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5.1.79 mstd
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Syntax: mstd (ideal_expression)mstd (module_expression)-
Type: list
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Purpose: returns a list whose first entry is a standard basis for the ideal, resp. module. If the monomial ordering is global, then the second entry is both a generating set for the ideal, resp. module, and a subset of the standard basis. If, additionally, the input is homogeneous then the second entry is a minimal generating set for the ideal, resp. module.
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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