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5.1.56 kbase
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Syntax: kbase (ideal_expression)kbase (module_expression)kbase (ideal_expression,int_expression)kbase (module_expression,int_expression)-
Type: the same as the input type of the first argument
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Purpose: with one argument: computes a vector space basis (consisting of monomials) of the quotient ring by the ideal, resp. of a free module by the module, in case it is finite dimensional and if the input is a standard basis with respect to the ring ordering. If the input is not a standard basis, the leading terms of the input are used and the result may have no meaning.
With two arguments: computes the part of a vector space basis of the respective quotient with degree of the monomials equal to the second argument. Here, the quotient does not need to be finite dimensional.-
Example: ring r=32003,(x,y,z),ds; ideal i=x2,y2,z; kbase(std(i)); → _[1]=xy → _[2]=y → _[3]=x → _[4]=1 i=x2,y3,xyz; // quotient not finite dimensional kbase(std(i),2); → _[1]=z2 → _[2]=yz → _[3]=xz → _[4]=y2 → _[5]=xy