
B.2.5 Module orderings
SINGULAR offers also orderings on the set of "monomials"
in Loc = Loc
Loc , where
denote the canonical
generators of Loc , the rfold direct sum of Loc .
(The function gen(i) yields ).
We have two possibilities: either to give priority to the component of a
vector in
Loc or (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 as above.
 (<,C):

denotes the module ordering (giving priority to the coefficients):
or (
and ).
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,<):
 denotes the module ordering (giving priority to the component):
or ( and
).
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):

denotes the module ordering (giving priority to the coefficients):
or (
and ).
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,<):
 denotes the module ordering (giving priority to the component):
or ( and
).
Example:
 ring r = 0, (x,y,z), (c,lp);
[x+y2,z3+xy];
==> [x+y2,xy+z3]
[x,x,x];
==> [x,x,x]

The output of a vector in with components
has the format
(up to permutation) unless the ordering starts with c .
In this case a vector is written as
.In all cases SINGULAR can read input in both formats.
