square-free factorization function
multivariate polynomial or rational function
name or list or set of names
The sqrfree function computes the square-free factorization of the multivariate polynomial or the rational function a in the variable(s) x over an algebraic number field.
The square-free factorization is returned in the form u,f1,e1,...,fn,en such that a=u⁢f1e1⁢⋯⁢fnen where fi is primitive and square-free, that is, gcd⁡fi,∂∂xfi=1 for all i and gcd⁡fi,fj=1 for all i≠j hence u is the content(a,x) times a unit.
In the case of two arguments, the second argument x denotes the main variable(s). In the case of one argument, all the names in the polynomial a are used as variables.
Note that the ei are not necessarily distinct as partial factorizations in the input are preserved as much as possible.
f ≔ x3⁢y−x3−x2⁢y2+x2⁢y
g ≔ x+y+1⁢expand⁡x+y+12⁢x−y−33⁢3⁢x+6⁢y−21
h ≔ x+y3expand⁡x2−y22⁢x2+1
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