read desing:

# The desing_trailing procedure only desingularizes the trailing
# coefficient, which means that the degree of the trailing coefficient
# will be minimized.
# The desing_leading procedure does the same for the leading coefficient,
# and the desing_both procedure treats both coefficients.
# The output is the operator you multiply by. The desingularization is
# then the product of the output times the input.


lprint("Trailing coefficient, Example T-1:");
L := 4*(x-1)*(x-2)*(x-3)*tau^2-(x-3)*(5*x^3-12*x^2-3*x+2)*tau-4*x^2*(x-2);
Multiply_L_on_the_left_by := desing_trailing(L, [tau,x]);
DesingularizedOperator := mult(%, L, [tau,x]);


lprint("Trailing coefficient, Example T-2:");
L := (x-1)*(x-2)*(x-3)*tau^2+(x-3)*(3*x^2-3*x+1)*tau+(x-2)*x^2;
Multiply_L_on_the_left_by := desing_trailing(L, [tau,x]);
DesingularizedOperator := mult(%, L, [tau,x]);


lprint("Trailing coefficient, Example T-3:");
L := (x-2)*(x-1)^3*tau^2+(-2*x+2+x^3)*x*(x-2)*tau+2*x^3*(x-1);
Multiply_L_on_the_left_by := desing_trailing(L, [tau,x]);
DesingularizedOperator := mult(%, L, [tau,x]);


lprint("Leading coefficient, Example L-1:");
L := (1+16*x)^2*tau^2-(224+512*x)*tau-(x+1)*(17+16*x)^2;
Multiply_L_on_the_left_by := desing_leading(L, [tau,x]);
DesingularizedOperator := mult(%, L, [tau,x]);


lprint("Both coefficients, Example B-1:");
L := 4*(x-1)*(x-2)*(x-3)*tau^2-(x-3)*(5*x^3-12*x^2-3*x+2)*tau-4*x^2*(x-2);
Multiply_L_on_the_left_by := desing_both(L, [tau,x]);
DesingularizedOperator := mult(%, L, [tau,x]);