Find integer solutions to a set of equations with more unknowns than equations

Hans van der Laan :

I am trying to build a system for which I need to find a solution to a set of linear equations with (much) more variables than equations.

The problem boils down to the following:

Imagine a set of equations:

A = A1*X1 + A2*X2 + ... + AnXn
B = B1*X1 + B2*X2 + ... + BnXn

How can I find one or multiple (positive) integer solutions to this system?

Note: I have been looking at the apache-commons-math library but I couldn't find any directions on how to solve/find a solution of a system with free variables.

Alexis Benichoux :

Use the Lenstra–Lenstra–Lovász lattice basis reduction algorithm to find the Hermite normal form of your system.

It's straaightforward in matlab http://fr.mathworks.com/help/symbolic/mupad_ref/linalg-hermiteform.html

Check NTL for c++ http://www.shoup.net/ntl/index.html

Guess you like

Origin http://10.200.1.11:23101/article/api/json?id=450120&siteId=1

Find integer solutions to a set of equations with more unknowns than equations

Find solutions to quadratic equations in one variable

Title basic programming set positive integer 7-21 Solutions of special equations (15 minutes)

Determinant: Calculation of Unknowns in a System of Equations: Cramer's Rule

+ Ode solver solutions of differential equations

Minimum Norm Solutions of Underdetermined Equations

Linear equations AX=b, AX=0 and least squares solutions of nonlinear equations (solution equations -> optimization problems)

Numerical solution of nonlinear equations, optimization problems and numerical solutions of initial value problems of ordinary differential equations in MATLAB

[PubMed Mathematics] Linear Algebra Chapter 4 - Linear Equations (2, General Solutions of Linear Equations | Theoretical Extension)

Linear equations

write equations

Solving equations and differential equations—MATLAB

(Solutions of equations + XOR problem switches Gaussian elimination) poj1222

Several solutions to quadratic equations of one variable are implemented using python code

More than 2019 cattle off summer school camp (ninth field) B: Quadratic equation (linear equations quadratic residue requirements under mod sense)

B - How Many Equations Can You Find dfs

Newton's iterative method to find approximate roots of equations

HDU-2266（How Many Equations Can You Find）

An array a of n integer elements, find the elements that appear more than n / 2

python calculation by multiple equations or nonlinear equations

Absolute value equations, inequalities

Gaussian elimination of linear equations

Seeking nonlinear equations python

NOIp 2014 solving equations

Various formulations of Maxwell equations

normal equation (normal equations)

Insert LaTeX equations and matrices

What is the normal equations

solution of linear equations matlab

Method elliptical differential equations