Re: question on recovering numerical factors from rational polynomials

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Fri, Feb 27, 2026 at 09:21:52AM -0800, American Citizen wrote:
> K=(25*x^2 + 100*y*x + 100*y^2)/(49*x^2 - 98*y*x + 49*y^2)
> ? factor(K)
> %9 =
> [  x - y -2]
> 
> [x + 2*y  2]
> 
> why isn't this
> 
> [       5  2]
> 
> [       7 -2]
> 
> [ x-y    -2]
> 
> [x+2y   2]
> 
> using content on the rational poly can sometimes lead to problems if a
> variable is in common with the terms.
> 
> how do I recover the rational number (5/7)^2 ?

Probably the most robust way if you are going to factor K anyway is 

K=(25*x^2 + 100*y*x + 100*y^2)/(49*x^2 - 98*y*x + 49*y^2)
? F=factor(K)
%17 = [x-y,-2;x+2*y,2]
? simplify(K/factorback(F))
%19 = 25/49

Cheers,
Bill.