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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.


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