#### D.8.3.11 sortandmap

Procedure from library `presolve.lib` (see presolve_lib).

Usage:
  sortandmap(id [,n1,p1,n2,p2...,o1,m1,o2,m2...]);
  id=poly/ideal/vector/module,
  p1,p2,...= polynomials (product of variables),
  n1,n2,...= integers,
  o1,o2,...= strings,
  m1,m2,...= integers
  (default: p1=product of all vars, n1=0, o1="dp",m1=0)
  the last pi (containing the remaining vars) may be omitted

Return:
  a ring R, in which a poly/ideal/vector/module IMAG is stored:
  - the ring R differs from the active basering only in the choice of monomial ordering and in the sorting of the variables.
  - IMAG is the image (under imap) of the input ideal/module id
  The new monomial ordering and sorting of vars is as follows:

        - each block of vars occurring in pi is sorted w.r.t. its complexity in id,
        - ni controls the sorting in i-th block (= vars occurring in pi):
          ni=0 (resp. ni!=0) means that least complex (resp. most complex) vars come
          first
        - oi and mi define the monomial ordering of the i-th block:
          if mi =0, oi=ordstr(i-th block)
          if mi!=0, the ordering of the i-th block itself is a blockordering,
            each subblock having ordstr=oi, such that vars of same complexity are
            in one block

  Note that only simple ordstrings oi are allowed: "lp","dp","Dp", "ls","ds","Ds".

Note:
  We define a variable x to be more complex than y (with respect to id) if val(x) > val(y) lexicographically, where val(x) denotes the valuation vector of x:
  consider id as list of polynomials in x with coefficients in the remaining variables. Then:
  val(x) = (maximal occurring power of x, # of all monomials in leading coefficient, # of all monomials in coefficient of next smaller power of x,...).

Example:

    LIB "presolve.lib";
    ring s = 32003,(x,y,z),dp;
    ideal i=x3+y2,xz+z2;
    def R_r=sortandmap(i);
    ==>
    ==> // 'sortandmap' created a ring, in which an object IMAG is stored.
    ==> // To access the object, type (if the name R was assigned to the return v\
       alue):
    ==>         setring R; IMAG;
    show(R_r);
    ==> // ring: (ZZ/32003),(x,y,z),(dp(3),C);
    ==> // minpoly = 0
    ==> // objects belonging to this ring:
    ==> // IMAG                           [0]  ideal, 2 generator(s)
    setring R_r; IMAG;
    ==> IMAG[1]=x3+y2
    ==> IMAG[2]=xz+z2
    kill R_r; setring s;
    def R_r=sortandmap(i,1,xy,0,z,0,"ds",0,"lp",0);
    ==>
    ==> // 'sortandmap' created a ring, in which an object IMAG is stored.
    ==> // To access the object, type (if the name R was assigned to the return v\
       alue):
    ==>         setring R; IMAG;
    show(R_r);
    ==> // ring: (ZZ/32003),(x,y,z),(ds(2),lp(1),C);
    ==> // minpoly = 0
    ==> // objects belonging to this ring:
    ==> // IMAG                           [0]  ideal, 2 generator(s)
    setring R_r; IMAG;
    ==> IMAG[1]=y2+x3
    ==> IMAG[2]=z2+xz
    kill R_r;

User manual for Singular version 4.4.1, 2025, generated by texi2html.