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5.1.46 groebner
Procedure from library standard.lib (see standard_lib).
- Syntax:
groebner ( ideal_expression )
groebner ( module_expression )
groebner ( ideal_expression, int_expression )
groebner ( module_expression, int_expression )
groebner ( ideal_expression, list of string_expressions
)
groebner ( ideal_expression, list of string_expressions
and int_expression )
groebner ( ideal_expression, int_expression )
- Type:
- type of the first argument
- Purpose:
- computes a standard basis of the first argument
I
(ideal or module) by a heuristically chosen method (default)
or by a method specified by further arguments of type string.
Possible methods are:
- the direct methods "std" or "slimgb" without
conversion,
- conversion methods "hilb" or "fglm" where
a Groebner basis is first computed with an "easy" ordering
and then converted to the ordering of the basering by the
Hilbert driven Groebner basis computation or by linear algebra.
The actual computation of the Groebner basis can be
specified by "std" or by "slimgb"
(not for all orderings implemented).
A further string "par2var" converts parameters to an extra
block of variables before a Groebner basis computation (and
afterwards back).
option(prot) informs about the chosen method.
- Note:
- If an additional argument, say
wait , of type int is given,
then the computation runs for at most wait seconds.
That is, if no result could be computed in wait seconds,
then the computation is interrupted, 0 is returned, a warning
message is displayed, and the global variable
Standard::groebner_error is defined.
This feature uses MP and hence it is available on UNIX platforms, only.
- Hint:
- Since there exists no uniform best method for computing standard
bases, and since the difference in performance of a method on
different examples can be huge, it is recommended to test, for hard
examples, first various methods on a simplified example (e.g. use
characteristic 32003 instead of 0 or substitute a subset of
parameters/variables by integers, etc.).
Example:
See also:
slimgb;
std;
stdfglm;
stdhilb.
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