D.7.1.11 sortandmap

Procedure from library presolve.lib (see presolve_lib).

Usage:

sortandmap(id,s1,s2[,n1,p1,n2,p2...,o1,m1,o2,m2...]);
id=poly/ideal/vector/module,
s1,s2 = strings (names for new ring and mapped id),
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

Create:

a new ring and map id into it, the new ring has same char as basering but with new ordering and vars sorted in the following manner:

- 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.!=0) means that less (resp. more) 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".

Return:

nothing

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;
sortandmap(i,"R_r","i");
// i is now an ideal in the new basering R_r
show(R_r);
→ // ring: (32003),(y,z,x),(dp(3),C);
→ // minpoly = 0
→ // objects belonging to this ring:
→ // i                    [0]  ideal, 2 generator(s)
kill R_r; setring s;
sortandmap(i,"R_r","i",1,xy,0,z,0,"ds",0,"lp",0);
show(R_r);
→ // ring: (32003),(x,y,z),(ds(2),lp(1),C);
→ // minpoly = 0
→ // objects belonging to this ring:
→ // i                    [0]  ideal, 2 generator(s)
kill R_r;