y^11-1568*X^2*y^8+3109*X^2*y^9+17581*X^3*y^11+3436*X^3*y^7-9216*X^3*y^8-11110*X^3*y^12-779*X^3*y^6+16336*X^3*y^9-20077*X^3*y^10+92*X^3*y^5+15*X^17-44*X^18*y-X^7*y^17+27*X^11*y-256*X^5*y^4-56*X^7*y^3+171*X^9*y^2+6*X^2*y^5+y^7;

P_Yy:=48*Y^14*y^15-5962*Y^14*y^8+865*Y^14*y^13-1900*Y^14*y^12-4427*Y^14*y^10+3194*Y^14*y^11-1147*Y^14*y^4+2995*Y^14*y^5+5367*Y^14*y^9+238*Y^14*y^3-4997*Y^14*y^6+6017*Y^14*y^7-15*Y^14*y^2-3*Y^14*y^16-25*Y^15*y^14+Y^15*y^15-2473*Y^15*y^8-Y^10-y^2*Y^7+5*y*Y^8+y*Y^9-868*Y^7*y^6+1114*Y^7*y^7-111*Y^8*y^14+15*Y^8*y^15-2777*Y^8*y^8+Y^3*y^13-3*Y^3*y^12-38*Y^3*y^10+11*Y^3*y^11+3*Y^3*y^5+64*Y^3*y^9-24*Y^3*y^6+41*Y^3*y^7-171*Y^4*y^8+5*Y^4*y^13-33*Y^4*y^12-96*Y^4*y^10+72*Y^4*y^11-26*Y^4*y^4+43*Y^4*y^5+129*Y^4*y^9-75*Y^4*y^6+142*Y^4*y^7-7*Y^5*y^14-352*Y^5*y^8+4*y^2*Y^17+y^2*Y^18+y^2*Y^19-3*Y^17*y^12-68*Y^17*y^10+22*Y^17*y^11+65*Y^17*y^4-81*Y^17*y^5+121*Y^17*y^9-25*Y^17*y^3+24*Y^17*y^6+75*Y^17*y^7-47*Y^18*y^8-8*Y^18*y^10+Y^18*y^11-Y^18*y^4+18*Y^18*y^5+26*Y^18*y^9-3*Y^18*y^3-41*Y^18*y^6+54*Y^18*y^7+Y^19*y^8+15*Y^19*y^4-20*Y^19*y^5-6*Y^19*y^3+15*Y^19*y^6-6*Y^19*y^7+30*Y^5*y^13-71*Y^5*y^12-361*Y^5*y^10+188*Y^5*y^11-37*Y^5*y^4+148*Y^5*y^5+429*Y^5*y^9-255*Y^5*y^6+290*Y^5*y^7-10*Y^6*y^14+Y^6*y^15-855*Y^6*y^8+89*Y^6*y^13-310*Y^6*y^12-718*Y^6*y^10+556*Y^6*y^11-7*Y^6*y^4+17*Y^6*y^5+841*Y^6*y^9+21*Y^6*y^3-239*Y^6*y^6+624*Y^6*y^7-86*Y^7*y^14+14*Y^7*y^15-1532*Y^7*y^8+227*Y^7*y^13-489*Y^7*y^12-1662*Y^7*y^10+1027*Y^7*y^11-291*Y^7*y^4+630*Y^7*y^5+1853*Y^7*y^9+65*Y^7*y^3-5*Y*y^8-Y*y^10+3*Y*y^9+Y*y^6+3*Y*y^7+720*Y^9*y^13-1558*Y^9*y^12-4978*Y^9*y^10+3199*Y^9*y^11-540*Y^9*y^4+822*Y^9*y^5+5345*Y^9*y^9+200*Y^9*y^3-1029*Y^9*y^6+1920*Y^9*y^7-35*Y^9*y^2-10*Y^9*y^16-445*Y^10*y^14+90*Y^10*y^15-6384*Y^10*y^8+2*Y^10*y+1450*Y^10*y^13+3*Y^10*y^17-2910*Y^10*y^12-4654*Y^10*y^10+4021*Y^10*y^11-348*Y^10*y^4+1705*Y^10*y^5+5448*Y^10*y^9+14*Y^10*y^3-4140*Y^10*y^6+6158*Y^10*y^7-19*Y^10*y^16-562*Y^11*y^14+197*Y^11*y^15-5151*Y^11*y^8-5*y^4*Y^2-14*Y^2*y^8-Y^2*y^12-4*Y^2*y^10+4*Y^2*y^11+13*Y^2*y^5+5*Y^2*y^9-20*Y^2*y^6+22*Y^2*y^7-58*Y^3*y^8+y*Y^12-y^5*Y+4*y*Y^11+2*Y^15*y^6+1223*Y^15*y^7-596*Y^16*y^8+7*Y^16*y^13-51*Y^16*y^12-352*Y^16*y^10+169*Y^16*y^11-279*Y^16*y^4+497*Y^16*y^5+520*Y^16*y^9+91*Y^16*y^3-605*Y^16*y^6+612*Y^16*y^7-134*Y^17*y^8+532*Y^8*y^13-1323*Y^8*y^12-2471*Y^8*y^10+2069*Y^8*y^11+46*Y^8*y^4+228*Y^8*y^5+2725*Y^8*y^9-19*Y^8*y^3-1110*Y^8*y^6+2197*Y^8*y^7-8*Y^8*y^2-3*Y^8*y^16-328*Y^9*y^14+95*Y^9*y^15-3814*Y^9*y^8+167*Y^15*y^13-597*Y^15*y^12-2365*Y^15*y^10+1408*Y^15*y^11+y^5+1330*Y^11*y^13+2*Y^11*y^17-3076*Y^11*y^12-8615*Y^11*y^10+6028*Y^11*y^11-74*Y^11*y^4-453*Y^11*y^5+8447*Y^11*y^9+155*Y^11*y^3+629*Y^11*y^6+1232*Y^11*y^7-50*Y^11*y^2-38*Y^11*y^16-690*Y^12*y^14+181*Y^12*y^15-9329*Y^12*y^8-Y^12*y^18+1811*Y^12*y^13+10*Y^12*y^17-3281*Y^12*y^12-5815*Y^12*y^10+4567*Y^12*y^11-1236*Y^12*y^4+3824*Y^12*y^5+7548*Y^12*y^9+203*Y^12*y^3-7324*Y^12*y^6+9582*Y^12*y^7-9*Y^12*y^2-43*Y^12*y^16-525*Y^13*y^14+174*Y^13*y^15-4105*Y^13*y^8+1334*Y^13*y^13+3*Y^13*y^17-2958*Y^13*y^12-7125*Y^13*y^10+5288*Y^13*y^11+543*Y^13*y^4-1384*Y^13*y^5+6859*Y^13*y^9-72*Y^13*y^3+1494*Y^13*y^6+523*Y^13*y^7-19*Y^13*y^2-37*Y^13*y^16-271*Y^14*y^14+3*y^4*Y^3+10*y^3*Y^4-2*y^3*Y^5-10*y^2*Y^6+7*y*Y^13-2*y*Y^14+y^2*Y^15-13*y^2*Y^16+259*Y^15*y^4-437*Y^15*y^5+2890*Y^15*y^9-54*Y^15*y^3-2*y^6+y^7;
P_Yx:=-x^9-2*Y*x^7+Y*x^6+6*x^2*Y^6+21*x^4*Y^13-21*x^7*Y^16+7*x^8*Y^17-x^9*Y^18-35*x^5*Y^14+35*x^6*Y^15-Y^8+x^10+37*Y^5*x^4-11*Y^5*x^3-310*Y^5*x^9-186*Y^5*x^7+260*Y^5*x^8-88*Y^5*x^5-197*Y^5*x^11+90*Y^5*x^12+9*Y^5*x^14+294*Y^5*x^10+124*Y^5*x^6-24*Y^5*x^13+58*Y^6*x^4-31*Y^6*x^3-483*Y^6*x^9-372*Y^6*x^7+443*Y^6*x^8-118*Y^6*x^5-324*Y^6*x^11+179*Y^6*x^12+30*Y^6*x^14+440*Y^6*x^10+251*Y^6*x^6-Y^6*x^15-85*Y^6*x^13+98*Y^7*x^4-16*Y^7*x^3-694*Y^7*x^9-344*Y^7*x^7+571*Y^7*x^8+2*Y^7*x^2-181*Y^7*x^5-494*Y^7*x^11+267*Y^7*x^12+29*Y^7*x^14+666*Y^7*x^10+230*Y^7*x^6-19*Y^7*x^15-92*Y^7*x^13+3*Y^8*x^4-7*Y^8*x^3-352*Y^8*x^9-271*Y^8*x^7+238*Y^8*x^8+2*Y^8*x^2-67*Y^8*x^5-528*Y^8*x^11+391*Y^8*x^12+3*Y^8*x^16+4*Y^8*x+66*Y^8*x^14+504*Y^8*x^10+190*Y^8*x^6-10*Y^8*x^15-200*Y^8*x^13-53*Y^9*x^4+41*Y^9*x^3+177*Y^9*x^9+305*Y^9*x^7-219*Y^9*x^8-29*Y^9*x^2+105*Y^9*x^5+4*Y^9*x^11+109*Y^9*x^12+13*Y^9*x^16+50*Y^9*x^14-129*Y^9*x^10-213*Y^9*x^6-27*Y^9*x^15-106*Y^9*x^13-171*Y^10*x^4+90*Y^10*x^3+1184*Y^10*x^9+799*Y^10*x^7-1163*Y^10*x^8+296*Y^10*x^5+447*Y^10*x^11-172*Y^10*x^12-8*Y^10*x^16+5*Y^10*x^14-841*Y^10*x^10-3*Y^10*x^17-500*Y^10*x^6+15*Y^10*x^15+22*Y^10*x^13-Y*x^9+3*Y*x^8-3*Y*x^11+2*Y*x^10-19*Y^2*x^9-5*Y^2*x^7+13*Y^2*x^8-3*Y^2*x^5-5*Y^2*x^11+3*Y^2*x^12+13*Y^2*x^10+2*Y^2*x^6+3*Y^3*x^4-46*Y^3*x^9-32*Y^3*x^7+40*Y^3*x^8-9*Y^3*x^5-32*Y^3*x^11+15*Y^3*x^12+43*Y^3*x^10+20*Y^3*x^6-Y^3*x^13+17*Y^4*x^4-145*Y^4*x^9-88*Y^4*x^7+131*Y^4*x^8-29*Y^4*x^5-61*Y^4*x^11+30*Y^4*x^12+113*Y^4*x^10+55*Y^4*x^6-19*Y^4*x^13-143*Y^11*x^4+30*Y^11*x^3+1792*Y^11*x^9+994*Y^11*x^7-1455*Y^11*x^8+289*Y^11*x^5+1392*Y^11*x^11-750*Y^11*x^12+6*Y^11*x^16-32*Y^11*x^14-1817*Y^11*x^10-542*Y^11*x^6-14*Y^11*x^15+256*Y^11*x^13+3*Y^12*x^4+1374*Y^12*x^9+345*Y^12*x^7-841*Y^12*x^8+68*Y^12*x^5+1286*Y^12*x^11-952*Y^12*x^12-18*Y^12*x^16-238*Y^12*x^14+Y^12*x^18-1502*Y^12*x^10+3*Y^12*x^17-160*Y^12*x^6+67*Y^12*x^15+570*Y^12*x^13-55*Y^13*x^9-309*Y^13*x^7+332*Y^13*x^8-102*Y^13*x^5+681*Y^13*x^11-517*Y^13*x^12-6*Y^13*x^16-117*Y^13*x^14-2*Y^13*x^18-446*Y^13*x^10+4*Y^13*x^17+211*Y^13*x^6+36*Y^13*x^15+269*Y^13*x^13-949*Y^14*x^9-547*Y^14*x^7+848*Y^14*x^8-473*Y^14*x^11+112*Y^14*x^12-Y^14*x^16-84*Y^14*x^14+Y^14*x^18+812*Y^14*x^10-4*Y^14*x^17+212*Y^14*x^6+33*Y^14*x^15+75*Y^14*x^13-1003*Y^15*x^9-230*Y^15*x^7+639*Y^15*x^8-784*Y^15*x^11+531*Y^15*x^12-4*Y^15*x^16+143*Y^15*x^14+1024*Y^15*x^10+2*Y^15*x^17-28*Y^15*x^15-325*Y^15*x^13-2*x*Y^7+7*x*Y^9-21*x^2*Y^10+x^4*Y^2-x^3*Y^3-4*x^3*Y^4+x^2*Y^11-7*x^3*Y^12+3*x^2*Y^5-418*Y^16*x^9+144*Y^16*x^8-648*Y^16*x^11+395*Y^16*x^12+15*Y^16*x^16+80*Y^16*x^14+670*Y^16*x^10-2*Y^16*x^17-43*Y^16*x^15-172*Y^16*x^13-49*Y^17*x^9-240*Y^17*x^11+234*Y^17*x^12-Y^17*x^16+38*Y^17*x^14+146*Y^17*x^10-2*Y^17*x^15-133*Y^17*x^13-21*Y^18*x^11+35*Y^18*x^12+Y^18*x^16+21*Y^18*x^14+7*Y^18*x^10-7*Y^18*x^15-35*Y^18*x^13;

f_37_9:=-X^2*Y^9+X^2*(X+1)*Y^8+X*(X+1)*(X^3+X^2+X-2)*Y^7-(X+1)*(X^5-X^4+2*X^3-4*X^2-6*X-1)*Y^6+(X^5-2*X^4+2*X^3-2*X^2-4*X-2)*(X+1)^2*Y^5+(X^7-2*X^4-4*X^3-6*X^2-X+1)*(X+1)^2*Y^4-X*(X^5-X^4-X^3-6*X^2-8*X-4)*(X+1)^2*Y^3-X*(X^4-X^3-X+2)*(X+1)^3*Y^2+X^2*(X^2-2*X-2)*(X+1)^3*Y+X^2*(X+1)^3;//used

Total degree=13;
Degree(f_37_9,X)=9;
Degree(f_37_9,Y)=9;

//==================================== X_H(41), H=<6^4>  ========================================

N_X:=(x^2*y-x*y+y-1)*x^3*(y-1)^2*(x^5*y^2-3*x^4*y^3-x^4*y^2+3*x^3*y^4+3*x^3*y^3-x^2*y^5-3*x^2*y^4-2*x^2*y^2+3*x^2*y+x*y^5+3*x*y^3-4*x*y^2-y^4+y^3+y-1)^3;
D_X:=y*(x^4*y-2*x^3*y^2-x^3*y+x^2*y^3+x^2*y^2+2*x^2*y-x^2-2*x*y^2+x*y+y-1)^2*(x^4*y-3*x^3*y^2+x^3*y+2*x^2*y^3+x^2*y^2-2*x^2*y-2*x*y^3+2*x*y^2+y^2-2*y+1)*(x^2*y^2-2*x^2*y-x*y^3+2*x*y^2-y+1)*(x-y+1)^3*(x-1)*(x*y-y+1)*(x*y-1);
X:=N_X/D_X;

N_Y:=(x^4*y-2*x^3*y^2-x^3*y+x^2*y^3+x^2*y^2+2*x^2*y-x^2-2*x*y^2+x*y+y-1)^15*(x^5*y^2-3*x^4*y^3+3*x^3*y^4+2*x^3*y^2-2*x^3*y-x^2*y^5-x^2*y^4-x^2*y^3+x^2*y^2+x^2*y+x*y^5-x*y^4+2*x*y^3-2*x*y^2-x*y+x-y^4+2*y^3-y^2)*(x^4*y-x^3*y^3-x^3*y+x^2*y^4+x^2*y-x^2-x*y^4+x*y^3-x*y^2+x*y+y^3-2*y^2+y)*(x^2*y-x^2-x*y^2+x*y-x+y-1)*(x^2*y-x*y^2-x*y+y^2-1)*(x-y+1)^15*(x-1)^7*(x*y-y+1)^5*y^9*(x*y-1)^4;
D_Y:=x^13*(x^5*y^2-3*x^4*y^3-x^4*y^2+3*x^3*y^4+3*x^3*y^3-x^2*y^5-3*x^2*y^4-2*x^2*y^2+3*x^2*y+x*y^5+3*x*y^3-4*x*y^2-y^4+y^3+y-1)^15*(x^3*y-x^2*y^2-x^2*y+x*y^2-y+1)*(x-y)*(x^2*y-x*y^2+y-1)*(y-1)^6*(x^2*y-x*y+y-1)^5;
Y:=N_Y/D_Y;

P_Xx := -39*X*x^12+109*X*x^13+X*x^22-6*X*x^21+15*X*x^20-21*X*x^19+20*X*x^18-7*X*x^17-41*X*x^16+119*X*x^15-155*X*x^14-36*X^2*x^12+121*X^2*x^13+14*X^2*x^22-62*X^2*x^21+136*X^2*x^20-181*X^2*x^19+175*X^2*x^18-108*X^2*x^17-64*X^2*x^16+252*X^2*x^15-260*X^2*x^14+33*X^2*x^11-23*X^2*x^10-X^2*x^23-25*X^3*x^9-141*X^3*x^12-489*X^3*x^13+87*X^3*x^22-254*X^3*x^21+400*X^3*x^20-429*X^3*x^19+410*X^3*x^18-255*X^3*x^17-46*X^3*x^16-31*X^3*x^15+511*X^3*x^14+428*X^3*x^11-179*X^3*x^10+31*X^3*x^8-12*X^3*x^23-494*X^4*x^9-1963*X^4*x^12-9*X^4*x^13+297*X^4*x^22-512*X^4*x^21+303*X^4*x^20+63*X^4*x^19+16*X^4*x^17-214*X^4*x^16-600*X^4*x^15+1439*X^4*x^14+1532*X^4*x^11+23*X^4*x^10+210*X^4*x^8+8*X^4*x^24-X^4*x^25-73*X^4*x^23-698*X^5*x^9-3211*X^5*x^12-44*X^5*x^5+3225*X^5*x^13+125*X^5*x^6+393*X^5*x^22-189*X^5*x^21-626*X^5*x^20+793*X^5*x^19+181*X^5*x^18-713*X^5*x^17+1041*X^5*x^16-2036*X^5*x^15+612*X^5*x^14-650*X^5*x^11+2088*X^5*x^10-89*X^5*x^8-65*X^5*x^7+28*X^5*x^24+5*X^5*x^25-5*X^5*x^26+X^5*x^27-171*X^5*x^23+4778*X^6*x^9+3308*X^6*x^12+6*X^6*x^2-7*X^6*x^3-204*X^6*x^5+3867*X^6*x^13+995*X^6*x^6-364*X^6*x^22+1258*X^6*x^21-1427*X^6*x^20-813*X^6*x^19+2923*X^6*x^18-2208*X^6*x^17+2680*X^6*x^16-3724*X^6*x^15-1041*X^6*x^14-7145*X^6*x^11+77*X^6*x^10-1779*X^6*x^8-1205*X^6*x^7-14*X^6*x^24+59*X^6*x^25-48*X^6*x^26+14*X^6*x^27-X^6*x^28+16*X^6*x^23+9023*X^7*x^9+4718*X^7*x^12+44*X^7*x^2-52*X^7*x^4-104*X^7*x^3+213*X^7*x^5+4033*X^7*x^13+1517*X^7*x^6-611*X^7*x^22+510*X^7*x^21+391*X^7*x^20-2546*X^7*x^19+1983*X^7*x^18+2825*X^7*x^17-3346*X^7*x^16+906*X^7*x^15-4631*X^7*x^14-1325*X^7*x^11-10919*X^7*x^10+1866*X^7*x^8-4787*X^7*x^7-32*X^7*x^24+59*X^7*x^25-117*X^7*x^26+54*X^7*x^27-7*X^7*x^28-6*x^12+492*X^14*x^5-4897*X^14*x^13-181*X^14*x^6-3842*X^14*x^22+2385*X^14*x^21+6781*X^14*x^20-2343*X^14*x^19-10345*X^14*x^18+1497*X^14*x^17+12640*X^14*x^16-2316*X^14*x^15-7179*X^14*x^14+3484*X^14*x^11-9428*X^14*x^10+2970*X^14*x^8-1880*X^14*x^7-664*X^13*x^24-203*X^13*x^25+363*X^13*x^26-231*X^13*x^27+81*X^13*x^28-10*X^13*x^29+127*X^13*x^23+2390*X^14*x^9+9568*X^14*x^12-170*X^14*x^4-265*X^12*x^23+6971*X^13*x^9-14383*X^13*x^12-341*X^13*x^4+135*X^13*x^3-346*X^13*x^5+20315*X^13*x^13+2782*X^13*x^6+3580*X^13*x^22-2322*X^13*x^21-5034*X^13*x^20+203*X^13*x^19+11015*X^13*x^18-1780*X^13*x^17-10018*X^13*x^16+615*X^13*x^15-1751*X^13*x^14-6561*X^13*x^11+4375*X^13*x^10-4166*X^13*x^8-2737*X^13*x^7+430*X^12*x^24+672*X^12*x^25-167*X^12*x^26-65*X^12*x^27-9*X^12*x^28+11*X^12*x^29-X^12*x^30+580*X^12*x^4+107*X^12*x^3-2369*X^12*x^5-20912*X^12*x^13+1436*X^12*x^6-5332*X^12*x^22+3828*X^12*x^21+5902*X^12*x^20+788*X^12*x^19-6652*X^12*x^18-15743*X^12*x^17+24295*X^12*x^16-8574*X^12*x^15+16471*X^12*x^14+24018*X^12*x^11+1049*X^12*x^10-2380*X^12*x^8+4176*X^12*x^7-2292*X^11*x^23-9390*X^12*x^9-11851*X^12*x^12-59*X^12*x^2-7*X^11*x^24-328*X^11*x^25+384*X^11*x^26-55*X^11*x^27-18*X^11*x^28+3*X^11*x^29+534*X^10*x^23+11*X^11*x+2253*X^11*x^9+19898*X^11*x^12+3*X^11*x^2+1030*X^11*x^4-335*X^11*x^3-273*X^11*x^5-9650*X^11*x^13-1954*X^11*x^6+3753*X^11*x^22+2228*X^11*x^21-4659*X^11*x^20+2160*X^11*x^19-14312*X^11*x^18+21492*X^11*x^17-4439*X^11*x^16+1709*X^11*x^15-10163*X^11*x^14+9258*X^11*x^11-22835*X^11*x^10+8604*X^11*x^8-1465*X^11*x^7-1215*X^10*x^24+421*X^10*x^25+87*X^10*x^26-50*X^10*x^27-5*X^10*x^28+3*X^10*x^29+11419*X^10*x^18-3588*X^10*x^17+7906*X^10*x^16-6753*X^10*x^15-8872*X^10*x^14-9777*X^10*x^11-6985*X^10*x^10-1424*X^10*x^8-5195*X^10*x^7+592*X^9*x^23+11593*X^10*x^9+9735*X^10*x^12+68*X^10*x^2+258*X^10*x^4-193*X^10*x^3-934*X^10*x^5+8108*X^10*x^13+3543*X^10*x^6+772*X^10*x^22-1163*X^10*x^21+6250*X^10*x^20-14536*X^10*x^19-370*X^9*x^24-316*X^9*x^25+225*X^9*x^26+16*X^9*x^27-29*X^9*x^28+4*X^9*x^29+157*X^8*x^23+3370*X^9*x^9-7002*X^9*x^12+29*X^9*x^2+1274*X^9*x^4-315*X^9*x^3-1987*X^9*x^5+10417*X^9*x^13-50*X^9*x^6-728*X^9*x^22+4931*X^9*x^21-8816*X^9*x^20+4092*X^9*x^19-926*X^9*x^18+4640*X^9*x^17+2332*X^9*x^16-12819*X^9*x^15+3102*X^9*x^14+710*X^9*x^11-1271*X^9*x^10-5115*X^9*x^8+4011*X^9*x^7+72*X^8*x^24-298*X^8*x^25+33*X^8*x^26+69*X^8*x^27-21*X^8*x^28+X^8*x^29-4434*X^8*x^15+5832*X^8*x^14+4734*X^8*x^11-6931*X^8*x^10+8046*X^8*x^8-2267*X^8*x^7+340*X^7*x^23-3277*X^8*x^9+4960*X^8*x^12+81*X^8*x^2+424*X^8*x^4-360*X^8*x^3+852*X^8*x^5-7180*X^8*x^13-1899*X^8*x^6+1112*X^8*x^22-2106*X^8*x^21+947*X^8*x^20-15*X^8*x^19-851*X^8*x^18+2435*X^8*x^17-111*X^8*x^16+5*x^11*X+8*x^15*X^21-x^11*X^20+6*x^10*X^19-15*x^9*X^18+6*x^5*X^16-8*X^21*x^23-7*X^22*x^22+21*X^22*x^21-35*X^22*x^20+35*X^22*x^19-21*X^22*x^18+7*X^22*x^17-15*x^4*X^15-x^6*X^17+20*x^3*X^14-15*x^2*X^13+6*x*X^12+47*X^20*x^23+48*X^21*x^22-112*X^21*x^21+112*X^21*x^20-112*X^21*x^18+112*X^21*x^17-48*X^21*x^16-4*X^20*x^24+344*X^20*x^18+39*X^20*x^17-222*X^20*x^16+108*X^20*x^15+7*X^20*x^14-210*X^19*x^23+7*X^20*x^12-21*X^20*x^13-171*X^20*x^22+238*X^20*x^21+7*X^20*x^20-378*X^20*x^19+71*X^19*x^24-51*X^19*x^25+31*X^19*x^26-9*X^19*x^27+X^19*x^28+240*X^18*x^23+77*X^19*x^12-13*X^19*x^13+452*X^19*x^22-313*X^19*x^21-332*X^19*x^20+457*X^19*x^19+422*X^19*x^18-985*X^19*x^17+417*X^19*x^16+247*X^19*x^15-233*X^19*x^14-35*X^19*x^11-16*X^17*x^23+96*X^18*x^12-97*X^18*x^13-566*X^18*x^22-138*X^18*x^21+1208*X^18*x^20-575*X^18*x^19-940*X^18*x^18+731*X^18*x^17+800*X^18*x^16-1320*X^18*x^15+627*X^18*x^14-143*X^18*x^11+76*X^18*x^10-42*X^18*x^24+181*X^18*x^25-179*X^18*x^26+64*X^18*x^27-8*X^18*x^28+9*X^17*x^7-529*X^17*x^24-14*X^17*x^25+343*X^17*x^26-180*X^17*x^27+31*X^17*x^28-X^17*x^29+425*X^16*x^24-159*X^16*x^25-337*X^16*x^26+279*X^16*x^27-74*X^16*x^28+6*X^16*x^29+690*X^16*x^23-17*X^17*x^9+923*X^17*x^12-590*X^17*x^13+806*X^17*x^22+257*X^17*x^21-1309*X^17*x^20-410*X^17*x^19+2844*X^17*x^18-2405*X^17*x^17-732*X^17*x^16+2694*X^17*x^15-1380*X^17*x^14-439*X^17*x^11+132*X^17*x^10-16*X^17*x^8+180*X^15*x^23-230*X^16*x^9-1833*X^16*x^12+5498*X^16*x^13-51*X^16*x^6-2012*X^16*x^22+1278*X^16*x^21+872*X^16*x^20-471*X^16*x^19-3405*X^16*x^18+3030*X^16*x^17+4540*X^16*x^16-6696*X^16*x^15-1096*X^16*x^14-1576*X^16*x^11+1366*X^16*x^10-215*X^16*x^8+165*X^16*x^7-170*X^15*x^24-283*X^15*x^25+342*X^15*x^26-248*X^15*x^27+87*X^15*x^28-10*X^15*x^29-695*X^14*x^23-2347*X^15*x^9-9275*X^15*x^12+125*X^15*x^5-1271*X^15*x^13-393*X^15*x^6+2126*X^15*x^22-2123*X^15*x^21-4351*X^15*x^20+4485*X^15*x^19+6111*X^15*x^18-4750*X^15*x^17-9091*X^15*x^16+6910*X^15*x^15+5333*X^15*x^14+7398*X^15*x^11+53*X^15*x^10+777*X^15*x^8+400*X^15*x^7+959*X^14*x^24+471*X^14*x^25-576*X^14*x^26+257*X^14*x^27-69*X^14*x^28+7*X^14*x^29+X^22*x^23+15*x^13+x^17-6*x^16+15*x^15-20*x^14+x^11-X^11-7*x*X^10-x*X^9-5*x*X^8-5*x*X^7-x*X^6+5*x^4*X^5-25*x^7*X^4-6*x^7*X^3+5*x^9*X^2-x^16*X^22;
P_Xy:= -32*X*y^15+96*X*y^16-177*X*y^17+215*X*y^18-170*X*y^19+82*X*y^20-21*X*y^21+2*X*y^22+y^16-5*y^17+10*y^18-10*y^19+5*y^20-y^21-33*y*X^18-37*y*X^17-28*y*X^16-9*y*X^15-9*y^11*X^3-y*X^14+4*y^5*X^9-5*y^10*X^4+24*y^6*X^8+2*y^3*X^12+y^6*X^6+56*y^4*X^11+5*y^14*X-5*y*X^21-17*y*X^20-y^11*X^2+5*y^4*X^10+9*y^6*X^7-y^8*X^5-3*y^2*X^13-40*y*X^19-6*y*X^22-293930*X^23*y^12+352716*X^23*y^11-352716*X^23*y^10+203490*X^23*y^13-116280*X^23*y^14-203490*X^23*y^8+54264*X^23*y^15-20349*X^23*y^16+5985*X^23*y^17-1330*X^23*y^18+210*X^23*y^19-21*X^23*y^20+X^23*y^21+21*X^23*y-210*X^23*y^2-54264*X^23*y^6+116280*X^23*y^7+1330*X^23*y^3-5985*X^23*y^4+20349*X^23*y^5+293930*X^23*y^9+638248*X^22*y^12-772616*X^22*y^11+755820*X^22*y^10-419900*X^22*y^13+213180*X^22*y^14+387600*X^22*y^8-77520*X^22*y^15+15504*X^22*y^16+1938*X^22*y^17-2850*X^22*y^18+1140*X^22*y^19-260*X^22*y^20+34*X^22*y^21-2*X^22*y^22+118*X^22*y^2+83334*X^22*y^6-201552*X^22*y^7-1100*X^22*y^3+6460*X^22*y^4-26790*X^22*y^5-600780*X^22*y^9+X^21*y^23-200174*X^21*y^12+238732*X^21*y^11-195924*X^21*y^10+101712*X^21*y^13-4844*X^21*y^14-31500*X^21*y^8-44386*X^21*y^15+45748*X^21*y^16-26757*X^21*y^17+10274*X^21*y^18-2512*X^21*y^19+307*X^21*y^20+14*X^21*y^21-10*X^21*y^22+82*X^21*y^2+12886*X^21*y^6-6391*X^21*y^7-612*X^21*y^3+2707*X^21*y^4-7622*X^21*y^5+108274*X^21*y^9+X^20*y^26-23*X^20*y^25+248*X^20*y^24-1662*X^20*y^23+1378582*X^20*y^12-1843570*X^20*y^11+1865433*X^20*y^10-709216*X^20*y^13+182134*X^20*y^14+948702*X^20*y^8+19926*X^20*y^15+26018*X^20*y^16-126517*X^20*y^17+158851*X^20*y^18-121414*X^20*y^19+65494*X^20*y^20-26079*X^20*y^21+7714*X^20*y^22+315*X^20*y^2+200272*X^20*y^6-487344*X^20*y^7-2800*X^20*y^3+15900*X^20*y^4-64705*X^20*y^5-1486243*X^20*y^9+662*X^19*y^2+185500*X^19*y^6-334723*X^19*y^7-5093*X^19*y^3+24109*X^19*y^4-78373*X^19*y^5-688248*X^19*y^9-2*X^19*y^27+38*X^19*y^26-320*X^19*y^25+1511*X^19*y^24-3885*X^19*y^23+2532759*X^19*y^12-1719578*X^19*y^11+1054389*X^19*y^10-3009694*X^19*y^13+2710555*X^19*y^14+494344*X^19*y^8-1701504*X^19*y^15+541629*X^19*y^16+211776*X^19*y^17-416797*X^19*y^18+297073*X^19*y^19-126192*X^19*y^20+28451*X^19*y^21+1653*X^19*y^22+189432*X^18*y^21-97246*X^18*y^22+492*X^18*y^2+175369*X^18*y^6-433654*X^18*y^7-3526*X^18*y^3+16616*X^18*y^4-59567*X^18*y^5-1475228*X^18*y^9+X^18*y^28-9*X^18*y^27-36*X^18*y^26+1006*X^18*y^25-7600*X^18*y^24+33419*X^18*y^23+1653013*X^18*y^12-1992589*X^18*y^11+1937594*X^18*y^10-1307359*X^18*y^13+1316943*X^18*y^14+889159*X^18*y^8-1573311*X^18*y^15+1619607*X^18*y^16-1199371*X^18*y^17+524756*X^18*y^18+8694*X^18*y^19-216572*X^18*y^20-4261856*X^17*y^11+2102088*X^17*y^10-6830653*X^17*y^13+5248102*X^17*y^14+197651*X^17*y^8-2479532*X^17*y^15+204938*X^17*y^16+629221*X^17*y^17-357607*X^17*y^18-138444*X^17*y^19+337268*X^17*y^20-259231*X^17*y^21+117798*X^17*y^22+534*X^17*y^2+53702*X^17*y^6-74831*X^17*y^7-3485*X^17*y^3+13393*X^17*y^4-32902*X^17*y^5-738389*X^17*y^9-5*X^17*y^28+75*X^17*y^27-441*X^17*y^26+903*X^17*y^25+3513*X^17*y^24-32151*X^17*y^23+6300378*X^17*y^12+2754027*X^16*y^12-1841694*X^16*y^11+1204640*X^16*y^10-3969724*X^16*y^13+5015246*X^16*y^14+347096*X^16*y^8-5022661*X^16*y^15+3552726*X^16*y^16-1227312*X^16*y^17-719871*X^16*y^18+1507990*X^16*y^19-1290161*X^16*y^20+712269*X^16*y^21-262528*X^16*y^22+345*X^16*y^2+47874*X^16*y^6-137231*X^16*y^7-1899*X^16*y^3+6464*X^16*y^4-17418*X^16*y^5-710708*X^16*y^9-X^16*y^29+28*X^16*y^28-301*X^16*y^27+1678*X^16*y^26-4750*X^16*y^25+484*X^16*y^24+55420*X^16*y^23+25387*X^15*y^25-66297*X^15*y^24+103581*X^15*y^23+4677914*X^15*y^12-3720340*X^15*y^11+2160172*X^15*y^10-4341946*X^15*y^13+3026360*X^15*y^14+187815*X^15*y^8-1888530*X^15*y^15+1751310*X^15*y^16-2292869*X^15*y^17+2566087*X^15*y^18-2083420*X^15*y^19+1158891*X^15*y^20-367386*X^15*y^21-23241*X^15*y^22+57*X^15*y^2-37583*X^15*y^6+23571*X^15*y^7+173*X^15*y^3-3139*X^15*y^4+15305*X^15*y^5-866359*X^15*y^9+5*X^15*y^29-110*X^15*y^28+1093*X^15*y^27-6492*X^15*y^26-5*X^14*y^29+102*X^14*y^28-938*X^14*y^27+5122*X^14*y^26-17997*X^14*y^25+39017*X^14*y^24-30904*X^14*y^23+2802953*X^14*y^12-1690347*X^14*y^11+895802*X^14*y^10-4001991*X^14*y^13+4642192*X^14*y^14+126553*X^14*y^8-4013357*X^14*y^15+2091733*X^14*y^16+193816*X^14*y^17-1674291*X^14*y^18+1893707*X^14*y^19-1284247*X^14*y^20+558719*X^14*y^21-118268*X^14*y^22-12*X^14*y^2-10221*X^14*y^6-15196*X^14*y^7+311*X^14*y^3-2131*X^14*y^4+7104*X^14*y^5-397225*X^14*y^9+3*X^13*y^29-73*X^13*y^28+801*X^13*y^27-5399*X^13*y^26+25144*X^13*y^25-84825*X^13*y^24+207827*X^13*y^23+478289*X^13*y^12-756348*X^13*y^11+784793*X^13*y^10-425143*X^13*y^13+1214579*X^13*y^14+278238*X^13*y^8-2832994*X^13*y^15+4336007*X^13*y^16-4616678*X^13*y^17+3468329*X^13*y^18-1708224*X^13*y^19+323834*X^13*y^20+292903*X^13*y^21-348615*X^13*y^22+24412*X^13*y^6-100079*X^13*y^7+57*X^13*y^3+2*X^13*y^4-3287*X^13*y^5-553550*X^13*y^9+18*X^12*y^29-152*X^12*y^28+810*X^12*y^27-3046*X^12*y^26+8450*X^12*y^25-17543*X^12*y^24+27063*X^12*y^23-X^12*y^30+399108*X^12*y^12-421517*X^12*y^11+370376*X^12*y^10-413588*X^12*y^13+582848*X^12*y^14+127663*X^12*y^8-854456*X^12*y^15+1011349*X^12*y^16-901339*X^12*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P_Yx := 462*x^12-Y^7-462*x^13-11*x^17+55*x^16-165*x^15+330*x^14-330*x^11+65577*Y^3*x^13+93409*Y^3*x^17-134470*Y^3*x^16+150324*Y^3*x^15-118919*Y^3*x^14+74762*Y^3*x^11-4*Y^3*x^24+76*Y^3*x^23+3201*Y^3*x^21+26929*Y^3*x^19+70447*Y^3*x^9-5536*Y^3*x^7-4906*Y^3*x^5-641*Y^3*x^22-10780*Y^3*x^20-54348*Y^3*x^18-95313*Y^3*x^10-23634*Y^3*x^8+9932*Y^3*x^6+196065*Y^4*x^12-1641*Y^4*x^4+134*Y^4*x^3-90861*Y^4*x^13-290874*Y^4*x^17+307002*Y^4*x^16-244886*Y^4*x^15+131550*Y^4*x^14-324451*Y^4*x^11+124*Y^4*x^24-5*Y^4*x^25-1295*Y^4*x^23-29356*Y^4*x^21-150644*Y^4*x^19-147764*Y^4*x^9+40074*Y^4*x^7+9144*Y^4*x^5+7687*Y^4*x^22+77575*Y^4*x^20+229455*Y^4*x^18+303972*Y^4*x^10+6367*Y^4*x^8-27370*Y^4*x^6-657481*Y^5*x^12+1411*Y^5*x^4-122*Y^5*x^3+373205*Y^5*x^13+215302*Y^5*x^17-176194*Y^5*x^16+155763*Y^5*x^15-184791*Y^5*x^14+736830*Y^5*x^11-840*Y^5*x^24+44*Y^5*x^25+6994*Y^5*x^23+101478*Y^5*x^21+281104*Y^5*x^19+115826*Y^5*x^9-85225*Y^5*x^7-9679*Y^5*x^5-33423*Y^5*x^22-204784*Y^5*x^20-272882*Y^5*x^18-477049*Y^5*x^10+76160*Y^5*x^8+38346*Y^5*x^6+965612*Y^6*x^12-1531*Y^6*x^4+120*Y^6*x^3-688328*Y^6*x^13+23118*Y^6*x^17+252150*Y^6*x^16-453274*Y^6*x^15+510023*Y^6*x^14-936770*Y^6*x^11-856*Y^6*x^24+538*Y^6*x^25-87*Y^6*x^26+5*Y^6*x^27-6298*Y^6*x^23-108915*Y^6*x^21-53802*Y^6*x^19-48764*Y^6*x^9+107053*Y^6*x^7+10357*Y^6*x^5+40929*Y^6*x^22+144070*Y^6*x^20-82908*Y^6*x^18+504109*Y^6*x^10-133751*Y^6*x^8-42798*Y^6*x^6+11*Y^7*x-1444703*Y^7*x^12-51*Y^7*x^2+258*Y^7*x^4+129*Y^7*x^3+667481*Y^7*x^13+274367*Y^7*x^17-313881*Y^7*x^16+24698*Y^7*x^15+21932*Y^7*x^14+1363074*Y^7*x^11+18133*Y^7*x^24-5646*Y^7*x^25+1017*Y^7*x^26-99*Y^7*x^27+4*Y^7*x^28-31787*Y^7*x^23+35581*Y^7*x^21+36541*Y^7*x^19-86159*Y^7*x^9-136220*Y^7*x^7-6323*Y^7*x^5+17826*Y^7*x^22-66622*Y^7*x^20-80748*Y^7*x^18-569161*Y^7*x^10+239956*Y^7*x^8+40393*Y^7*x^6+2025152*Y^8*x^12+141*Y^8*x^2+1158*Y^8*x^4-617*Y^8*x^3+Y^8*x^29-1925427*Y^8*x^13+868427*Y^8*x^17-839927*Y^8*x^16+319128*Y^8*x^15+797964*Y^8*x^14-1028206*Y^8*x^11-40043*Y^8*x^24+15848*Y^8*x^25-3733*Y^8*x^26+520*Y^8*x^27-38*Y^8*x^28+50088*Y^8*x^23-156505*Y^8*x^21+85816*Y^8*x^19+369504*Y^8*x^9+89105*Y^8*x^7+1147*Y^8*x^5+15875*Y^8*x^22+189610*Y^8*x^20-552287*Y^8*x^18-12428*Y^8*x^10-251694*Y^8*x^8-18566*Y^8*x^6-871703*Y^9*x^12-51*Y^9*x^2-3047*Y^9*x^4+631*Y^9*x^3-4*Y^9*x^29+987242*Y^9*x^13+72278*Y^9*x^17-757714*Y^9*x^16+892013*Y^9*x^15-864735*Y^9*x^14+357297*Y^9*x^11+30079*Y^9*x^24-15792*Y^9*x^25+4800*Y^9*x^26-883*Y^9*x^27+91*Y^9*x^28-22317*Y^9*x^23+7231*Y^9*x^21-651159*Y^9*x^19-267497*Y^9*x^9-61470*Y^9*x^7+6199*Y^9*x^5-22939*Y^9*x^22+253979*Y^9*x^20+620046*Y^9*x^18+125468*Y^9*x^10+177389*Y^9*x^8+4569*Y^9*x^6+1243788*Y^10*x^12+64*Y^10*x^2+2365*Y^10*x^4-473*Y^10*x^3+2*Y^10*x^29-1387312*Y^10*x^13+236014*Y^10*x^17-1010984*Y^10*x^16+1053015*Y^10*x^15+169075*Y^10*x^14-220554*Y^10*x^11-26542*Y^10*x^24+9760*Y^10*x^25-2207*Y^10*x^26+335*Y^10*x^27-35*Y^10*x^28+35530*Y^10*x^23-129973*Y^10*x^21-316812*Y^10*x^19+379995*Y^10*x^9-1986*Y^10*x^7-8588*Y^10*x^5+11397*Y^10*x^22+250771*Y^10*x^20+244963*Y^10*x^18-422587*Y^10*x^10-127968*Y^10*x^8+18952*Y^10*x^6+337294*Y^11*x^12+30*Y^11*x^2-2125*Y^11*x^4+159*Y^11*x^3+3*Y^11*x^29+676135*Y^11*x^13-587769*Y^11*x^17-297548*Y^11*x^16+1245696*Y^11*x^15-1468013*Y^11*x^14-678474*Y^11*x^11+11406*Y^11*x^24-7090*Y^11*x^25+1492*Y^11*x^26-53*Y^11*x^27-26*Y^11*x^28+16037*Y^11*x^23+85202*Y^11*x^21-681886*Y^11*x^19-108776*Y^11*x^9+27432*Y^11*x^7+8691*Y^11*x^5-89006*Y^11*x^22+197072*Y^11*x^20+929567*Y^11*x^18+415508*Y^11*x^10-11681*Y^11*x^8-19272*Y^11*x^6-132534*Y^12*x^12-10*Y^12*x^2-515*Y^12*x^4+210*Y^12*x^3+Y^12*x^30-18*Y^12*x^29+331197*Y^12*x^13-616544*Y^12*x^17-20318*Y^12*x^16+599506*Y^12*x^15-636185*Y^12*x^14+130775*Y^12*x^11+9937*Y^12*x^24-4606*Y^12*x^25+1915*Y^12*x^26-630*Y^12*x^27+140*Y^12*x^28-18081*Y^12*x^23-39390*Y^12*x^21-440772*Y^12*x^19+53666*Y^12*x^9-44086*Y^12*x^7-3102*Y^12*x^5+24162*Y^12*x^22+147510*Y^12*x^20+743401*Y^12*x^18-135197*Y^12*x^10+29488*Y^12*x^8+20081*Y^12*x^6+289609*Y^13*x^12+320*Y^13*x^4-28*Y^13*x^3+208267*Y^13*x^13-751668*Y^13*x^17+366351*Y^13*x^16+307281*Y^13*x^15-594851*Y^13*x^14-343510*Y^13*x^11+4585*Y^13*x^24-976*Y^13*x^25-73*Y^13*x^26+61*Y^13*x^27-7*Y^13*x^28-7161*Y^13*x^23-16706*Y^13*x^21-370557*Y^13*x^19+73823*Y^13*x^9+22705*Y^13*x^7-1592*Y^13*x^5+2578*Y^13*x^22+124281*Y^13*x^20+665693*Y^13*x^18+93863*Y^13*x^10-72028*Y^13*x^8-269*Y^13*x^6-217553*Y^14*x^12-500*Y^14*x^4+70*Y^14*x^3-3*Y^14*x^29+482441*Y^14*x^13-501574*Y^14*x^17+362634*Y^14*x^16+11393*Y^14*x^15-405160*Y^14*x^14-54343*Y^14*x^11+4460*Y^14*x^24-2565*Y^14*x^25+1098*Y^14*x^26-296*Y^14*x^27+45*Y^14*x^28-7254*Y^14*x^23-22937*Y^14*x^21-224175*Y^14*x^19-63623*Y^14*x^9-73*Y^14*x^7+1311*Y^14*x^5+11390*Y^14*x^22+78529*Y^14*x^20+413711*Y^14*x^18+119258*Y^14*x^10+15689*Y^14*x^8-1981*Y^14*x^6-124951*Y^15*x^12-72*Y^15*x^4+65*Y^15*x^3-Y^15*x^29+125664*Y^15*x^13-343425*Y^15*x^17+314743*Y^15*x^16-167870*Y^15*x^15-14624*Y^15*x^14+73891*Y^15*x^11+4041*Y^15*x^24-1768*Y^15*x^25+568*Y^15*x^26-122*Y^15*x^27+16*Y^15*x^28-8045*Y^15*x^23-35036*Y^15*x^21-147684*Y^15*x^19+18434*Y^15*x^9-7488*Y^15*x^7-1257*Y^15*x^5+16624*Y^15*x^22+72592*Y^15*x^20+259714*Y^15*x^18-38485*Y^15*x^10-660*Y^15*x^8+5135*Y^15*x^6+20064*Y^16*x^12+153*Y^16*x^4-17132*Y^16*x^13-166111*Y^16*x^17+185676*Y^16*x^16-144085*Y^16*x^15+65998*Y^16*x^14-30454*Y^16*x^11+955*Y^16*x^24-293*Y^16*x^25+52*Y^16*x^26-4*Y^16*x^27-2220*Y^16*x^23-14096*Y^16*x^21-68400*Y^16*x^19+12937*Y^16*x^9+6964*Y^16*x^7-830*Y^16*x^5+5213*Y^16*x^22+34325*Y^16*x^20+115896*Y^16*x^18+12613*Y^16*x^10-17272*Y^16*x^8+36*Y^16*x^6-11099*Y^17*x^12+54*Y^17*x^4+12528*Y^17*x^13-30126*Y^17*x^17+39023*Y^17*x^16-36003*Y^17*x^15+12351*Y^17*x^14-10885*Y^17*x^11+17*Y^17*x^24-2*Y^17*x^25-40*Y^17*x^23-891*Y^17*x^21-11679*Y^17*x^19-14356*Y^17*x^9+3220*Y^17*x^7+52*Y^17*x^5+85*Y^17*x^22+4453*Y^17*x^20+20579*Y^17*x^18+23216*Y^17*x^10+909*Y^17*x^8-1407*Y^17*x^6-14502*Y^18*x^12+8284*Y^18*x^13-2035*Y^18*x^17+3117*Y^18*x^16-4038*Y^18*x^15+491*Y^18*x^14+10883*Y^18*x^11+3*Y^18*x^24-25*Y^18*x^23-159*Y^18*x^21-808*Y^18*x^19-5022*Y^18*x^9-656*Y^18*x^7+80*Y^18*x^5+81*Y^18*x^22+331*Y^18*x^20+1477*Y^18*x^18-906*Y^18*x^10+3651*Y^18*x^8-252*Y^18*x^6-1505*Y^19*x^12-1476*Y^19*x^13-1991*Y^19*x^17+3239*Y^19*x^16-3912*Y^19*x^15+3413*Y^19*x^14+3812*Y^19*x^11+Y^19*x^24-11*Y^19*x^23-125*Y^19*x^21-368*Y^19*x^19+1007*Y^19*x^9-351*Y^19*x^7+50*Y^19*x^22+209*Y^19*x^20+900*Y^19*x^18-3363*Y^19*x^10+416*Y^19*x^8+45*Y^19*x^6+931*Y^20*x^12-1361*Y^20*x^13-612*Y^20*x^17+1222*Y^20*x^16-1629*Y^20*x^15+1612*Y^20*x^14-187*Y^20*x^11-31*Y^20*x^19+461*Y^20*x^9-9*Y^20*x^7+2*Y^20*x^20+188*Y^20*x^18-450*Y^20*x^10-147*Y^20*x^8+234*Y^21*x^12-213*Y^21*x^13-50*Y^21*x^17+124*Y^21*x^16-189*Y^21*x^15+206*Y^21*x^14-195*Y^21*x^11-Y^21*x^19+10*Y^21*x^9+11*Y^21*x^18+78*Y^21*x^10-20*Y^21*x^8+15*Y^22*x^12-6*Y^22*x^13+Y^22*x^14-20*Y^22*x^11-6*Y^22*x^9+15*Y^22*x^10+9*x^2*Y^3-6*x^2*Y^2+x^2*Y+x^8*Y^22+5*x^7*Y^21+10*x^6*Y^20+10*x^5*Y^19+5*x^4*Y^18+x^3*Y^17+15*x^3*Y^16+x^2*Y^15+7*x^2*Y^14+9*x^2*Y^13-x*Y^12-5*x*Y^11-5*x*Y^10-x*Y^9-13*x*Y^8-2*x^2*Y^6+7*x^2*Y^5-5110*Y*x^12+50*Y*x^4-11*Y*x^3+6439*Y*x^13+473*Y*x^17-1644*Y*x^16+3739*Y*x^15+3173*Y*x^11+6*Y*x^19+1391*Y*x^9+261*Y*x^7-111*Y*x^5-80*Y*x^18-1953*Y*x^10-848*Y*x^8+71*Y*x^6+20215*Y^2*x^12-426*Y^2*x^4+78*Y^2*x^3-32815*Y^2*x^13-11387*Y^2*x^17+23172*Y^2*x^16-36132*Y^2*x^15+40918*Y^2*x^14-14789*Y^2*x^11-Y^2*x^23-115*Y^2*x^21-1667*Y^2*x^19-14625*Y^2*x^9-1113*Y^2*x^7+1206*Y^2*x^5+16*Y^2*x^22+509*Y^2*x^20+4638*Y^2*x^18+15992*Y^2*x^10+7850*Y^2*x^8-1518*Y^2*x^6-47216*Y^3*x^12+1272*Y^3*x^4-171*Y^3*x^3-55*x^9-x^7+x^18+165*x^10+11*x^8-5847*Y*x^14-2*x^2*Y^4;
P_Yy := -11*Y^16*y^2+20*y^6-15*y^7+29*Y^11*y+5*Y^19*y^3-y^3+6*y^4-15*y^5+Y^14-y^9+5*Y^15*y+10*Y^18*y^3+9*Y^17*y^2+13*Y^13*y+6*y^8+18*Y^21*y^5+9*Y^20*y^4+55*Y^4*y^2-125*Y^5*y^2+2*Y^12*y-Y^6*y+7*Y^22*y^5+Y^23*y^5+8*Y^7*y-4*Y^23*y^8+Y^23*y^9-4*Y^23*y^6+6*Y^23*y^7-20*Y^8*y-67*Y^22*y^12+131*Y^22*y^11-130*Y^22*y^10+18*Y^22*y^13-2*Y^22*y^14+29*Y^22*y^8-14*Y^22*y^6-11*Y^22*y^7+39*Y^22*y^9+909*Y^21*y^12-1239*Y^21*y^11+688*Y^21*y^10+107*Y^21*y^13-729*Y^21*y^14+304*Y^21*y^8+639*Y^21*y^15-302*Y^21*y^16+86*Y^21*y^17-14*Y^21*y^18+Y^21*y^19+20*Y^21*y^6-212*Y^21*y^7-276*Y^21*y^9-3967*Y^20*y^12-4524*Y^20*y^11+7106*Y^20*y^10+9937*Y^20*y^13-8186*Y^20*y^14+1779*Y^20*y^8+3003*Y^20*y^15+142*Y^20*y^16-646*Y^20*y^17+290*Y^20*y^18-60*Y^20*y^19+5*Y^20*y^20+166*Y^20*y^6-697*Y^20*y^7-11*Y^20*y^5-4346*Y^20*y^9-57839*Y^19*y^12+25689*Y^19*y^11+8982*Y^19*y^10+51823*Y^19*y^13-18444*Y^19*y^14+7622*Y^19*y^8-5857*Y^19*y^15+8976*Y^19*y^16-3567*Y^19*y^17+249*Y^19*y^18+275*Y^19*y^19-95*Y^19*y^20+10*Y^19*y^21+20*Y^19*y^4+78*Y^19*y^5-16670*Y^19*y^9-415*Y^19*y^6-842*Y^19*y^7-191865*Y^18*y^12+199156*Y^18*y^11-95229*Y^18*y^10+61871*Y^18*y^13+54438*Y^18*y^14+10443*Y^18*y^8-66792*Y^18*y^15+22047*Y^18*y^16+7130*Y^18*y^17-8878*Y^18*y^18+3241*Y^18*y^19-561*Y^18*y^20+92*Y^18*y^21-41*Y^18*y^22-Y^18*y^24+11*Y^18*y^23-2485*Y^18*y^6-250*Y^18*y^7+98*Y^18*y^4+447*Y^18*y^5+7118*Y^18*y^9-17*Y^10*y-293885*Y^17*y^12+533520*Y^17*y^11-424289*Y^17*y^10-72701*Y^17*y^13+202882*Y^17*y^14-25794*Y^17*y^8-81538*Y^17*y^15-43834*Y^17*y^16+52245*Y^17*y^17-11563*Y^17*y^18-7497*Y^17*y^19+5171*Y^17*y^20-868*Y^17*y^21-187*Y^17*y^22-9*Y^17*y^24+87*Y^17*y^23-6169*Y^17*y^6+4760*Y^17*y^7-Y^17*y^3+64*Y^17*y^4+1770*Y^17*y^5+167827*Y^17*y^9-257952*Y^16*y^12+950395*Y^16*y^11-1012879*Y^16*y^10-372701*Y^16*y^13+388044*Y^16*y^14-160966*Y^16*y^8-55959*Y^16*y^15-119409*Y^16*y^16+64321*Y^16*y^17+18185*Y^16*y^18-30403*Y^16*y^19+11234*Y^16*y^20-415*Y^16*y^21-788*Y^16*y^22+184*Y^16*y^3+162*Y^16*y^4-319*Y^16*y^5+559321*Y^16*y^9-3*Y^16*y^25+4*Y^16*y^24+170*Y^16*y^23-2366*Y^16*y^6+22151*Y^16*y^7-16733*Y^15*y^20+16891*Y^15*y^21-9374*Y^15*y^22+166627*Y^15*y^12+1160594*Y^15*y^11-1466926*Y^15*y^10-1173228*Y^15*y^13+981956*Y^15*y^14-246294*Y^15*y^8-271072*Y^15*y^15-68856*Y^15*y^16+31466*Y^15*y^17+26212*Y^15*y^18-7024*Y^15*y^19+4*Y^15*y^27-62*Y^15*y^26+408*Y^15*y^25-1557*Y^15*y^24+4193*Y^15*y^23+2*Y^15*y^2-15553*Y^15*y^6+49810*Y^15*y^7-184*Y^15*y^3+1550*Y^15*y^4+1069*Y^15*y^5+836076*Y^15*y^9+2158706*Y^14*y^12+624035*Y^14*y^11-1993185*Y^14*y^10-3136781*Y^14*y^13+1241611*Y^14*y^14-271573*Y^14*y^8+904744*Y^14*y^15-1187539*Y^14*y^16+396513*Y^14*y^17+52412*Y^14*y^18-21664*Y^14*y^19-46157*Y^14*y^20+22556*Y^14*y^21+6099*Y^14*y^22+Y^14*y^29-16*Y^14*y^28+112*Y^14*y^27-411*Y^14*y^26+560*Y^14*y^25+1550*Y^14*y^24-7445*Y^14*y^23-7*Y^14*y+107*Y^14*y^2+22943*Y^14*y^6-49993*Y^14*y^7+144*Y^14*y^3-1614*Y^14*y^4+2247*Y^14*y^5+1282044*Y^14*y^9+2287288*Y^13*y^12-911514*Y^13*y^11-365709*Y^13*y^10-1556723*Y^13*y^13-993357*Y^13*y^14-204488*Y^13*y^8+2396477*Y^13*y^15-1388236*Y^13*y^16-143746*Y^13*y^17+498236*Y^13*y^18-90228*Y^13*y^19-128288*Y^13*y^20+42796*Y^13*y^21+47875*Y^13*y^22+3*Y^13*y^29-48*Y^13*y^28+303*Y^13*y^27-731*Y^13*y^26-1529*Y^13*y^25+15821*Y^13*y^24-45397*Y^13*y^23-41*Y^13*y^2+2037*Y^13*y^6+45990*Y^13*y^7-149*Y^13*y^3+4598*Y^13*y^4-12188*Y^13*y^5+500935*Y^13*y^9+2987243*Y^12*y^12+1075625*Y^12*y^11-2001069*Y^12*y^10-5588702*Y^12*y^13+3097534*Y^12*y^14+442438*Y^12*y^8+1253503*Y^12*y^15-2425036*Y^12*y^16+513162*Y^12*y^17+1128356*Y^12*y^18-1086678*Y^12*y^19+357848*Y^12*y^20+67267*Y^12*y^21-119308*Y^12*y^22-Y^12*y^28+37*Y^12*y^27-485*Y^12*y^26+3602*Y^12*y^25-17726*Y^12*y^24+59048*Y^12*y^23+218*Y^12*y^2+44798*Y^12*y^6-312905*Y^12*y^7-492*Y^12*y^3-3514*Y^12*y^4+13892*Y^12*y^5+511343*Y^12*y^9+17*Y^9*y+3159735*Y^11*y^12-2929114*Y^11*y^11+1233779*Y^11*y^10-931071*Y^11*y^13-2192727*Y^11*y^14-331952*Y^11*y^8+3239808*Y^11*y^15-1379059*Y^11*y^16-936354*Y^11*y^17+1343035*Y^11*y^18-305685*Y^11*y^19-466178*Y^11*y^20+433916*Y^11*y^21-131043*Y^11*y^22+18*Y^11*y^29-124*Y^11*y^28+287*Y^11*y^27+1221*Y^11*y^26-10952*Y^11*y^25+32259*Y^11*y^24-22710*Y^11*y^23-Y^11*y^30-309*Y^11*y^2+75664*Y^11*y^6+67158*Y^11*y^7+1493*Y^11*y^3+5668*Y^11*y^4-45676*Y^11*y^5+88885*Y^11*y^9+3849652*Y^10*y^11-1732228*Y^10*y^10-2509978*Y^10*y^13+4618010*Y^10*y^14+851043*Y^10*y^8-1487436*Y^10*y^15-3165390*Y^10*y^16+4580497*Y^10*y^17-2575837*Y^10*y^18+159600*Y^10*y^19+784798*Y^10*y^20-601244*Y^10*y^21+222257*Y^10*y^22-2143560*Y^10*y^12-9*Y^10*y^28+164*Y^10*y^27-1269*Y^10*y^26+5005*Y^10*y^25-6522*Y^10*y^24-34826*Y^10*y^23+397*Y^10*y^2-50706*Y^10*y^6-235191*Y^10*y^7-2413*Y^10*y^3+1249*Y^10*y^4+30445*Y^10*y^5-556491*Y^10*y^9+938443*Y^9*y^12-1543692*Y^9*y^11+137301*Y^9*y^10+1804400*Y^9*y^13-3600210*Y^9*y^14-667693*Y^9*y^8+1775758*Y^9*y^15+2348591*Y^9*y^16-4940399*Y^9*y^17+4183479*Y^9*y^18-1700697*Y^9*y^19-145107*Y^9*y^20+641278*Y^9*y^21-419461*Y^9*y^22-3*Y^9*y^29+57*Y^9*y^28-457*Y^9*y^27+1763*Y^9*y^26-830*Y^9*y^25-26521*Y^9*y^24+148089*Y^9*y^23-408*Y^9*y^2+141115*Y^9*y^6+29611*Y^9*y^7+3596*Y^9*y^3-4710*Y^9*y^4-45363*Y^9*y^5+942053*Y^9*y^9-3397754*Y^8*y^12+2714409*Y^8*y^11-315795*Y^8*y^10+431619*Y^8*y^13+3271769*Y^8*y^14+407264*Y^8*y^8-3118296*Y^8*y^15-855530*Y^8*y^16+4233025*Y^8*y^17-4178925*Y^8*y^18+1989687*Y^8*y^19-159100*Y^8*y^20-440161*Y^8*y^21+333208*Y^8*y^22-4106*Y^8*y^3+10826*Y^8*y^4+25699*Y^8*y^5-812164*Y^8*y^9+Y^8*y^29-19*Y^8*y^28+133*Y^8*y^27-189*Y^8*y^26-3514*Y^8*y^25+30581*Y^8*y^24-130635*Y^8*y^23+459*Y^8*y^2-148193*Y^8*y^6+115721*Y^8*y^7+1639376*Y^7*y^12-1259459*Y^7*y^11-96163*Y^7*y^10-87444*Y^7*y^13-1477107*Y^7*y^14-192961*Y^7*y^8+778406*Y^7*y^15+1484268*Y^7*y^16-2799718*Y^7*y^17+2219601*Y^7*y^18-873713*Y^7*y^19-8094*Y^7*y^20+224565*Y^7*y^21-145169*Y^7*y^22+6*Y^7*y^27-159*Y^7*y^26+1839*Y^7*y^25-12329*Y^7*y^24+52746*Y^7*y^23-311*Y^7*y^2+122601*Y^7*y^6-163492*Y^7*y^7+3618*Y^7*y^3-14231*Y^7*y^4-6959*Y^7*y^5+610274*Y^7*y^9+Y^2*y^2-498473*Y^6*y^12-161564*Y^6*y^11+632629*Y^6*y^10+713707*Y^6*y^13-638761*Y^6*y^14+5735*Y^6*y^8+770056*Y^6*y^15-1016764*Y^6*y^16+947275*Y^6*y^17-537355*Y^6*y^18+131606*Y^6*y^19+53520*Y^6*y^20-67518*Y^6*y^21+33107*Y^6*y^22+10*Y^6*y^26-203*Y^6*y^25+1848*Y^6*y^24-9845*Y^6*y^23+187*Y^6*y^2-88182*Y^6*y^6+176397*Y^6*y^7-2785*Y^6*y^3+12752*Y^6*y^4-2615*Y^6*y^5-454763*Y^6*y^9+2*y^14*Y-17*y^13*Y+65*y^12*Y-350*Y*y^9+245*Y*y^8-97*y^4*Y+15*y^3*Y-157*y^11*Y+277*y^10*Y+39*Y*y^7-259*Y*y^6+237*Y*y^5+456866*Y^5*y^12-25493*Y^5*y^11-182599*Y^5*y^10-698388*Y^5*y^13+614406*Y^5*y^14+153663*Y^5*y^8-404258*Y^5*y^15+236344*Y^5*y^16-121600*Y^5*y^17+39645*Y^5*y^18+4714*Y^5*y^19-14656*Y^5*y^20+9162*Y^5*y^21-3264*Y^5*y^22+39041*Y^5*y^9+5*Y^5*y^25-90*Y^5*y^24+715*Y^5*y^23+48671*Y^5*y^6-154457*Y^5*y^7+1833*Y^5*y^3-9825*Y^5*y^4+9690*Y^5*y^5-207654*Y^4*y^12+115944*Y^4*y^11-64104*Y^4*y^10+224292*Y^4*y^13-150161*Y^4*y^14-122439*Y^4*y^8+62040*Y^4*y^15-12897*Y^4*y^16-1764*Y^4*y^17+3124*Y^4*y^18-2109*Y^4*y^19+1115*Y^4*y^20-433*Y^4*y^21+110*Y^4*y^22+Y^4*y^24-16*Y^4*y^23-15558*Y^4*y^6+78749*Y^4*y^7-952*Y^4*y^3+5980*Y^4*y^4-9649*Y^4*y^5+96326*Y^4*y^9+38440*Y^3*y^12-36534*Y^3*y^11+35705*Y^3*y^10-29759*Y^3*y^13+14129*Y^3*y^14+38866*Y^3*y^8-2552*Y^3*y^15-1435*Y^3*y^16+1272*Y^3*y^17-460*Y^3*y^18+87*Y^3*y^19-7*Y^3*y^20+819*Y^3*y^6-20135*Y^3*y^7+368*Y^3*y^3-2510*Y^3*y^4+5099*Y^3*y^5-41381*Y^3*y^9-2873*Y^2*y^12+4155*Y^2*y^11-5464*Y^2*y^10+1486*Y^2*y^13-409*Y^2*y^14-5448*Y^2*y^8-60*Y^2*y^15+112*Y^2*y^16-50*Y^2*y^17+11*Y^2*y^18-Y^2*y^19+2054*Y^2*y^7-97*Y^2*y^3+661*Y^2*y^4-1518*Y^2*y^5+6464*Y^2*y^9-12*Y^3*y^2+976*Y^2*y^6;

f_41_4 := -X^5*Y^6+(-5*X^5+1+5*X+5*X^2+X^3+7*X^4)*Y^5-X*(5*X^4-18*X^3+6*X^2-18*X-7)*Y^4-X*(X^4+6*X^3-6*X+1)*Y^3-X*(7*X^4-18*X^3-6*X^2-18*X-5)*Y^2-X*(X^5-5*X^4+5*X^3-X^2+7*X+5)*Y+X;

Total degree=11;
Degree(f_41_4,X)=6;
Degree(f_41_4,Y)=6;

//==================================== X_H(41), H=<6^5>  ========================================

N_X:=-y*(x - y + 1)^3*(x*y - 1)*(x^3*y - x^2*y^2 - x^2*y + x*y^2 - y + 1)*(x^4*y - 3*x^3*y^2 + x^3*y + 2*x^2*y^3 + x^2*y^2 - 2*x^2*y - 2*x*y^3 + 2*x*y^2 + y^2 - 2*y + 1)*(x^4*y - 2*x^3*y^2 - x^3*y + x^2*y^3 + x^2*y^2 + 2*x^2*y - x^2 - 2*x*y^2 + x*y + y - 1)^3;
D_X:=(y-1)*x^3*(x-y)*(x^2*y - x*y + y - 1)*(x^2*y - x^2 - x*y^2 + x*y - x + y - 1)*(x^5*y^2 - 3*x^4*y^3 - x^4*y^2 + 3*x^3*y^4 + 3*x^3*y^3 - x^2*y^5 - 3*x^2*y^4 - 2*x^2*y^2 + 3*x^2*y + x*y^5 + 3*x*y^3        - 4*x*y^2 - y^4 + y^3 + y - 1)^3;
X:=N_X/D_X;

N_Y:=-(y-1)^3*x^6*(x^2*y - x*y + y - 1)^2*(x^2*y - x*y^2 - x*y + y^2 - 1)*(x^5*y^2 - 3*x^4*y^3 - x^4*y^2 + 3*x^3*y^4 + 3*x^3*y^3 - x^2*y^5 - 3*x^2*y^4 - 2*x^2*y^2 + 3*x^2*y + x*y^5 + 3*x*y^3        - 4*x*y^2 - y^4 + y^3 + y - 1)^6;
D_Y:=y^4*(x-1)^2*(x - y + 1)^6*(x*y - 1)^2*(x*y - y + 1)^2*(x^3*y - x^2*y^2 - x^2*y + x*y^2 - y + 1)*(x^4*y - 3*x^3*y^2 + x^3*y + 2*x^2*y^3 + x^2*y^2 - 2*x^2*y - 2*x*y^3 + 2*x*y^2 + y^2 - 2*y + 1)*(x^4*y - 2*x^3*y^2 - x^3*y + x^2*y^3 + x^2*y^2 + 2*x^2*y - x^2 - 2*x*y^2 + x*y + y - 1)^6;	
Y:=N_Y/D_Y;

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30-61365*Y^16*x^10+6764*Y^16*x^5-6005*Y^16*x^6-2542*Y^16*x^3-13719*Y^16*x^7+16867*Y^16*x^8+x^8*Y^21-62*Y^17*x^29-12181*Y^17*x^23-30199*Y^17*x^21+28064*Y^17*x^22-20*Y^7*x^23+10*Y^7*x^21+200*Y^7*x^22+124616*Y^16*x^12-30215*Y^16*x^11-40817*Y^16*x^13+33632*Y^16*x^9-17185*Y^16*x^24+9401*Y^16*x^25+89*Y^17*x+4444*Y^18*x^10-458*Y^18*x^5+861*Y^18*x^6-173*Y^18*x^3+694*Y^18*x^7-7305*Y^18*x^8-7324*Y^6*x^16+131*Y^2*x^16-160*Y^2*x^15+Y^2*x^20-10*Y^2*x^19+42*Y^2*x^18-95*Y^2*x^17+283*Y^2*x^14+8856*Y^6*x^15+1536*Y^6*x^20-2504*Y^6*x^19-379*Y^6*x^18+17357*Y^18*x^12-27337*Y^18*x^11+17077*Y^18*x^13+11100*Y^18*x^9+647*Y^18*x^24+Y^18*x^32-9*Y^18*x^31+2428*Y^18*x^25+64*Y^18*x^30+407*Y^15*x+6390*Y^20*x^17+4322*Y^20*x^14+5673*Y^6*x^17-3795*Y^13*x^9+4356*Y^13*x^24-987*Y^13*x^25+11389*Y^13*x^10+4880*Y^13*x^5-20633*Y^13*x^6+60*Y^13*x^3+25481*Y^13*x^7-5851*Y^13*x^8-4328*Y^13*x^23-28542*Y^13*x^21+3906*Y^13*x^22-18544*Y^6*x^14-80590*Y^10*x^16+132532*Y^10*x^15+22206*Y^10*x^20+7127*Y^10*x^19-47498*Y^10*x^18+59760*Y^10*x^17-46*Y^10*x^2-112057*Y^10*x^14+181996*Y^13*x^12-95826*Y^13*x^11-73049*Y^13*x^13-10683*Y^10*x^8-3882*Y^10*x^23-20843*Y^10*x^21+10357*Y^10*x^22+3*x^6*Y^20+15426*Y^17*x^20-30095*Y^17*x^19+45120*Y^17*x^18+26306*Y^17*x^17-442*Y^17*x^2+85731*Y^17*x^14+3*x*Y^10+3687*Y^18*x^16-8431*Y^18*x^15+2*Y^18*x^20-12569*Y^18*x^19-3676*Y^18*x^18+16174*Y^18*x^17+67*Y^18*x^2-17973*Y^18*x^14+Y^22*x^24-7380*Y^17*x^25-5*Y^17*x^30+13448*Y^17*x^10-1623*Y^17*x^5+1278*Y^17*x^6-33*Y^20*x^29+33*Y^20*x^26+21*Y^20*x^28+2*Y^20*x^27-68449*Y^15*x^18+111503*Y^15*x^17-1829*Y^15*x^2+81720*Y^15*x^14+24738*Y^7*x^10-308*Y^7*x^5+746*Y^7*x^6-161*Y^7*x^7-1087*Y^7*x^8+1535*Y^5*x^7-3563*Y^5*x^8-Y^5*x^23+164*Y^5*x^21-18*Y^5*x^22+994*Y^15*x^16-144413*Y^15*x^15-51823*Y^15*x^20+28167*Y^15*x^19-100450*Y^17*x^16+28177*Y^17*x^15-429*Y^15*x^4-16*Y^15*x^29-1215*Y^15*x^26-26*Y^15*x^28+244*Y^15*x^27+770*Y^21*x^16-291*Y^21*x^15-279*Y^21*x^20+218*Y^21*x^19+196*Y^21*x^18-701*Y^21*x^17-199*Y^21*x^14-4501*Y^20*x^16-1680*Y^20*x^15+2099*Y^20*x^20-1404*Y^20*x^19-2513*Y^20*x^18+40495*Y^7*x^12-45157*Y^7*x^11-9959*Y^7*x^13-4764*Y^7*x^9-3*Y^7*x^24+3507*Y^15*x^3+23100*Y^15*x^7-25460*Y^15*x^8-14120*Y^15*x^23+39991*Y^15*x^21+4193*Y^15*x^22+Y^18+35*Y^14+1050*Y^5*x^12+5677*Y^5*x^11-8623*Y^5*x^13+5672*Y^5*x^9-7075*Y^5*x^10+41*Y^5*x^5-376*Y^5*x^6-11*x^5*Y^4-x^4*Y^5;

f_41_5:=Y^8*X^8-2*Y^4*(3*Y^3+Y-1-2*Y^2)*X^7+(28*Y^5+Y^2-Y-21*Y^6+1-2*Y^3+8*Y^7-13*Y^4)*X^6+(-52*Y^5+49*Y^4+5*Y-3+16*Y^6-17*Y^3)*X^5+(48*Y^5-Y^2+36*Y^3-7*Y^6-70*Y^4+3-7*Y)*X^4+(Y-1)*(5*Y^5-28*Y^4+29*Y^3-6*Y^2-2*Y+1)*X^3+Y^2*(-5-25*Y^2+20*Y+11*Y^3)*X^2-3*Y^2*(Y-1)^3*X+Y^2*(Y-1)^3;				    	

Total degree=16;
Degree(f_41_5,X)=8;
Degree(f_41_5,Y)=8;
//==================================== X_H(43), H=<3^3>  ========================================

N_X:=y*(y-1)*x^3*(x-1)^2*(x-y)*(x-y+1)^2*(x^2*y - x*y + y - 1)^2*(x^4*y - 2*x^3*y^2 - x^3*y + x^2*y^3 + x^2*y^2 + 2*x^2*y - x^2 - 2*x*y^2 + x*y + y - 1)*(x^5*y^2 - 3*x^4*y^3 + 3*x^3*y^4 + 2*x^3*y^2 - 2*x^3*y - x^2*y^5 - x^2*y^4 - x^2*y^3 + x^2*y^2 + x^2*y + x*y^5 -x*y^4 + 2*x*y^3 - 2*x*y^2 - x*y + x - y^4 + 2*y^3 - y^2)*(x^5*y^2 - 3*x^4*y^3 - x^4*y^2 + 3*x^3*y^4 + 3*x^3*y^3 - x^2*y^5 - 3*x^2*y^4 - 2*x^2*y^2 + 3*x^2*y + x*y^5 + 3*x*y^3- 4*x*y^2 - y^4 + y^3 + y - 1)^3;
D_X:=(x*y - 1)*(x^2*y - x*y^2 + y - 1)^5*(x^2*y^2 - 2*x^2*y - x*y^3 + 2*x*y^2 - y + 1)*(x^5*y^2 - x^5*y - 2*x^4*y^3 + 2*x^4*y + x^3*y^4 + 3*x^3*y^3 - 4*x^3*y^2 + x^3 - 2*x^2*y^4 + x^2*y^3 + x^2*y^2 -x^2*y + x*y^4 - x*y^3 + x*y^2 - x*y - y^3 + 2*y^2 - y)^4;
X:=N_X/D_X;

N_Y:=(y-1)^4*x^6*(x^2*y - x*y + y - 1)^2*(x^2*y - x*y^2 - x*y + y^2 - 1)*(x^2*y - x^2 - x*y^2 + x*y - x + y - 1)*(x^3*y - x^2*y^2 - x^2*y + x*y^2 - y + 1)*(x^4*y - 3*x^3*y^2 + x^3*y + 2*x^2*y^3 + x^2*y^2 - 2*x^2*y - 2*x*y^3 + 2*x*y^2 + y^2 - 2*y + 1)*(x^4*y - x^3*y^3 - x^3*y + x^2*y^4 + x^2*y - x^2 - x*y^4 + x*y^3 - x*y^2 + x*y + y^3 - 2*y^2 + y)*(x^5*y^2 - 3*x^4*y^3 - x^4*y^2 + 3*x^3*y^4 + 3*x^3*y^3 - x^2*y^5 - 3*x^2*y^4 - 2*x^2*y^2 + 3*x^2*y + x*y^5 + 3*x*y^3- 4*x*y^2 - y^4 + y^3 + y - 1)^6;
D_Y:=y^2*(x-y)*(x - y + 1)^2*(x*y - 1)^2*(x^2*y - x*y^2 + y - 1)^6*(x^4*y - 2*x^3*y^2 - x^3*y + x^2*y^3 + x^2*y^2 + 2*x^2*y - x^2 - 2*x*y^2 + x*y + y - 1)*(x^5*y^2 - 3*x^4*y^3 + 3*x^3*y^4 + 2*x^3*y^2 - 2*x^3*y - x^2*y^5 - x^2*y^4 - x^2*y^3 + x^2*y^2 + x^2*y + x*y^5 -x*y^4 + 2*x*y^3 - 2*x*y^2 - x*y + x - y^4 + 2*y^3 - y^2)*(x^5*y^2 - x^5*y - 2*x^4*y^3 + 2*x^4*y + x^3*y^4 + 3*x^3*y^3 - 4*x^3*y^2 + x^3 - 2*x^2*y^4 + x^2*y^3 + x^2*y^2 -x^2*y + x*y^4 - x*y^3 + x*y^2 - x*y - y^3 + 2*y^2 - y)^6;
Y:=N_Y/D_Y;

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

f_43_3:=1+X^4*Y^10-3*X^4*(2*X+5)*Y^9+X^4*(48*X^2+92+111*X+2*X^3)*Y^8-X^3*(15*X^5+526*X^2+128*X^4+15+313*X^3+329*X)*Y^7+X^3*(15*X^6+X^7+92*X^5+128+1499*X^2+329*X^4+1011*X+1011*X^3)*Y^6-X^2*(1499*X^2+1499*X^3+526*X^4+313*X+2+111*X^5+6*X^6)*Y^5+X^2*(313*X^3+48*X^4+1011*X^2+526*X+48)*Y^4-X^2*(329*X+111+128*X^2+2*X^3)*Y^3+X*(15*X^2+6+92*X)*Y^2-15*X*Y;

Total degree=16;
Degree(f_43_3,X)=10;
Degree(f_43_3,Y)=10;
