SimpleAlgebraSoftware

A lightweight algebra library for working with matrices, vectors and linear expressions.

Features

Matrices in $\mathbb{R}^{n \times m}$

• Solve linear systems
• Gauss elimination
• Matrix multiplication
• Calculate determinants with Laplace Expansion

Vectors in $\mathbb{R}^{n}$

• Basic operations (addition, scaling, …)
• Scalar product

Linear expressions

• Basic operations

Examples

Solve a linear system

import static structures.Matrix.*;

...

double[][] v = {
    {1, 1, 0, 0, 0, 0, 0, 1},
    {0, 1, 1, 0, 0, 0, 0, 2},
    {0, 0, 1, 1, 0, 0, 0, 3},
    {0, 0, 0, 1, 1, 1, 1, 4}
};

System.out.println(Arrays.toString(linearSolve(v)));

// Output ->
// [1.0*e + 1.0*f + 1.0*g - 2.0,
//  -1.0*e - 1.0*f - 1.0*g + 3.0,
//   1.0*e + 1.0*f + 1.0*g - 1.0,
//  -1.0*e - 1.0*f - 1.0*g + 4.0,
//   1.0*e, 1.0*f, 1.0*g]

double[][] u = {
    {3, 11, 10, 9000},
    {6,  2,  2, 5000},
    {150, 220, 120, 194000}
};

System.out.println(Arrays.toString(linearSolve(u)));

// Output -> [600.0, 200.0, 500.0]

Work with LinearExpression

LinearExpression e1 = new LinearExpression("-3*y + 5*x + 5");
LinearExpression e2 = new LinearExpression("1*x - 5*y - 20 +2*y");
LinearExpression e3 =  e1.add(e2);

System.out.println(e3);
//Output -> 6.0*x - 6.0*y - 15.0

System.out.println(e3.multiplyConstant(5));
//Output -> 30.0*x - 30.0*y - 75.0

Multiply matrices and calculate determinants

import static structures.Matrix.*;

...

double [][] c = {
    {2,1,3},
    {0,4,1},
    {5,2,6}
};

System.out.println(laplaceExpansion(c));
//Output -> -11.0

double[][] a = {{1,2,3},{4,5,6},{7,8,9}};
double[][] b = {{1,2},{4,5},{7,8}};

System.out.println(Arrays.deepToString(multiplyMatrix(a, b)));
//Output -> [[30.0, 36.0], [66.0, 81.0], [102.0, 126.0]]