PMatrixModp

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Class PMatrixModp

Object
  MatrixModp
      PMatrixModp

All Implemented Interfaces:: Comparable, GroupElt

Direct Known Subclasses:: PSLEltModp

public class PMatrixModp
extends MatrixModp

Square matrices modulo a byte p as in the superclass MatrixModp, but modulo scalar multiples of the identity. The underlying matrix is multiplied by a scalar so that the first non-zero entry in row-major order is 1.

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

All operations returning mod p values (matrix entries, det, 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.

Author:: Mark McConnell

Constructor Summary
`PMatrixModp(byte[][] x, byte p)` Constructor extending `MatrixModp.MatrixModp(byte[][], byte)`.
`PMatrixModp(int n, byte[] x, byte p)` Extends the "ρ" constructor `MatrixModp.MatrixModp(int, byte[], byte)`.
`PMatrixModp(MatrixModp x)` Projectivizes its argument.

Method Summary
`boolean`	`commutesWith(GroupElt y)` Whether `this` and `y` commute.
`GroupElt`	`conjugate(GroupElt y)` Returns `y * this * y^(-1)`.
`GroupElt`	`conjugateYinvXY(GroupElt y)` Returns `y^(-1) * this * y`.
`byte`	`det()` Return the determinant--but beware, the result is well-defined only up to n-th powers in the field.
`GroupElt`	`getIdentity()` Returns the identity element of the same class as `this`.
`GroupElt`	`inverse()` Returns the inverse element for `this`.
`boolean`	`isOrthogonal(byte d)` Whether this preserves the quadratic form `{1,1,d}` up to scalar multiples.
`GroupElt`	`mult(GroupElt y)` Returns the product `this * y`.
`protected void`	`projectivize(byte[][] a)` Overwrites its argument with a scalar multiple so that the first non-zero entry in row-major order is 1.

Methods inherited from class MatrixModp

compareTo, det, equals, getEntry, getOrder, getP, getSize, hashCode, isDiagonal, isIdentity, isJordanCanonical, isPermShaped, isSignedPerm, isUnipotentUpperTriangular, isUpperTriangular, main, power, toString

Methods inherited from class Object

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

Constructor Detail

PMatrixModp

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

Constructor extending

MatrixModp.MatrixModp(byte[][],
       byte)

PMatrixModp

public PMatrixModp(MatrixModp x)

Projectivizes its argument.

PMatrixModp

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

Extends the "ρ" constructor MatrixModp.MatrixModp(int, byte[], byte).

Method Detail

projectivize

protected void projectivize(byte[][] a)

Overwrites its argument with a scalar multiple so that the first non-zero entry in row-major order is 1. Assumes a is square and all entries are least positive residues; the result is in the same form.

isOrthogonal

public boolean isOrthogonal(byte d)

Whether this preserves the quadratic form {1,1,d} up to scalar multiples. If d is not zero mod p and p > 2, the group of all orthogonal matrices depends up to isomorphism only on whether d is a quadratic residue mod p.

det

public final byte det()

Return the determinant--but beware, the result is well-defined only up to n-th powers in the field.

Overrides:: det in class MatrixModp