### 5.1.152 stdfglm

Procedure from library `standard.lib` (see standard_lib).

Syntax:
  `stdfglm (` ideal_expression `)`
  `stdfglm (` ideal_expression`,` string_expression `)`

Type:
  ideal

Purpose:
  computes the standard basis of the ideal in the basering via `fglm` from the ordering given as the second argument to the ordering of the basering. If no second argument is given, "dp" is used. The standard basis for the given ordering (resp. for "dp") is computed via the command groebner except if a further argument "std" or "slimgb" is given in which case std resp. slimgb is used.

Example:

       ring r  = 0,(x,y,z),lp;
    ideal i = y3+x2,x2y+x2,x3-x2,z4-x2-y;
    stdfglm(i);                   //uses fglm from "dp" (with groebner) to "lp"
    ==> _[1]=z12
    ==> _[2]=yz4-z8
    ==> _[3]=y2+y-z8-z4
    ==> _[4]=xy-xz4-y+z4
    ==> _[5]=x2+y-z4
    stdfglm(i,"std");             //uses fglm from "dp" (with std) to "lp"
    ==> _[1]=z12
    ==> _[2]=yz4-z8
    ==> _[3]=y2+y-z8-z4
    ==> _[4]=xy-xz4-y+z4
    ==> _[5]=x2+y-z4
    ring s  = (0,x),(y,z,u,v),lp;
    minpoly = x2+1;
    ideal i = u5-v4,zv-u2,zu3-v3,z2u-v2,z3-uv,yv-zu,yu-z2,yz-v,y2-u,u-xy2;
    weight(i);
    ==> 2,3,4,5
    stdfglm(i,"(a(2,3,4,5),dp)"); //uses fglm from "(a(2,3,4,5),dp)" to "lp"
    ==> _[1]=v2
    ==> _[2]=u
    ==> _[3]=zv
    ==> _[4]=z2
    ==> _[5]=yv
    ==> _[6]=yz-v
    ==> _[7]=y2

See also: fglm; groebner; slimgb; std; stdhilb.

User manual for Singular version 4.4.1, 2025, generated by texi2html.