- Invariant Pair: Function to compute simple invariant pairs inside a contour (inside a circle).*
- Solvent: Function to compute solvents inside a contour (inside a circle).*
- Condition number for an invariant pair: Function to compute a condition number for an invariant pair using its contour integral definition.*
- Condition number for a solvent: Function to compute a condition number for a solvent using its the contour integral definition.*
- Number of eigenvalues inside a circle: Function to compute the number of eigenvalues of a matrix polynomial, inside of a given contour (inside a circle).*

- Condition number for an invariant pair: Function to compute a condition number for an invariant pair using its contour integral definition.
- Condition number for a solvent: Function to compute a condition number for a solvent using its contour integral definition.
- Invariant Pair: Function to compute simple invariant pairs inside a contour (inside a circle).
- Invariant Pair Circles: Function to compute simple invariant pairs inside a contour (inside a circle).
- Solvent: Function to compute solvents inside a contour (inside a circle).
- Number of eigenvalues inside a circle: Function to compute the number of eigenvalues of a matrix polynomial, inside of a given contour (inside a circle).
- Newton's Method to approximate Invariant Pairs: Function to approximate an Invariant Pair using Newton's method. We use the contour integral definition in the special case when the contour is a circle.
- Newton's Method with line search to approximate Invariant Pairs: Function to approximate an Invariant Pair using Newton's method and incorporating line search technique to improve convergence. We use the contour integral definition in the special case when the contour is a circle.
- Newton's Method with line search and Samanskii to approximate Invariant Pairs: Function to approximate an Invariant Pair using Newton's method and incorporating line search and Samanskii techniques to improve convergence. We use the contour integral definition in the special case when the contour is a circle.