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D.8.1.13 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, 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)
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- 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:
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