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D.13.4.15 tInitialIdeal

Procedure from library tropical.lib (see tropical_lib).

Usage:
tInitialIdeal(i,w); i ideal, w intvec

Assume:
i is an ideal in Q[t,x_1,...,x_n] and w=(w_0,...,w_n)

Return:
ideal ini, the t-initial ideal of i with respect to w

Example:
 
LIB "tropical.lib";
==> Welcome to polymake version
==> Copyright (c) 1997-2015
==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt)
==> http://www.polymake.org
ring r=0,(t,x,y),dp;
ideal i=t2x-y+t3,t2x-y-2t3x;
intvec w=-1,2,0;
// the t-initial forms of the generators are
tInitialForm(i[1],w),tInitialForm(i[2],w);
==> x-y x-y
// and they do not generate the t-initial ideal of i
tInitialIdeal(i,w);
==> _[1]=-x+y
==> _[2]=2xy
==> _[3]=2x
==> _[4]=2xy2