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Let $f=ax^2+b$ be a polynomial in $Q[x]$, how to define $f$ in sage?

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sage: var('a b')
(a, b)
sage: R.<X> = QQ[]
sage: f = a * X * X + b
sage: f
X^2*a + b
sage: R 
Univariate Polynomial Ring in X over Rational Field

You can get more information about polynomials in this tutorial here.

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