MatrixPower

Compute-engine's own MatrixPower, widened to accept a ModularMatrix or a word in place of an ordinary matrix.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageMatrixPower!↗

MatrixPower(m, k)$m$ raised to the integer power $k$, in $\mathrm{PSL}(2,\mathbb{Z})$

Typed signatures

Type	Package	Applies
(matrix, real) -> matrix	compute-engine	always
(expression<ModularMatrix> | matrix | real | string, real) -> expression<ModularMatrix> | matrix | real	modularreplaces compute-engine	always

Domain: Compute engine

Examples

Basic #

An ordinary matrix is compute-engine's: the Fibonacci matrix to the tenth

live ↗

In$\mathrm{MatrixPower}(\bigl\lbrack\bigl\lbrack1, 1\bigr\rbrack, \bigl\lbrack1, 0\bigr\rbrack\bigr\rbrack, 10)$Out$\bigl\lbrack\bigl\lbrack89, 55\bigr\rbrack, \bigl\lbrack55, 34\bigr\rbrack\bigr\rbrack$

A word in $L$ and $R$, squared in $\mathrm{PSL}(2,\mathbb{Z})$

live ↗

In$\mathrm{MatrixPower}(\text{LR}, 2)$Out$\mathrm{ModularMatrix}(2, 3, 3, 5)$

Scope #

A modular matrix cubed

live ↗

In$\mathrm{MatrixPower}(\mathrm{ModularMatrix}(1, 1, 0, 1), 3)$Out$\mathrm{ModularMatrix}(1, 3, 0, 1)$

A negative power is a power of the inverse

live ↗

In$\mathrm{MatrixPower}(\mathrm{ModularMatrix}(1, 1, 0, 1), -3)$Out$\mathrm{ModularMatrix}(1, -3, 0, 1)$

About

Examples	4
Checked against	Wolfram Language 1 agree1 differSageMath 1 agree1 error
Crosswalk	Wolfram Language

Implementation

mappedsagepackages/oracle/src/mappings.ts

See also: ModularMatrix