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5.1.144 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
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See also:
fglm;
groebner;
slimgb;
std;
stdhilb.
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