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how do I compute a polynomial pseudo-remainder in sage?

asked 2021-05-25 18:21:41 +0200

Tim02130 gravatar image

Most symbolic algebra systems provide a function, typically called "prem" or something like that, to compute the pseudo-remainder of two polynomials. Sage does provide other elementary functions for manipulating polynomials, e.g. "factor", but does not seem to provide this one. Perhaps something could be done by using the sage.rings.polynomial package, but that would be overkill for my immediate problem. Is there ANY way to do this simply?

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answered 2021-05-25 19:25:02 +0200

tmonteil gravatar image

Does the following satisfy your needs ?

sage: R.<x> = QQ[]
sage: R
Univariate Polynomial Ring in x over Rational Field
sage: P,Q = (1+x+x^2+x^3, 1+2*x^2)
sage: P.quo_rem(Q)
(1/2*x + 1/2, 1/2*x + 1/2)

To get the doc of the quo_rem method:

sage: P.quo_rem?
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Asked: 2021-05-25 18:21:41 +0200

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Last updated: May 25 '21