D.7.1.12 sortvars

Procedure from library presolve.lib (see presolve_lib).

Usage:

sortvars(id[,n1,p1,n2,p2,...]);
id=poly/ideal/vector/module,
p1,p2,...= polynomials (product of vars),
n1,n2,...=integers
(default: p1=product of all vars, n1=0)
the last pi (containing the remaining vars) may be omitted

Compute:

sort variables with respect to their complexity in id

Return:

list of two elements, an ideal and a list:

[1]: ideal, variables of basering sorted w.r.t their complexity in id ni controls the ordering in i-th block (= vars occurring in pi): ni=0 (resp.!=0) means that less (resp. more) complex vars come first [2]: a list with 4 entries for each pi: ideal ai : vars of pi in correct order, intvec vi: permutation vector describing the ordering in ai, intmat Mi: valuation matrix of ai, the columns of Mi being the valuation vectors of the vars in ai intvec wi: size of 1-st, 2-nd,... block of identical columns of Mi (vars with same valuation)

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=0,(x,y,z,w),dp;
ideal i = x3+y2+yw2,xz+z2,xyz-w2;
sortvars(i,0,xy,1,zw);
→ [1]:
→    _[1]=y
→    _[2]=x
→    _[3]=w
→    _[4]=z
→ [2]:
→    [1]:
→       _[1]=y
→       _[2]=x
→    [2]:
→       2,1
→    [3]:
→       2,3,
→       1,1,
→       2,0,
→       0,2 
→    [4]:
→       1,1
→    [5]:
→       _[1]=w
→       _[2]=z
→    [6]:
→       2,1
→    [7]:
→       2,2,
→       2,1,
→       0,2 
→    [8]:
→       1,1