Find polynomial with given residues modulo two other polynomials

math

asked 2021-12-12 11:24:49 +0200

updated 2021-12-14 16:59:03 +0200

slelievre
17654 ●22 ●160 ●348 http://carva.org/samue...

Find a polynomial f(x) of degree 3, which when divided by x^2 - 4, gives a remainder 2x - 5, and divided by x^2 + x + 3 gives a remainder -5x - 9.

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Is your question related to SageMath? Do you know about the Chinese Remainder Theorem?

vdelecroix ( 2021-12-12 18:02:07 +0200 )edit

May i suggest a change in the title of the question? i think it should contain a fast description of the problem, like "find a polynomial, given some residues".

alvaro ( 2021-12-13 23:20:46 +0200 )edit

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answered 2021-12-12 18:45:08 +0200

Max Alekseyev

5701 ●5 ●36 ●122

One'd need to employ CRT here - for example:

R.<x> = PolynomialRing(QQ)
print( crt([2*x-5,-5*x-9],[x^2-4,x^2+x+3]) )

gives x^3 + x^2 - 2*x - 9.

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Asked: 2021-12-12 11:24:49 +0200

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Last updated: Dec 14 '21

Find polynomial with given residues modulo two other polynomials edit