MatrixModp

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Class MatrixModp

Object
  MatrixModp

All Implemented Interfaces:: Comparable, GroupElt

Direct Known Subclasses:: PMatrixModp

public class MatrixModp
extends Object
implements GroupElt, Comparable

Square matrices with byte entries modulo a rational prime p. All operations returning mod p values (entries of the matrix, entries of the inverse matrix, etc.) will return least positive residues. The constructors convert all matrix entries to their least positive residues. If p is negative, it's silently made positive.

It follows that this implementation requires 2 ≤ p ≤ 127. For example, if you try to set p to 131, it will be wrapped to -125, which will be rejected because its absolute value is not prime.

Operations on two MatrixModps will throw IllegalArgumentException if the degrees or the primes don't match.

Author:: Mark McConnell

Constructor Summary
`MatrixModp(byte[][] x, byte p)` Builds a matrix with entries taken from the square array x mod p.
`MatrixModp(int n, byte[] x, byte p)` Inspired by APL's `ravel` function ρ (rho), this constructor returns the n by n matrix whose entries, in row major order, come from `x`.

Method Summary
`boolean`	`commutesWith(GroupElt y)` Whether `this` and `y` commute.
`int`	`compareTo(Object o)` Compares matrices lexicographically, taking the entries as least positive residues mod p in row-major order; however, a matrix in Jordan canonical form always comes before one that's not.
`GroupElt`	`conjugate(GroupElt y)` Returns `y * this * y^(-1)`.
`GroupElt`	`conjugateYinvXY(GroupElt y)` Returns `y^(-1) * this * y`.
`byte`	`det()` Returns the determinant.
`static byte`	`det(byte[][] a, byte p)` Returns the determinant of `a` mod p.
`boolean`	`equals(Object o)` Tests for equality in the mathematical sense, not by `==`.
`byte`	`getEntry(int i, int j)` Returns the (i,j)-th entry.
`GroupElt`	`getIdentity()` Returns the identity element of the same class as `this`.
`int`	`getOrder(Group G)` Returns the order of this element.
`byte`	`getP()` Returns the prime p.
`int`	`getSize()` If this matrix is n-by-n, returns n.
`int`	`hashCode()` Must be consistent with `equals(java.lang.Object)`.
`GroupElt`	`inverse()` Returns the inverse element for `this`.
`boolean`	`isDiagonal()`
`boolean`	`isIdentity()` Tests whether this is the identity element among `GroupElt`s of its class.
`boolean`	`isJordanCanonical()` Whether `this` is in Jordan canonical form.
`boolean`	`isPermShaped()` Whether the matrix has exactly one non-zero entry in each row and in each column.
`boolean`	`isSignedPerm()` Whether the matrix has exactly one non-zero entry in each row and in each column, and each non-zero entry is either 1 or -1.
`boolean`	`isUnipotentUpperTriangular()` Whether the matrix is upper-triangular with 1's on the diagonal.
`boolean`	`isUpperTriangular()`
`static void`	`main(String[] args)` For testing.
`GroupElt`	`mult(GroupElt y)` Returns the product `this * y`.
`GroupElt`	`power(int i)` Returns the i-th power of this element.
`String`	`toString()` For example, prints a 2 by 2 matrix as `[a b; c d]`.

Methods inherited from class Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

MatrixModp

public MatrixModp(byte[][] x,
                  byte p)

Builds a matrix with entries taken from the square array x mod p. The array structure is cloned, so changes to x later won't affect what's here. Entries are converted to their least positive residues mod p. As the comment on the class explains, we're effectively requiring 2 ≤ p ≤ 127.
Throws:: IllegalArgumentException - If x is not square or p is not prime.

MatrixModp

public MatrixModp(int n,
                  byte[] x,
                  byte p)

Inspired by APL's ravel function ρ (rho), this constructor returns the n by n matrix whose entries, in row major order, come from x. If x is too short, we cycle through it from the beginning as often as necessary. x must have length at least 1. Entries are converted to their least positive residues mod p.

Method Detail

det

public byte det()

Returns the determinant.

det

public static byte det(byte[][] a,
                       byte p)

Returns the determinant of a mod p. Doesn't change a.