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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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