Singular Manual: initial

| #### 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

User manual for Singular version 4-1-1p3, 2018, generated by texi2html.