org.uacalc.alg.op

Class Operations

java.lang.Object

org.uacalc.alg.op.Operations

public class Operations
extends java.lang.Object

This is a factory class with static methods to make Operations.

Method Summary

Modifier and Type	Method and Description
static void	binaryOpToCSV(java.lang.String desc, Operation binop, java.io.PrintStream out)
static boolean	commutes(int[] map, Operation op0, Operation op1) Test if map defines a homomorphism wrt these operations.
static boolean	commutes(Operation unaryOp, Operation op) This tests if an operation commutes with a unary operation.
static boolean	equalValues(Operation op0, Operation op1) Test if these have the same int values on the common sized set.
static int[]	findDifference(Operation op0, Operation op1)
static int[]	findDifference(Operation op0, Operation op1, ProgressReport report) Find an argument where these operations differ.
static boolean	isAssociative(Operation op) Test if an operation is binary and associative.
static boolean	isCommutative(Operation op) Test if an operation is binary and commutative.
static boolean	isIdempotent(Operation op) Test if an operation is idempotent.
static boolean	isMaltsev(Operation op) Check if a ternary operation is a Maltsev operation.
static boolean	isTotal(Operation op)
static boolean	isTotallySymmetric(Operation op) Test if an operation is totally symmetric; that is, invariant under all permutation of the variables.
static void	main(java.lang.String[] args)
static Operation	makeBinaryIntOperation(OperationSymbol symbol, int algSize, int[][] table)
static Operation	makeBinaryLeftShift(int vecSize, int rootSize) This maps a pair of vectors (x,y) to (y_{k-1},x_0, ..., x_{k-2}); see McKenzie's finite forbidden lattices.
static Operation	makeCompositionOp(int n, int pow)
static Operation	makeConstantIntOperation(int algSize, int elt)
static Operation	makeConstantIntOperation(java.lang.String symbolPrefix, int algSize, int elt)
static java.util.List<Operation>	makeConstantIntOperations(int algSize)
static Operation	makeDerivedOperation(Operation op, int[] reductionArray, int newArity) The operation derived by equating variables.
static Operation	makeFullCycle(int algSize)
static Operation	makeIntOperation(Operation opx) This makes a new operation that agrees with the original but is table based and so faster.
static Operation	makeIntOperation(OperationSymbol symbol, int algSize, int[] valueTable) Construct an Operation from a valueTable.
static Operation	makeIntOperation(java.lang.String symbol, int arity, int algSize, int[] valueTable) Construct an Operation from a valueTable.
static java.util.List<Operation>	makeIntOperations(java.util.List<Operation> ops)
static java.util.List<Operation>	makeJonssonOperationsFromNUF(Operation nuf) Make the Jonsson terms from a near unanimity operation, omitting the two projections.
static Operation	makeLeftShift(int vecSize, int rootSize) The unary operation that cyclically shifts a vector left.
static java.util.Map<OperationSymbol,Operation>	makeMap(java.util.List<Operation> ops) This makes a hash map from the operation symbols to the operations.
static Operation	makeMatrixDiagonalOp(int vecSize, int rootSize)
static Operation	makeModuleOperation(int modulus, int[] coeffs)
static Operation	makeOperationFromScript(OperationSymbol symbol, int arity, int algSize, java.lang.String[] script) The script should be the body of the definition of intValueAt(int[] args).
static Operation	makeRandomOperation(int n, OperationSymbol opSym) Make an operation with the the given opeation symbol and set size.
static Operation	makeRandomOperation(int n, OperationSymbol opSym, java.util.Random random) Make an operation with the the given opeation symbol and set size.
static java.util.List<Operation>	makeRandomOperations(int n, SimilarityType simType) Make a list of operations corresponding to a similarity type and a set size.
static java.util.List<Operation>	makeRandomOperations(int n, SimilarityType simType, long seed) Make a list of operations corresponding to a similarity type and a set size.
static Operation	makeTransposition(int algSize, int a0, int a1) Make a unary operation interchanging a0 and a1.
static int	power(int base, int pow)
static Operation	ternaryDiscriminator(int size)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

commutes

public static boolean commutes(Operation unaryOp,
                               Operation op)

This tests if an operation commutes with a unary operation. It can be used to test if an operation is a endomorphism (or automorphism).

commutes

public static boolean commutes(int[] map,
                               Operation op0,
                               Operation op1)

Test if map defines a homomorphism wrt these operations. The operations must have the same arity.

Parameters:

map - an array defining the map

op0 - the first operation

op1 - the second operation

Returns:

true or false

isTotal

public static boolean isTotal(Operation op)

isIdempotent

public static final boolean isIdempotent(Operation op)

Test if an operation is idempotent.

isCommutative

public static final boolean isCommutative(Operation op)

Test if an operation is binary and commutative.

isTotallySymmetric

public static final boolean isTotallySymmetric(Operation op)

Test if an operation is totally symmetric; that is, invariant under all permutation of the variables.

isAssociative

public static final boolean isAssociative(Operation op)

Test if an operation is binary and associative.

isMaltsev

public static final boolean isMaltsev(Operation op)

Check if a ternary operation is a Maltsev operation.

Parameters:

op -

Returns:

findDifference

public static final int[] findDifference(Operation op0,
                                         Operation op1)

findDifference

public static final int[] findDifference(Operation op0,
                                         Operation op1,
                                         ProgressReport report)

Find an argument where these operations differ.

Parameters:

op0 -

op1 -

Returns:

an int[] as a witness or null if they agree.

Throws:

java.lang.IllegalArgumentException - if the arities or set sizes differ.

makeMap

public static java.util.Map<OperationSymbol,Operation> makeMap(java.util.List<Operation> ops)

This makes a hash map from the operation symbols to the operations.

equalValues

public static boolean equalValues(Operation op0,
                                  Operation op1)

Test if these have the same int values on the common sized set. So they are equal except they may have different symbos

ternaryDiscriminator

public static Operation ternaryDiscriminator(int size)

makeRandomOperation

public static Operation makeRandomOperation(int n,
                                            OperationSymbol opSym)

Make an operation with the the given opeation symbol and set size.

Parameters:

n - the set size

opSym - the operation symbol

Returns:

the operation

makeRandomOperation

public static Operation makeRandomOperation(int n,
                                            OperationSymbol opSym,
                                            java.util.Random random)

Make an operation with the the given opeation symbol and set size.

Parameters:

n - the set size

opSym - the operation symbol

random - a random number generator.

Returns:

the operation

makeRandomOperations

public static java.util.List<Operation> makeRandomOperations(int n,
                                                             SimilarityType simType)

Make a list of operations corresponding to a similarity type and a set size.

Parameters:

n - the set size

simType - the similarity type

Returns:

a list of operations

makeRandomOperations

public static java.util.List<Operation> makeRandomOperations(int n,
                                                             SimilarityType simType,
                                                             long seed)

Make a list of operations corresponding to a similarity type and a set size.

Parameters:

n - the set size

simType - the similarity type

seed - a random seed or -1

Returns:

a list of operations

makeDerivedOperation

public static Operation makeDerivedOperation(Operation op,
                                             int[] reductionArray,
                                             int newArity)

The operation derived by equating variables. If f(x,y,z) is an operation and [1, 0, 1] is the reductionArray, then the derived operation is g(x,y) = f(y,x,y).

Parameters:

reductionArray - an int array that can be viewed as a map from the int less than the arity of op into the arity of the derived operation.

makeJonssonOperationsFromNUF

public static java.util.List<Operation> makeJonssonOperationsFromNUF(Operation nuf)

Make the Jonsson terms from a near unanimity operation, omitting the two projections. See the file nuf.pdf.

power

public static final int power(int base,
                              int pow)

makeLeftShift

public static Operation makeLeftShift(int vecSize,
                                      int rootSize)

The unary operation that cyclically shifts a vector left.

makeBinaryLeftShift

public static Operation makeBinaryLeftShift(int vecSize,
                                            int rootSize)

This maps a pair of vectors (x,y) to (y_{k-1},x_0, ..., x_{k-2}); see McKenzie's finite forbidden lattices.

makeMatrixDiagonalOp

public static Operation makeMatrixDiagonalOp(int vecSize,
                                             int rootSize)

makeModuleOperation

public static Operation makeModuleOperation(int modulus,
                                            int[] coeffs)

makeCompositionOp

public static Operation makeCompositionOp(int n,
                                          int pow)

makeOperationFromScript

public static Operation makeOperationFromScript(OperationSymbol symbol,
                                                int arity,
                                                int algSize,
                                                java.lang.String[] script)
                                         throws javax.script.ScriptException

The script should be the body of the definition of intValueAt(int[] args).

Throws:

javax.script.ScriptException

makeIntOperations

public static java.util.List<Operation> makeIntOperations(java.util.List<Operation> ops)

makeIntOperation

public static Operation makeIntOperation(Operation opx)

This makes a new operation that agrees with the original but is table based and so faster.

Parameters:

opx - the original operation

Returns:

the new operation

makeIntOperation

public static Operation makeIntOperation(java.lang.String symbol,
                                         int arity,
                                         int algSize,
                                         int[] valueTable)

Construct an Operation from a valueTable.

Parameters:

valueTable - a Horner encode table of the values of the operation.

makeIntOperation

public static Operation makeIntOperation(OperationSymbol symbol,
                                         int algSize,
                                         int[] valueTable)

Construct an Operation from a valueTable.

Parameters:

valueTable - a Horner encode table of the values of the operation.

makeBinaryIntOperation

public static Operation makeBinaryIntOperation(OperationSymbol symbol,
                                               int algSize,
                                               int[][] table)

makeConstantIntOperation

public static Operation makeConstantIntOperation(int algSize,
                                                 int elt)

makeTransposition

public static Operation makeTransposition(int algSize,
                                          int a0,
                                          int a1)

Make a unary operation interchanging a0 and a1.

Parameters:

algSize -

a0 -

a1 -

Returns:

makeFullCycle

public static Operation makeFullCycle(int algSize)

makeConstantIntOperation

public static Operation makeConstantIntOperation(java.lang.String symbolPrefix,
                                                 int algSize,
                                                 int elt)

makeConstantIntOperations

public static java.util.List<Operation> makeConstantIntOperations(int algSize)

binaryOpToCSV

public static void binaryOpToCSV(java.lang.String desc,
                                 Operation binop,
                                 java.io.PrintStream out)

main

public static void main(java.lang.String[] args)
                 throws java.lang.Exception

Throws:

java.lang.Exception