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D.13.4.39 initial
Procedure from library tropical.lib (see tropical_lib).
- Usage:
- initial(f,w); f poly, w intvec or bigintmat
initial(I,w); I ideal, w intvec or bigintmat
- Assume:
- I reduced Groebner basis,
w in the maximal Groebner cone of I with respect to the current ordering
- Return:
- poly or ideal, the initial form of f or the 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
LIB "poly.lib";
==> // ** redefining bino (LIB "poly.lib";)
==> // ** redefining hilbPoly (LIB "poly.lib";)
==> // ** redefining hilbPoly (LIB "poly.lib";)
==> // ** redefining substitute (LIB "poly.lib";)
==> // ** redefining substitute (LIB "poly.lib";)
==> // ** redefining cyclic (LIB "poly.lib";)
==> // ** redefining cyclic (LIB "poly.lib";)
==> // ** redefining elemSymmPoly (LIB "poly.lib";)
==> // ** redefining elemSymmPoly (LIB "poly.lib";)
==> // ** redefining elemSymmId (LIB "poly.lib";)
==> // ** redefining elemSymmId (LIB "poly.lib";)
==> // ** redefining katsura (LIB "poly.lib";)
==> // ** redefining katsura (LIB "poly.lib";)
==> // ** redefining kat_var (LIB "poly.lib";)
==> // ** redefining kat_var (LIB "poly.lib";)
==> // ** redefining freerank (LIB "poly.lib";)
==> // ** redefining freerank (LIB "poly.lib";)
==> // ** redefining is_zero (LIB "poly.lib";)
==> // ** redefining is_zero (LIB "poly.lib";)
==> // ** redefining maxcoef (LIB "poly.lib";)
==> // ** redefining maxcoef (LIB "poly.lib";)
==> // ** redefining maxdeg (LIB "poly.lib";)
==> // ** redefining maxdeg (LIB "poly.lib";)
==> // ** redefining maxdeg1 (LIB "poly.lib";)
==> // ** redefining maxdeg1 (LIB "poly.lib";)
==> // ** redefining mindeg (LIB "poly.lib";)
==> // ** redefining mindeg (LIB "poly.lib";)
==> // ** redefining mindeg1 (LIB "poly.lib";)
==> // ** redefining mindeg1 (LIB "poly.lib";)
==> // ** redefining normalize (LIB "poly.lib";)
==> // ** redefining normalize (LIB "poly.lib";)
==> // ** redefining rad_con (LIB "poly.lib";)
==> // ** redefining rad_con (LIB "poly.lib";)
==> // ** redefining lcm (LIB "poly.lib";)
==> // ** redefining lcm (LIB "poly.lib";)
==> // ** redefining content (LIB "poly.lib";)
==> // ** redefining content (LIB "poly.lib";)
==> // ** redefining mod2id (LIB "poly.lib";)
==> // ** redefining mod2id (LIB "poly.lib";)
==> // ** redefining id2mod (LIB "poly.lib";)
==> // ** redefining id2mod (LIB "poly.lib";)
==> // ** redefining subrInterred (LIB "poly.lib";)
==> // ** redefining subrInterred (LIB "poly.lib";)
==> // ** redefining newtonDiag (LIB "poly.lib";)
==> // ** redefining newtonDiag (LIB "poly.lib";)
ring r = 0,(x,y,z),dp;
ideal I = cyclic(3);
intvec w = 1,1,1;
option(redSB);
ideal stdI = std(I);
stdI;
==> stdI[1]=x+y+z
==> stdI[2]=y2+yz+z2
==> stdI[3]=z3-1
ideal inI = initial(stdI,w);
inI;
==> inI[1]=x+y+z
==> inI[2]=y2+yz+z2
==> inI[3]=z3
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