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5.1.58 kbase

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
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
See ideal; module; vdim.

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