Hi Martin,
What about Sage implementation for
1. weighting vector(s) "a(w1, w2...wn)",
2. free module orderings (e.g. c/C) mixed somewhere in between? Does
Sage have such a concept?
In Sage i'd imagine something like:
{{{
TermOrder = WeightVector(2,5) + ModuleOrder('c') + WeightVector(-1,-2)
+ MatrixOrder(1,1,0,-1)
}}}
corresponding to:
{{{
> ring R =0,(x, y), (a(2,5), c, a(-1,-2), M(1,1,0,-1)); R;
// characteristic : 0
// number of vars : 2
// block 1 : ordering a
// : names x y
// : weights 2 5
// block 2 : ordering c
// block 3 : ordering a
// : names x y
// : weights -1 -2
// block 4 : ordering M
// : names x y
// : weights 1 1
// : weights 0 -1
> deg(x); // note that the 1st "a"/"M"/weighted ordering is used for "deg"
2
> deg(y);
5
}}}
Best regards,
Oleksandr
On Sep 4, 1:33 pm, Martin Albrecht <m...@informatik.uni-bremen.de>
wrote:
> > Currently, the ordering of a ring is determined by a string "name":
> > TermOrder.__init__(self, name='lex', n = 0, blocks=True)
> > respectively "order": PolynomialRing(base_ring, arg1=None, arg2=None,
> > sparse=False, order='degrevlex', names=None, name=None,
> > implementation=None)
> > Of course, it seems natural to define a matrix ordering by passing a
> > matrix:
> > sage: M = Matrix(2,2, [1,3,1,0])
> > sage: R.<x,y> = PolynomialRing(QQ,2,order=M)
>
> > But it is perhaps not so nice to break compatibility with the current
> > way of defining an ordering by strings.
>
> > Closer to Singular syntax would be
> > sage: R.<x,y> = PolynomialRing(QQ,2,order='M(1,3,1,0)')
>
> Think this would be rather un-pythonic: converting an object into a string
> instead of using it directly.
>
> > But what about block orderings? If one allows a matrix ordering to be
> > defined by a matrix, then I guess the blocks should be listed:
> > sage: P.<a,b,c,d,e> = PolynomialRing(QQ,5,order=[M,'degrevlex'])
>
> Have you seen this?
>
> sage: TermOrder('deglex',3) + TermOrder('degrevlex',2)
> deglex(3),degrevlex(2) term order
>
> > Or, if one goes with strings:
> > sage: P.<a,b,c,d,e> = PolynomialRing(QQ,5,order='M(1,3,1,0),degrevlex
> > (3)'])
>
> I would like to avoid this string business as much as possible. I find it
> rather ugly (that's personal taste of course)
>
> Cheers,
> Martin
>
> --
> name: Martin Albrecht
> _pgp:http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99
> _otr: 47F43D1A 5D68C36F 468BAEBA 640E8856 D7951CCF
> _www:http://www.informatik.uni-bremen.de/~malb
> _jab: martinralbre...@jabber.ccc.de
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