Top
Back: Local orderings
Forward: Matrix orderings
FastBack: Representation of mathematical objects
FastForward: Mathematical background
Up: Monomial orderings
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

B.2.5 Module orderings

SINGULAR offers also orderings on the set of "monomials" 572#572 in Loc 573#573 = Loc 574#574Loc 575#575, where 576#576 denote the canonical generators of Loc 573#573, the r-fold direct sum of Loc 551#551. (The function gen(i) yields 415#415).

We have two possibilities: either to give priority to the component of a vector in Loc 573#573or (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 551#551as above.

(<,C):
577#577 denotes the module ordering (giving priority to the coefficients):
         578#578 or ( 579#579 and 340#340).

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,<):
580#580 denotes the module ordering (giving priority to the component):
         581#581 or (582#582 and 544#544).

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):
583#583 denotes the module ordering (giving priority to the coefficients):
         578#578 or ( 579#579 and 584#584).

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,<):
585#585 denotes the module ordering (giving priority to the component):
         586#586 or (582#582 and 544#544).

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 333#333 in 573#573 with components 587#587 has the format 588#588(up to permutation) unless the ordering starts with c. In this case a vector is written as 589#589.In all cases SINGULAR can read input in both formats.


Top Back: Local orderings Forward: Matrix orderings FastBack: Representation of mathematical objects FastForward: Mathematical background Up: Monomial orderings Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 4.4.1, 2025, generated by texi2html.