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D.8.1.12 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 occuring in pi):
       ni=0 (resp. ni!=0) means that less (resp. more) complex vars come first
  [2]: a list with 4 entries for each pi:
       _[1]: ideal ai : vars of pi in correct order,
       _[2]: intvec vi: permutation vector describing the ordering in ai,
       _[3]: intmat Mi: valuation matrix of ai, the columns of Mi being the
                  valuation vectors of the vars in ai
       _[4]: 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 occuring power of x, # of all monomials in leading coefficient, # of all monomials in coefficient of next smaller power of x,...).

Example:
 


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