example lift over Q(t): bad perfomance / hung machine

[seelisch]

This was a forum entry from September 22, 2008; no problem for Magma but bad perf. in SINGULAR resp. hung machine:

ring R = (0,t), (w,x,y,z), dp; poly f = w^{3 + x}3 + y^{3 + z}3 + t*((w+x)*(w+2*y)*(w+3*z) + 3*x*y*(w+x+z)); ideal jac = jacob(f); print(lift(jac, x^4));

[seelisch]

Magma V2.16-11 gives normal form (plus coefficients for GB elements to arrive at this normal form) immediately:

Q<s> := PolynomialRing?(Rationals()); F<t> := FieldOfFractions?(Q);

R := PolynomialRing?(F, 4, "grevlex"); AssignNames?(~R, ["w", "x", "y", "z"]); w := R.1; x := R.2; y := R.3; z := R.4;

f := w^{3 + x}3 + y^{3 + z}3 + t*((w+x)*(w+2*y)*(w+3*z) + 3*x*y*(w+x+z)); jac := JacobianIdeal?(f); j := GroebnerBasis?(jac);

n, C := NormalForm?(x^{4, j);}

n; C;

[hannes]

see # 154