# Questions tagged [polynomials]

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

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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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### Discrete Convolution or Polynomial Multiplication

Given two non empty lists of integers, your submission should calculate and return the discrete convolution of the two. Interestingly, if you consider the list elements as coefficients of polynomials, ...
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### Find real roots of a polynomial

Write a self-contained program which when given a polynomial and a bound will find all real roots of that polynomial to an absolute error not exceeding the bound. Constraints I know that Mathematica ...
953 views

### Factor a polynomial over a finite field or the integers

Without using any built-in factoring/polynomial functions, factor a polynomial completely into irreducibles over the integers or a finite field. Input Your program/function will receive some prime (or ...
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### Symbolic Differentiation of Polynomials

Symbolic Differentiation 1: Gone Coefishin' Task Write a program that takes in a polynomial in x from stdin (1 < deg(p) < 128) and differentiates it. The input polynomial will be a string of ...
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### Calculate the n-th iterate of a polynomial for a specific value; fⁿ(x)

Given a polynomial function f (e.g. as a list p of real coefficients in ascending or descending order), a non-negative integer n, and a real value x, return:    f n(x) i.e. the value of f (f (f (…f (x)...
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### Polynomialception

Given two polynomials f,g of arbitrary degree over the integers, your program/function should evaluate the first polynomial in the second polynomial. ...
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### Find Integral Roots of A Polynomial

Challenge The challenge is to write a program that takes the coefficients of any n-degree polynomial equation as input and returns the integral values of x for which the equation holds true. The ...
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### Computing a specific coefficient in a product of polynomials

Generator functions This gives the context for why this challenge came to life. Feel free to ignore. Generator functions are a nice way of encoding the solution to a problem of combinatorics. You ...
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### Shamir's Secret Sharing

Given n (the number of players), t (the threshold value), and s (the secret), output the <... 2k views

### Polynomial Long Division

Implement polynomial long division, an algorithm that divides two polynomials and gets the quotient and remainder: (12x^3 - 5x^2 + 3x - 1) / (x^2 - 5) = 12x - 5 R 63x - 26 In your programs, you will ...
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### Implement Shamir's Secret Sharing reconstruction

Shamir's secret sharing scheme is a simple way of protecting a secret by splitting it into several parts needed to reconstruct it. Your task is to implement Shamir's Secret Sharing reconstruction ...
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### Rational Polynomial Interpolation

Explanation In this task you'll be given a set of N points (x1,y1),…,(xN,yN) with distinct xi values and your task is to interpolate a polynomial through these points. If you know what Lagrange ...
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### Calculate Power Series Coefficients

Given a polynomial $p(x)$ with integral coefficients and a constant term of $p(0) = \pm 1$, and a non-negative integer $N$, return the $N$-th coefficient of the power series (sometimes called &...
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### Diamond Puzzles!

Explanation: Last year in math class, on homework we would occasionally get these extremely simple, although equally annoying questions called diamond puzzles. These were basically questions where we ...
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### Symbolic Integration of Polynomials

Apply an indefinite integral to a given string. The only rules you will be using are defined as such: ∫cx^(n)dx = (c/(n+1))x^(n+1) + C, n ≠ -1 c, C, and n are all constants. Specifications: You ...
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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 $(p∘q)(X) = p(q(X)) \equiv X \mod X^{n+1}$, ...
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### Polynomial Laplace transform

This is a repost of this challenge, intended to revamp it for looser I/O formats and updated rules You are to write a program which takes an integer polynomial in $t$ as input and outputs the ...
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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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### Fundamental Solution of the Pell Equation

Given some positive integer $n$ that is not a square, find the fundamental solution $(x,y)$ of the associated Pell equation $$x^2 - n\cdot y^2 = 1$$ Details The fundamental $(x,y)$ is a pair of ...
When learning to factorise quadratics in the form $x^2 + ax + b$, a common technique is to find two numbers, $p, q$ such that $$pq = b \\ p + q = a$$ as, for such numbers, $x^2 + ax + b = (x + p)(... 22 votes 8 answers 1k views ### Find the polynomial We know that f is a polynomial with non-negative integer coefficients. Given f(1) and f(1+f(1)) return f. You may output f as a list of coefficients, an ASCII formatted polynomial, or similar. ... 18 votes 19 answers 4k views ### Evaluate polynomial expression string Create a function which takes a polynomial equation, a value for x and returns the result of the operation. Example: given ... 15 votes 16 answers 898 views ### Euler-Poincaré-Characteristic of Polyhedra Given a triangulation of the surface of a polyhedron p, calculate its Euler-Poincaré-Characteristic χ(p) = V-E+F, where ... 14 votes 5 answers 941 views ### Algebraic curve plotter An algebraic curve is a certain "1D subset" of the "2D-plane" that can be described as set of zeros {(x,y) in R^2 : f(x,y)=0 }of a polynomial <... 12 votes 2 answers 418 views ### Decompose Polynomials Given an integral polynomial of degree strictly greater than one, completely decompose it into a composition of integral polynomials of degree strictly greater than one. Details An integral ... 12 votes 6 answers 526 views ### Is it a factor of a polynomial? A polynomial is divisible by a factor (x-n) if f(n)=0 for a function f. Your job: to ... 9 votes 8 answers 515 views ### Expand roots into a polynomial Challenge Given the roots of a polynomial separated by spaces as input, output the expanded form of the polynomial. For example, the input 1 2 represents this ... 9 votes 5 answers 553 views ### Computing a specific coefficient in a quotient of polynomials Context After "Computing a specific coefficient in a product of polynomials", asking you to compute a specific coefficient of polynomial multiplication, I wish to create a "mirror" challenge, asking ... 8 votes 2 answers 775 views ### Laplace transform of a polynomial [duplicate] Your goal is to write a program that will print out the Laplace transform of a polynomial function with integer coefficients$f(x)$. The Laplace transform of$f(x)$is defined as$\int_0^\infty f(... 