# Questions tagged [polynomials]

For challenges involving polynomials, mathematical expressions that consist of variables and coefficients.

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### Sum of square roots (as an algebraic number)

An algebraic number is a number that is a root of a non-zero polynomial with integer coefficients. It is well-known that the sum of two algebraic numbers is algebraic. In particular, the sum of a list ...
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### Order of an algebraic number

Consider some arbitrary polynomial with integer coefficients, $$a_n x^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0 = 0$$ We'll assume that $a_n \ne 0$ and $a_0 \ne 0$. The solutions to this polynomial ...
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### Polynomial Interpolation

Write a program that performs Polynomial Interpolation using true arbitrary precision rational numbers. The input looks like this: f(1) = 2/3 f(2) = 4/5 f(3) = 6/7 ... You may assume that there's ...
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### Approximate a root of an odd degree polynomial

Every odd degree polynomial has at least one real root. However this root does not have to be a rational number so your task is to output a sequence of rational numbers that approximates it. Rules ...
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### Golfing Expressions

We can write mathematical expressions using the standard math operators (,),+,...
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### Partial Fractions

Given an input of a string, output the partial fraction in string form. The partial fraction decomposition of a rational fraction of the form $\frac{f(x)}{g(x)}$, where $f$ and $g$ are ...
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### Shortest Program to Solve a Quartic Equation

Write the shortest program to solve a quartic equation. A quartic equation is a polynomial equation of the form: $ax^4 + bx^3 + cx^2 + dx + e=0$ A solution for $x$ is a number such that the above ...
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### Locally invert a Polynomial

Challenge Given a polynomial $p$ with real coefficients of order $1$ and degree $n$, find another polynomial $q$ of degree at most $n$ such that $(p∘q)(X) = p(q(X)) \equiv X \mod X^{n+1}$, ...