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7.3.10 kbase (plural)

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 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.

when called with two arguments: computes the part of a vector space basis of the respective quotient with degree (of monomials) equal to the second argument. Here, the quotient does not need to be finite dimensional.

Note:
in the non-commutative case, a ring modulo an ideal has a ring stucture if and only if the ideal is two-sided. kbase respects module-grading given by the isHomog attribute of input modules.
Example:
 
See ideal (plural); module (plural); vdim (plural).


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