|
B.2.5 Module orderings
offers also orderings on the set of "monomials"
We have two possibilities: either to give priority to the component of a
vector in
or (which is the default in ) 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
as above.
- (<,C):
-
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)
|
- (C,<):
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)
|
- (<,c):
-
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)
|
- (c,<):
Example:
| ring r = 0, (x,y,z), (c,lp);
[x+y2,z3+xy];
==> [x+y2,xy+z3]
[x,x,x];
==> [x,x,x]
|
(up to permutation) unless the ordering starts with c .
In all cases can read input in both formats.
|