Hi Martin, Michael,
clearly that example was too quickly made up and is somewhat redundant
(due to 2 variables).
a(w_1, ..., w_n) is the elementary comparison wrt the scalar product
of an exponent with the vector (w_1, ..., w_n) (denoted by $>_
{(w_1, ..., w_n)}$). Any matrix ordering is exactly a block-ordering
comprising n weightings (wrt its row-vectors),
e.g. M(A, B, C, D) is exactly the same as (a(A,B), a(C,D)), lp(2) = M
(1,0,0,1) = (a(1,0), a(0,1)) etc.
I'd say that (>_w) is an elementary building block for any
TermOrdering.
my point was that comparison of module components may be done
somewhere between two term orderings.
Maybe the following example would be a bit better:
consider a free module over the Weyl algebra as K<x1, x2, Dx1, Dx2;
relations >^{r} wrt the ordering which compares 1st the degree in D-
exponents, 2nd module components, and at last whole exponents wrt dp:
(a(0,0,1,1), C, dp).
Regards,
Oleksandr
On Sep 9, 1:31 pm, Michael Brickenstein <[email protected]> wrote:
> Hi!
> It seems to me, that restricted to rings and ideals,
> the ordering looks like
> 2 5
> -1 -2
> So, the Matrix M(1,1,0,-1) is probably useless in this example.
>
> Michael
> Am 09.09.2009 um 12:56 schrieb Martin Albrecht:
>
>
>
> > Hi there,
>
> > I have to say that I don't like the
>
> > WeightVector(2,5) + ModuleOrder('c')
>
> > syntax. WeightVector is a modification of the following term order (in
> > Singular). It feels much more natural to me to simply do:
>
> > TermOrder('lex',weights=(2,5))
>
> > Also, I don't really understand what
>
> >> 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
>
> > does exactly. As far as I can see a(X,Y) modifies the following
> > ordering which
> > eventually is the Matrix odering (1,1,0,-1). What's the role of the
> > second
> > a(X,Y) in the example above?
>
> > 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: [email protected]
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