Ask Your Question
0

Find polynomial with given residues modulo two other polynomials

asked 2021-12-12 11:24:49 +0100

Georgi gravatar image

updated 2021-12-14 16:59:03 +0100

slelievre gravatar image

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.

edit retag flag offensive close merge delete

Comments

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

vdelecroix gravatar imagevdelecroix ( 2021-12-12 18:02:07 +0100 )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 gravatar imagealvaro ( 2021-12-13 23:20:46 +0100 )edit

1 Answer

Sort by ยป oldest newest most voted
2

answered 2021-12-12 18:45:08 +0100

Max Alekseyev gravatar image

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.

edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

1 follower

Stats

Asked: 2021-12-12 11:24:49 +0100

Seen: 34 times

Last updated: Dec 14 '21