Singular

D.8.2.12 sortvars

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 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 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 occuring power of x, # of all monomials in leading coefficient, # of all monomials in coefficient of next smaller power of x,...).

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