groebner_basis() algorithm
How to define the default algorithm in the function groebner_basis()?
I only found "If only a system is given - e.g. ‘magma’ - the default algorithm is chosen for that system."
How to define the default algorithm in the function groebner_basis()?
I only found "If only a system is given - e.g. ‘magma’ - the default algorithm is chosen for that system."
The method groebner_basis
for ideals in polynomial rings is documented at
http://doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/polynomial/multi_polynomial_ideal.html#sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal.groebner_basis.
This documentation can also be accessed by creating an ideal in a polynomial ring
sage: x, y = QQ['x, y'].gens()
sage: J = ideal(x^5 + y^4 - 1, x^3 + y^3 - 1)
and typing
sage: J.groebner_basis?
The method groebner_basis
takes an optional algorithm
argument.
Choices for this argument are
In other words, the algorithm is described by a string of the form '<system>:<command>'
where
<system>
can be one of singular
, libsingular
, toy
, macaulay2
, magma
,
ginv
, giac
and each system has one or more possible <command>
values.
The documentation says that "If only a system is given - e.g. ‘magma’ - the default algorithm is chosen for that system."
This means that
algorithm='magma'
will work as algorithm='magma:GroebnerBasis'
algorithm='singular'
will work as algorithm='singular:groebner'
algorithm='libsingular'
will work as algorithm='libsingular:groebner'
algorithm='macaulay2'
will work as algorithm='macaulay2:gb'
algorithm='toy'
will work as algorithm='toy:buchberger2'
algorithm='giac'
will work as algorithm='giac:gbasis'
One way to figure out which is the default algorithm for each system is to read the code
for the method groebner_basis
, which you can access by typing
sage: J.groebner_basis??
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Asked: 2016-10-31 05:36:46 +0100
Seen: 836 times
Last updated: Nov 04 '16