5.1.56 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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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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