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5.1.137 std
Syntax:
std ( ideal_expression)
std ( module_expression)
std ( ideal_expression, intvec_expression )
std ( module_expression, intvec_expression )
std ( ideal_expression, intvec_expression, intvec_expression )
std ( module_expression, intvec_expression, intvec_expression )
std ( ideal_expression, poly_expression )
std ( module_expression, vector_expression )
std ( ideal_expression, ideal_expression )
std ( module_expression, module_expression )
std ( ideal_expression, poly_expression, intvec_expression, intvec_expression )
std ( module_expression, poly_expression, intvec_expression, intvec_expression )
Type:
- ideal or module
Purpose:
- returns a standard basis of an ideal or module with respect to the
monomial ordering of the basering.
A standard basis is a set of generators such that
the leading terms generate the leading ideal, resp. module.
Use an optional
second argument of type intvec as Hilbert series
(result of hilb(i,1) , see hilb),
if the ideal, resp. module, is homogeneous
(Hilbert driven standard basis computation, stdhilb).
If the ideal is quasihomogeneous with some weights w and if the Hilbert series
is computed w.r.t. to these weights, then use w as third argument.
Use an optional second argument of type poly/vector/ideal, resp. module,
to construct the standard basis from an already computed one (given as the
first argument) and additional generator(s) (the second argument).
4 arguments G,p,hv,w are the combination of the above:
standard basis G , additional generator p , hilbert function hv w.r.t. weights w .
Note:
- The
standard basis is computed with a (more or less) straight-forward
implementation of the classical
Buchberger (resp. Mora) algorithm. For global orderings, use the
groebner command instead (see groebner), which heuristically
chooses the "best" algorithm to compute a Groebner basis.
To view the progress of long running computations, use
option(prot) (see option(prot)).
Example:
See
facstd;
fglm;
groebner;
ideal;
mstd;
option;
ring;
stdfglm;
stdhilb.
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