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 r-fold 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.