/*
* Redberry: symbolic tensor computations.
*
* Copyright (c) 2010-2015:
* Stanislav Poslavsky
* Bolotin Dmitriy
*
* This file is part of Redberry.
*
* Redberry is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* Redberry is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Redberry. If not, see {
/**
* Returns array that represents this permutation in one-line notation.
*
* @return array that represents this permutation in one-line notation
*/
int[] oneLine();
/**
* Returns immutable array that represents this permutation in one-line notation.
*
* @return immutable array that represents this permutation in one-line notation
*/
IntArray oneLineImmutable();
/**
* Returns an array of disjoint cycles that represent this permutation.
*
* @return array of disjoint cycles that represent this permutation
*/
int[][] cycles();
/**
* Returns image of specified point under the action of this permutation.
*
* @param i point
* @return image of specified point under the action of this permutation
*/
public int newIndexOf(int i);
// /**
// * Returns image of specified point under the action of this permutation.This method is same as
// * {@link #newIndexOf(int)}, but throws exception if specified point greater then the internal low-level array that
// * represents this permutation.
// *
// * @param i point
// * @return image of specified point under the action of this permutation
// * @throws java.lang.IndexOutOfBoundsException if {@code i > length()}
// */
// public int newIndexOfInternal(int i);
/**
* Returns image of specified point under the action of this permutation. This method is absolutely same as
* {@link #newIndexOf(int)} without any difference.
*
* @param i point
* @return image of specified point under the action of this permutation
*/
public int imageOf(int i);
/**
* Returns image of specified set of points under the action of this permutation.
*
* @param set set
* @return image of specified set under this permutation
*/
public int[] imageOf(int[] set);
/**
* Permutes array and returns the result.
*
* @param array array
* @return permuted array
*/
public int[] permute(int[] array);
/**
* Permutes array and returns the result.
*
* @param array array
* @return permuted array
*/
public char[] permute(char[] array);
/**
* Permutes array and returns the result.
*
* @param array array
* @return permuted array
*/
public T[] permute(T[] array);
/**
* Permutes list and returns the result.
*
* @param array array
* @return permuted array
*/
public List permute(List array);
/**
* Returns conjugation of specified element by this permutation, i.e. this^-1 * p * this
*
* @param p permutation
* @return conjugation of specified element by this permutation, i.e. this^-1 * p * this
* @throws InconsistentGeneratorsException if the result of composition is inconsistent symmetry (antisymmetry with odd
* parity of permutation)
*/
public Permutation conjugate(Permutation p);
/**
* Returns commutator of this and specified permutation, i.e. this^-1 * p^-1 * this * p.
*
* @param p permutation
* @return commutator of this and specified permutation, i.e. this^-1 * p^-1 * this * p
* @throws InconsistentGeneratorsException if the result of composition is inconsistent symmetry (antisymmetry with odd
* parity of permutation)
*/
public Permutation commutator(Permutation p);
/**
* Returns image of specified point under the action of inverse of this permutation.
*
* @param i point
* @return image of specified point under the action of inverse of this permutation
*/
public int newIndexOfUnderInverse(int i);
/**
* Returns true if this permutation is antisymmetry and false otherwise.
*
* @return true if this permutation is antisymmetry and false otherwise
*/
public boolean antisymmetry();
/**
* If this is antisymmetry, then converts this permutation to symmetry.
*
* @return same permutation with {@code false} antisymmetry
*/
public Permutation toSymmetry();
/**
* Changes sign (symmetry to antisymmetry and vice versa) of this permutation
*
* @return same permutation with changed sign
*/
public Permutation negate();
/**
* Returns the result of {@code this * other}. Applying the resulting permutation is equivalent to applying
* {@code other} after {@code this}.
*
* @param other other permutation
* @return the result of {@code this * other}
* @throws InconsistentGeneratorsException if the result of composition is inconsistent symmetry (antisymmetry with odd
* parity of permutation)
*/
public Permutation composition(Permutation other);
/**
* Returns the result of {@code this * a * b}. Applying the resulting permutation is equivalent to applying
* {@code b} after {@code a} after {@code this}.
*
* @param a other permutation
* @param b other permutation
* @return the result of {@code this * a * b}
* @throws InconsistentGeneratorsException if the result of composition is inconsistent symmetry (antisymmetry with odd
* permutation parity)
*/
public Permutation composition(Permutation a, Permutation b);
/**
* Returns the result of {@code this * a * b * c}. Applying the resulting permutation is equivalent to applying
* {@code c} after {@code b} after {@code a} after {@code this}.
*
* @param a other permutation
* @param b other permutation
* @param c other permutation
* @return the result of {@code this * a * b * c}
* @throws InconsistentGeneratorsException if the result of composition is inconsistent symmetry (antisymmetry with odd
* permutation parity)
*/
public Permutation composition(Permutation a, Permutation b, Permutation c);
/**
* Returns the result of {@code this * other.inverse()}. Applying the resulting permutation is equivalent
* to applying {@code other.inverse()} after {@code this}.
*
* @param other other permutation
* @return the result of {@code this * other.inverse()}
* @throws InconsistentGeneratorsException if the result of composition is inconsistent symmetry (antisymmetry with odd
* permutation parity)
*/
public Permutation compositionWithInverse(Permutation other);
/**
* Returns the inverse permutation of this.
*
* @return the inverse permutation of this
*/
public Permutation inverse();
/**
* Returns {@code true} if this represents identity permutation
*
* @return {@code true} if this is identity permutation
*/
public boolean isIdentity();
/**
* Returns the identity permutation with the degree of this permutation
*
* @return identity permutation with the degree of this permutation
*/
public Permutation getIdentity();
/**
* Calculates and returns the order of this permutation.
*
* @return order of this permutation
* @see Permutations#orderOfPermutation(int[])
*/
public BigInteger order();
/**
* Returns true if order of this permutation is odd and false otherwise.
*
* @return true if order of this permutation is odd and false otherwise
*/
public boolean orderIsOdd();
/**
* Returns a largest moved point plus one.
*
* @return largest moved point plus one
*/
public int degree();
/**
* Returns length of the underlying array (at low-level).
*
* @return length of the underlying array (at low-level)
*/
public int length();
/**
* Returns this raised to the specified exponent.
*
* @param exponent exponent
* @return this raised to the specified exponent
*/
public Permutation pow(int exponent);
/**
* Returns parity of this permutations.
*
* @return parity of this permutations
*/
public int parity();
/**
* Inserts identity action on the set [0, 1, ..., size - 1]; as result the degree of resulting permutation will be
* size + degree of this.
*
* @param size size of the set
*/
public Permutation moveRight(int size);
/**
* Returns lengths of cycles in disjoint cycle notation.
*
* @return lengths of cycles in disjoint cycle notation
*/
int[] lengthsOfCycles();
/**
* Returns a string representation of this permutation in one-line notation.
*
* @return a string representation of this permutation in one-line notation
*/
String toStringOneLine();
/**
* Returns a string representation of this permutation in disjoint cycles notation.
*
* @return a string representation of this permutation in disjoint cycles notation
*/
String toStringCycles();
}
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