Hi Simon,
Thanks for the explanation! Everything seems to work fine now.
I gave a positive review on trac for the added features, perhaps
someone else could do a technical review of the patch.
Best,
Anne
On 3/26/11 11:11 PM, Simon King wrote:
Hi Anne,
On 27 Mrz., 00:39, Anne Schilling<a...@math.ucdavis.edu> wrote:
Hi Simon,
I am not sure this is the smallest example, but I get some error messages when
playing with the quotients:
sage: n=3
sage: F = FreeAlgebra(ZZ,n,'x',implementation='letterplace')
That's the other restriction (besides homegeneity): The letterplace
Gröbnerbase computation works with fields. So, sadly, ZZ is not
possible, but it should work with QQ.
This is documented in Singular at
http://www.singular.uni-kl.de/Manual/3-1-0/sing_425.htm
(All algebras are assumed to be associative $K$-algebras for some
field $K$.) and in my code as well, namely in the doc string of
LetterplaceIdeal ("In the two-sided case over a field, one can compute
Groebner bases ..."), and later on it gives an exammple:
Also, it is currently not possible to compute a Groebner basis
when
the base ring is not a field:
sage: FZ.<a,b,c> = FreeAlgebra(ZZ,
implementation='letterplace')
sage: J = FZ*[a^3-b^3]*FZ
sage: J.groebner_basis(2)
Traceback (most recent call last):
...
RuntimeError: Error in Singular function call 'system':
system(...) failed
I don't know whether that restriction can be lifted, and *if* it is,
whether the Singular team is working on it.
I guess, what I should do is to test at the beginning of the
groebner_basis method whether we have a field, and give a clear error
message. Also I should mention that restriction in the doc string of
the groebner_basis method.
Best regards,
Simon
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