#### D.8.3.12 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. 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 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]=x
    ==>    _[2]=y
    ==>    _[3]=z
    ==>    _[4]=w
    ==> [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

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