
D.8.2.13 valvars
Procedure from library presolve.lib (see presolve_lib).
 Usage:
 valvars(id[,n1,p1,n2,p2,...]);
id=poly/ideal/vector/module,
p1,p2,...= polynomials (product of vars),
n1,n2,...= integers,
ni controls the ordering of vars occuring in pi: ni=0 (resp. ni!=0)
means that less (resp. more) complex vars come first (default: p1=product of all vars, n1=0),
the last pi (containing the remaining vars) may be omitted
 Compute:
 valuation (complexity) of variables with respect to id.
ni controls the ordering of vars occuring in pi:
ni=0 (resp. ni!=0) means that less (resp. more) complex vars come first.
 Return:
 list with 3 entries:
 [1]: intvec, say v, describing the permutation such that the permuted
ring variables are ordered with respect to their complexity in id
[2]: list of intvecs, ith intvec, say v(i) describing permutation
of vars in a(i) such that v=v(1),v(2),...
[3]: list of ideals and intmat's, say a(i) and M(i), where
a(i): factors of pi,
M(i): valuation matrix of a(i), such that the jth column of M(i)
is the valuation vector of jth generator of a(i)

 Note:
 Use
sortvars in order to actually sort the variables!
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,a,b),dp;
ideal i=ax2+ay3b2x,abz+by2;
valvars (i,0,xyz);
==> [1]:
==> 1,2,3,4,5
==> [2]:
==> [1]:
==> 3,1,2
==> [2]:
==> 1,2
==> [3]:
==> [1]:
==> _[1]=x
==> _[2]=y
==> _[3]=z
==> [2]:
==> 2,3,1,
==> 1,1,1,
==> 1,1,0
==> [3]:
==> _[1]=a
==> _[2]=b
==> [4]:
==> 1,2,
==> 3,1,
==> 0,2

