Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Compute the Popov decomposition of a matrix of univariate polynomials
computes the Popov decomposition of the matrix mat consisting of univariate polynomials.
gives the Popov decomposition of the matrix mat regarded as univariate polynomials in the variable x.
Compute the Popov decomposition for a 3×3 matrix of quartic polynomials:
Check that the determinant is a constant:
Check that the necessary matrix identity is satisfied:
Check that the maximal degrees in each row move successively to the right:
Create a tool to generate a 3×3 matrix of quartic polynomials:
If the input matrix does not have full row rank, there will be zero rows at the bottom of the Popov form (as many as the row rank deficiency):
Generate a 3×3 matrix of quartic polynomials:
Compute the Popov decomposition over the integers modulo a prime:
Check the necessary matrix identity:
This work is licensed under a Creative Commons Attribution 4.0 International License