Polynomial: find the common factor

alexana
1 ●1 ●1 ●2

5251 ●3 ●44 ●116

Hello, assuming I have a polynomial like this:

sage: var('y, x')
(y, x)
sage: y = x^2 + 6*x^3 + 3*x^4

When I use collect_common_factors(), I get:

(3*x^2 + 6*x + 1)*x^2

Now, is there a way to know which are the common_factors collected?

In this case, I'm expecting this output:

x^2

Thank you everyone!

2 Answers

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Volker Braun
3301 ●11 ●30 ●75

If are dealing with polynomials only you should look into using polynomial rings.

sage: R.<x> = QQ[]
sage: y = x^2 + 6*x^3 + 3*x^4
sage: y.factor()
(3) * x^2 * (x^2 + 2*x + 1/3)
sage: list(_)
[(x, 2), (x^2 + 2*x + 1/3, 1)]

calc314
4191 ●22 ●48 ●113

I can't find a specific function to get the terms out of a polynomial, but here is some code that should do the job for a function just of x.

var('x,y')
y = 2*x^2 + x^3 + 10*x^4
info=y.coeffs()
terms=[a[0]*x^a[1] for a in info]
gcd(terms)

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