D.7.1.14 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 occurring in pi: ni=0 (resp.!=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 occurring in pi:

ni=0 (resp.!=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
       ringvariables are ordered with respect to their complexity in id
  [2]: list of intvecs, i-th 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 j-th column of M(i)
             is the valuation vector of j-th 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 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,a,b),dp;
ideal i=ax2+ay3-b2x,abz+by2;
valvars (i,0,xyz);
==> [1]:
==>    3,1,2,4,5
==> [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 

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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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