matrixzq

Functions to carry out operations on matrices over Zq (Z/qZ) in pure Python without using Numpy or Scipy.

All matrix elements are expected to be nonnegative integers in the range [0, q-1]. All computations are carried out modulo q, where q is an integer greater than 1.

The modulus q is stored as a global variable __Q. It must be set using the set_modulus() function before calling functions that set or carry out arithmetic operations (add, multiply, etc.) on the matrix elements.

If the modulus q is not a prime then any operation that involves division (invert, solve) is undefined.

Documentation

Read the documentation

We have provided basic Python functions rather than a more-complicated class so you can easily extract and work with the underlying list of lists.

History

• v1.2.0 (2026-10-07)

  • Fixed problem in invert when leading element is zero
  • Fixed determinant for 1x1 matrix
  • Added stricter check that input to new_matrix is properly rectangular
  • Added method new_matrix_from_string

• v1.1.1 (2024-10-11)

  • Fixed error in determinant method when adding prior total to a 2 x 2 matrix.

• v1.1.0 (2024-02-13)

  • Added new functions sprint_matrix and sprint_vector to print directly to strings.
  • Added roundfrac2int to round a fraction to an integer without using float operations.
  • Change name of test module from matrixzq_t.py to test_matrixzq.py to work better with pytest.

Acknowledgements

This code was inspired by and some parts are derived from LinearAlgebraPurePython.py by Thom Ives
https://github.com/ThomIves/BasicLinearAlgebraToolsPurePy
https://integratedmlai.com/basic-linear-algebra-tools-in-pure-python-without-numpy-or-scipy/

David Ireland
https://di-mgt.com.au/contact/
This document last updated 2026-10-07