
D.8.2.12 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 ith 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 1st, 2nd,... 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:
 LIB "presolve.lib";
ring s=0,(x,y,z,w),dp;
ideal i = x3+y2+yw2,xz+z2,xyzw2;
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

