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3.8 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:

computes the vector space basis of the factor-module that equals ring (resp. free module) modulo the ideal (resp. submodule), generated by the initial terms of the given generators.
If the factor-module is not of finite dimension, -1 is returned. If the generators form a Groebner basis, this is the same as the vector space basis of the factor-module.

Note:
you have the ring structure on the ring modulo the ideal if and only if the ideal is two-sided.

Example:
 
  ring r=0,(x,y,z),dp;
  matrix d[3][3];
  d[1,2]=-z;
  d[1,3]=2x;
  d[2,3]=-2y;
  ncalgebra(1,d);
  ideal i=x2,y2,z2-1;
  i=std(i);
  i;
==> i[1]=z2-1
==> i[2]=yz-y
==> i[3]=xz+x
==> i[4]=y2
==> i[5]=2xy-z-1
==> i[6]=x2
  kbase(i);
==> _[1]=z
==> _[2]=y
==> _[3]=x
==> _[4]=1
  vdim(i);
==> 4
  ideal j=x,z-1;
  j=std(j);
  kbase(j,3);
==> _[1]=y3
See ideal; module; vdim.


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