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5.1.97 mstd
Syntax:
mstd ( ideal_expression )
mstd ( module_expression )
Type:
- list
Purpose:
- returns a list whose first entry is a standard basis for the ideal, resp.
module, whose second entry is a generating set for the
ideal, resp. module.
If the coefficient ring is a field and either the ideal/module is homogeneous or
the ordering is local, this second entry is a minimal generating set.
Example:
| ring r=0,(x,y,z,t),dp;
poly f=x3+y4+z6+xyz;
ideal j=jacob(f),f;
j=homog(j,t);j;
==> j[1]=3x2+yz
==> j[2]=4y3+xzt
==> j[3]=6z5+xyt3
==> j[4]=0
==> j[5]=z6+y4t2+x3t3+xyzt3
mstd(j);
==> [1]:
==> _[1]=3x2+yz
==> _[2]=4y3+xzt
==> _[3]=6z5+xyt3
==> _[4]=xyzt3
==> _[5]=y2z2t3
==> _[6]=yz3t4
==> _[7]=xz3t4
==> _[8]=yz2t7
==> _[9]=xz2t7
==> _[10]=y2zt7
==> _[11]=xy2t7
==> [2]:
==> _[1]=3x2+yz
==> _[2]=4y3+xzt
==> _[3]=6z5+xyt3
==> _[4]=xyzt3
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See
ideal;
minbase;
module;
std.
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