Substitution algorithms for rational matrix equations

Solution of matrix equations of the form r(X) = A, where r is a rational function and X and A are square matrices.

The three algorithms in this submission solve equations of the form r(X) = A, where r is a rational function and A and X are square matrices of the same size.

The function invrat_horn() implements [1, Algorithm 2] whereas invrat_pow() and invrat_ps() implement [2, Algorithm 3.1] and [2, Algorithm 3.2], respectively.

[1] M. Fasi and B. Iannazzo. Computing primary solutions of equations involving primary matrix functions. Linear Algebra Appl., 560:17–42, 2019.

[2] M. Fasi and B. Iannazzo. Substitution algorithms for rational matrix equations. MIMS EPrint 2019.8, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, May 2019.