### 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.

User manual for Singular version 4-0-3, 2016, generated by texi2html.