Questions tagged [polynomials]

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

Filter by
Sorted by
Tagged with
12
votes
5answers
1k views

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 ...
19
votes
14answers
2k views

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, ...
20
votes
1answer
896 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 ...
25
votes
1answer
1k views

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 ...
21
votes
12answers
2k views

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 ...
20
votes
25answers
1k views

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)...
17
votes
12answers
2k views

Shamir's Secret Sharing

Given n (the number of players), t (the threshold value), and s (the secret), output the <...
22
votes
12answers
2k views

Polynomialception

Given two polynomials f,g of arbitrary degree over the integers, your program/function should evaluate the first polynomial in the second polynomial. ...
11
votes
7answers
4k views

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 ...
15
votes
5answers
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 ...
24
votes
9answers
1k views

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 &...
20
votes
4answers
443 views

Locally invert a Polynomial

Challenge Given a polynomial p with real coefficients of order 1 and degree n, find another ...
12
votes
18answers
1k views

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 ...
7
votes
2answers
282 views

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 ...
29
votes
26answers
3k views

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 ...
19
votes
17answers
2k views

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 ...
18
votes
19answers
3k 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 ...
14
votes
5answers
810 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 <...
21
votes
8answers
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. ...
8
votes
2answers
599 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(...
15
votes
14answers
820 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 ...