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 <brickenst...@mfo.de> 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: martinralbre...@jabber.ccc.de --~--~---------~--~----~------------~-------~--~----~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---