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# How to compute such resultant?

I need to compute such resultant: $f(x)&space;=&space;{Res}_y&space;({A}_1&space;(y),&space;{C}_0&space;(x)&space;+&space;y{C}_1&space;(x))$ Where ${A}_1,&space;{C}_0,&space;{C}_1&space;$ - polynomials over Z.

How can i do this in sage?

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## 1 Answer

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Setup:

R.<x> = PolynomialRing(ZZ)
A1 = R.random_element(degree=2)
C0 = R.random_element(degree=2)
C1 = R.random_element(degree=2)
S.<y> = PolynomialRing(R)


Execution:

sage: A1(y).resultant(C0 + y*C1)
x^4 - 6*x^3 + 5*x^2 - 4*x + 2

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## Comments

Thanks, I tried to set a polynomials over another fields, especially C1, and face with data type problem, would it be correct to use change_ring to bring everything into the same form?

( 2022-09-26 22:59:15 +0100 )edit

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Asked: 2022-09-26 19:00:28 +0100

Seen: 195 times

Last updated: Sep 26 '22