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D.4.15.2 modSat

Procedure from library moddiq.lib (see moddiq_lib).

Usage:
modSat(I,J); I,J ideal

Return:
a standard basis of (I:J^\infty)

Note:
The procedure computes a standard basis of (I:J^\infty) (over the rational numbers) by using modular methods.

Example:
 
LIB "moddiq.lib";
ring r=0,x(1..6),dp;
ideal i=cyclic(6);
ideal j=-15*var(5)+16*var(6)^3-60*var(6)^2+225*var(6)-4,2*var(5)^2-7*var(5)+2*var(6)^2-7*var(6)+28,(4*var(6)-1)*var(5)-var(6)+4,4*var(1)+var(5)+var(6),4*var(2)+var(5)+var(6),4*var(3)+var(5)+var(6),4*var(4)+var(5)+var(6); 
modSat(i,modSat(i,j)[1])[1];
poly F     = x(1)^5+x(2)^5+(x(1)-x(2))^2*x(1)*x(2)*x(3);
ideal J    = jacob(F);
modSat(J,maxideal(1));
See also: modular; sat.


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