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B.2.5 Module orderings
SINGULAR offers also orderings on the set of "monomials"
570#570 in Loc 571#571 = Loc
572#572Loc 573#573, where
574#574 denote the canonical
generators of Loc 571#571, the r-fold direct sum of Loc 549#549.
(The function gen(i) yields 413#413).
We have two possibilities: either to give priority to the component of a
vector in
Loc 571#571or (which is the default in SINGULAR) to give priority
to the coefficients.
The orderings (<,c) and (<,C) give priority to the
coefficients; whereas
(c,<) and (C,<) give priority to the components.
Let < be any of the monomial orderings of
Loc 549#549as above.
- (<,C):
-
575#575 denotes the module ordering (giving priority to the coefficients):
576#576 or (
577#577 and 338#338).
Example:
| ring r = 0, (x,y,z), ds;
// the same as ring r = 0, (x,y,z), (ds, C);
[x+y2,z3+xy];
==> x*gen(1)+xy*gen(2)+y2*gen(1)+z3*gen(2)
[x,x,x];
==> x*gen(3)+x*gen(2)+x*gen(1)
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- (C,<):
- 578#578 denotes the module ordering (giving priority to the component):
579#579 or (580#580 and
542#542).
Example:
| ring r = 0, (x,y,z), (C,lp);
[x+y2,z3+xy];
==> xy*gen(2)+z3*gen(2)+x*gen(1)+y2*gen(1)
[x,x,x];
==> x*gen(3)+x*gen(2)+x*gen(1)
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- (<,c):
-
581#581 denotes the module ordering (giving priority to the coefficients):
576#576 or (
577#577 and 582#582).
Example:
| ring r = 0, (x,y,z), (lp,c);
[x+y2,z3+xy];
==> xy*gen(2)+x*gen(1)+y2*gen(1)+z3*gen(2)
[x,x,x];
==> x*gen(1)+x*gen(2)+x*gen(3)
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- (c,<):
- 583#583 denotes the module ordering (giving priority to the component):
584#584 or (580#580 and
542#542).
Example:
| ring r = 0, (x,y,z), (c,lp);
[x+y2,z3+xy];
==> [x+y2,xy+z3]
[x,x,x];
==> [x,x,x]
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The output of a vector 331#331 in 571#571 with components
585#585 has the format
586#586(up to permutation) unless the ordering starts with c .
In this case a vector is written as
587#587.In all cases SINGULAR can read input in both formats.
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