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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
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See
ideal;
module;
vdim.
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