|
5.1.24 eliminate
Syntax:
eliminate ( ideal_expression, product_of_ring_variables )
eliminate ( module_expression, product_of_ring_variables )
eliminate ( ideal_expression, intvec_expression )
eliminate ( module_expression, intvec_expression )
eliminate ( ideal_expression, product_of_ring_variables, intvec_hilb )
eliminate ( module_expression, product_of_ring_variables, intvec_hilb )
Type:
- the same as the type of the first argument
Purpose:
- eliminates variables occurring as factors/entries of the second argument from an
ideal (resp. a submodule of a free module), by intersecting it
(resp. each component of the submodule) with the subring not containing these variables.
eliminate does not need a special ordering nor a standard basis as input.
Note:
- Since elimination is expensive, for homogeneous input it might be useful
first to compute the Hilbert function of the ideal (first
argument) with a fast ordering (e.g.,
dp ). Then make use of it to speed
up the computation: a Hilbert-driven elimination uses the intvec
provided as the third argument.
If the ideal (resp. module) is not homogeneous with weights 1,
this intvec will be silently ignored.
Example:
See
hilb;
ideal;
module;
std.
|