read(ratpar); f1 := y^5+2*x*y^2+2*x*y^3+x^2*y-4*x^3*y+2*x^5; # 17 seconds f2 := -1-4*y+5*y^2-3*y^3-3*y^4-5*x*y-10*x*y^2+x^2-10*x^2*y+2*x^2*y^2+3*x^3+ 4*x^3*y+5*x^4; # 18 seconds f3 := 25+1326*y*x+3740*x^3*y+3252*x^2*y+3582*y^3*x^2+4030*x^3*y^2+1476*x^2*y^4+102* y^6*x+546*y^5*x+1590*y^4*x+244*x+184*y+518*y^2+720*y^3+854*x^2+1338*x^3+576*y^4 +1101*x^4+282*y^5+14*y^7+y^8+84*y^6+4770*y^2*x^2+2706*y^3*x+2646*y^2*x+18*x^7+ 508*x^5+132*x^6+x^8+2264*x^4*y+2124*x^3*y^3+1716*x^4*y^2+738*y*x^5+354*y^2*x^5+ 570*x^4*y^3+550*x^3*y^4+122*y*x^6+28*y^6*x^2+318*x^2*y^5+8*y^7*x+56*y^3*x^5+56* y^5*x^3+70*y^4*x^4+28*y^2*x^6+8*y*x^7; # 198 seconds f4 := 36*x^2+9*y^2+36*x*y-34*x^3*y+3*x^4*y^2+12*y^3*x-7*x^2*y^2+3*y^4*x^2+x^6+6*y^4 +y^6-4*x^4; # 542 seconds f5 := y^7+6*y^6+27/4*x*y^6+33/4*y^5+48*x^2*y^5-1/3*x*y^5+106*x*y^4-8/3*y^4+6*x^2*y^ 4+10/3*x^3*y^4+31/9*x^2*y^3+128/3*y^3+16*x^3*y^3+19/2*x*y^3+6*x^4*y^3+27/4*x^3* y^2+4/9*x^4*y^2-8/9*x*y^2+40*x^5*y^2+26*x^2*y^2+9/4*x^2*y-5/9*x^3*y+3*x^5*y+96* x^4*y+16/9*x^6*y+9/2*x^4+54*x^3-8/3*x^6+x^7+22/9*x^5; # 679 seconds f6 := 3*x*y^4-y+12*x*y^5-2*y^5+6*x^2*y^3+6*x^2*y^5+4*x^3*y^3+4*x^3*y^2-2*x^2-6*y^3+ 3*y^6-2*y^4-4*y^2+6*y^7+4*y^8+3*x^2*y-5*y*x+12*y^6*x+y^2*x^2+y^3*x-y^2*x+x^4*y+ 4*y^7*x+12*x^2*y^4+x^3+y^9; # 810 seconds # The following curve is copied from page 6 in "Determining Simple Points on # Rational Algebraic Curves" from J. Rafael Sendra and Franz Winkler, RISC-Linz # Report Series No. 93-23. f7 := x3^5*x1*x2^4+x3^4*x1*x2^5+x3^5*x1^2*x2^3+x3^3*x1^5*x2^2-19*x3^3*x1^2*x2^5 -53*x3^3*x1^3*x2^4+x3^4*x1^5*x2+x1^5*x2^5+x3^5*x1^5+43*x3^4*x1^3*x2^3 +x3^3*x1^4*x2^3+12*x3^2*x1^4*x2^4+57*x3^2*x1^3*x2^5-19*x3^2*x1^5*x2^3 -36*x3*x1^4*x2^5+x3^5*x2^5+21*x3*x1^5*x2^4-15*x3^5*x1^3*x2^2; f7:=subs(x1=x,x2=y,x3=1,f7); # 1146 seconds tijd:=time(): for i from 1 to 7 do lprint(`-------- Example`,i,`-------------------`);lprint(); print(f.i); if type(degree(f.i,{x,y}),odd) then v.i:=ratpar(f.i,x,y,s,line) else v.i:=ratpar(f.i,x,y,s,t) fi; t.i:=time()-tijd; tijd:=time(); print(v.i); print(time=t.i); od: