org.matheclipse.core.polynomials

Class ExprTermOrder

java.lang.Object

org.matheclipse.core.polynomials.ExprTermOrder

All Implemented Interfaces:

java.io.Serializable

public final class ExprTermOrder
extends java.lang.Object
implements java.io.Serializable

Term order class for ordered polynomials. Implements the most used term orders: graded, lexicographical, weight aray and block orders. For the definitions see for example the articles Kredel, "Admissible term orderings used in computer algebra systems" and Sit, "Some comments on term-ordering in Gröbner basis computations". Note: the naming is not quite easy to understand: in case of doubt use the term orders with "I" in the name, like IGRLEX (the default) or INVLEX. Not all algorithms may work with all term orders since not all are well-founded, so watch your step. This class does not implement orders by linear forms over Q[t]. Objects of this class are immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	ExprTermOrder.EVComparator Comparator for ExpVectors.

Field Summary

Fields

Modifier and Type	Field and Description
static int	DEFAULT_EVORD
static int	GRLEX
static int	IGRLEX
static int	INVLEX
static int	ITDEGLEX
static int	LEX
static int	MAX_EVORD
static int	MIN_EVORD
static int	REVILEX
static int	REVITDEG
static int	REVITDG
static int	REVLEX
static int	REVTDEG

Constructor Summary

Constructors

Constructor and Description
ExprTermOrder() Constructor for default term order.
ExprTermOrder(int evord) Constructor for given term order.
ExprTermOrder(int ev1, int ev2, int r, int split) Constructor for given split order.
ExprTermOrder(long[] w) Constructor for given exponent weights.
ExprTermOrder(long[][] w) Constructor for given exponent weights.

Method Summary

Modifier and Type	Method and Description
ExprTermOrder	blockOrder(int s) Create block term order at split index.
ExprTermOrder	blockOrder(int s, ExprTermOrder t) Create block term order at split index.
ExprTermOrder	blockOrder(int s, ExprTermOrder t, int len) Create block term order at split index.
ExprTermOrder	blockOrder(int s, int len) Create block term order at split index.
ExprTermOrder	contract(int k, int len) Contract variables.
boolean	equals(java.lang.Object B) Comparison with any other object.
ExprTermOrder	extend(int r, int k) Extend variables.
ExprTermOrder	extendLower(int r, int k) Extend lower variables.
ExprTermOrder.EVComparator	getAscendComparator() Get the ascending order comparator.
ExprTermOrder.EVComparator	getDescendComparator() Get the descending order comparator.
int	getEvord() Get the first defined order indicator.
int	getEvord2() Get the second defined order indicator.
int	getSplit() Get the split index.
ExprTermOrder.EVComparator	getSugarComparator() Get the sugar order comparator.
long[][]	getWeight() Get the weight array.
int	hashCode() Hash code.
static long[]	longArrayPermutation(java.util.List<java.lang.Integer> P, long[] a) Permutation of a long array.
ExprTermOrder	permutation(java.util.List<java.lang.Integer> P) Permutation of the termorder.
ExprTermOrder	reverse() Reverse variables.
ExprTermOrder	reverse(boolean partial) Reverse variables.
static ExprTermOrder	reverseWeight(long[][] w) Weight ExprTermOrder with reversed weight vectors.
static int	revert(int evord) Revert exponent order.
java.lang.String	toScript() String representation of ExprTermOrder.
java.lang.String	toScriptOrder(int ev) Script and String representation of ExprTermOrder name.
java.lang.String	toScriptPlain() Script representation of ExprTermOrder without prefix and weight matrix.
java.lang.String	toString() String representation of ExprTermOrder.
java.lang.String	toStringPlain() String representation of ExprTermOrder without prefix and weight matrix.
java.lang.String	weightToScript() Script representation of weight matrix.
java.lang.String	weightToString() String representation of weight matrix.

Methods inherited from class java.lang.Object

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

Field Detail

LEX

public static final int LEX

See Also:

Constant Field Values

MIN_EVORD

public static final int MIN_EVORD

See Also:

Constant Field Values

INVLEX

public static final int INVLEX

See Also:

Constant Field Values

GRLEX

public static final int GRLEX

See Also:

Constant Field Values

IGRLEX

public static final int IGRLEX

See Also:

Constant Field Values

REVLEX

public static final int REVLEX

See Also:

Constant Field Values

REVILEX

public static final int REVILEX

See Also:

Constant Field Values

REVTDEG

public static final int REVTDEG

See Also:

Constant Field Values

REVITDG

public static final int REVITDG

See Also:

Constant Field Values

ITDEGLEX

public static final int ITDEGLEX

See Also:

Constant Field Values

REVITDEG

public static final int REVITDEG

See Also:

Constant Field Values

MAX_EVORD

public static final int MAX_EVORD

See Also:

Constant Field Values

DEFAULT_EVORD

public static final int DEFAULT_EVORD

See Also:

Constant Field Values

Constructor Detail

ExprTermOrder

public ExprTermOrder()

Constructor for default term order.

ExprTermOrder

public ExprTermOrder(int evord)

Constructor for given term order.

Parameters:

evord - requested term order indicator / enumerator.

ExprTermOrder

public ExprTermOrder(long[] w)

Constructor for given exponent weights.

Parameters:

w - weight vector of longs.

ExprTermOrder

public ExprTermOrder(long[][] w)

Constructor for given exponent weights.

Parameters:

w - weight array of longs.

ExprTermOrder

public ExprTermOrder(int ev1,
                     int ev2,
                     int r,
                     int split)

Constructor for given split order.

Parameters:

ev1 - requested term order indicator for first block.

ev2 - requested term order indicator for second block.

r - max number of exponents to compare.

split - index.

Method Detail

blockOrder

public ExprTermOrder blockOrder(int s)

Create block term order at split index.

Parameters:

s - split index.

Returns:

block ExprTermOrder with split index.

blockOrder

public ExprTermOrder blockOrder(int s,
                                int len)

Create block term order at split index.

Parameters:

s - split index.

len - length of ExpVectors to compare

Returns:

block ExprTermOrder with split index.

blockOrder

public ExprTermOrder blockOrder(int s,
                                ExprTermOrder t)

Create block term order at split index.

Parameters:

s - split index.

t - second term order.

Returns:

block ExprTermOrder with split index.

blockOrder

public ExprTermOrder blockOrder(int s,
                                ExprTermOrder t,
                                int len)

Create block term order at split index.

Parameters:

s - split index.

t - second term order.

len - length of ExpVectors to compare

Returns:

block ExprTermOrder with split index.

getEvord

public int getEvord()

Get the first defined order indicator.

Returns:

evord.

getEvord2

public int getEvord2()

Get the second defined order indicator.

Returns:

evord2.

getSplit

public int getSplit()

Get the split index.

Returns:

split.

getWeight

public long[][] getWeight()

Get the weight array.

Returns:

weight.

getDescendComparator

public ExprTermOrder.EVComparator getDescendComparator()

Get the descending order comparator. Sorts the highest terms first.

Returns:

horder.

getAscendComparator

public ExprTermOrder.EVComparator getAscendComparator()

Get the ascending order comparator. Sorts the lowest terms first.

Returns:

lorder.

getSugarComparator

public ExprTermOrder.EVComparator getSugarComparator()

Get the sugar order comparator. Sorts the graded lowest terms first.

Returns:

sugar.

equals

public boolean equals(java.lang.Object B)

Comparison with any other object.

Overrides:

equals in class java.lang.Object

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code.

Overrides:

hashCode in class java.lang.Object

See Also:

Object.hashCode()

weightToString

public java.lang.String weightToString()

String representation of weight matrix.

Returns:

string representation of weight matrix.

weightToScript

public java.lang.String weightToScript()

Script representation of weight matrix.

Returns:

script representation of weight matrix.

toScript

public java.lang.String toScript()

String representation of ExprTermOrder.

Returns:

script representation of ExprTermOrder.

toString

public java.lang.String toString()

String representation of ExprTermOrder.

Overrides:

toString in class java.lang.Object

See Also:

Object.toString()

toStringPlain

public java.lang.String toStringPlain()

String representation of ExprTermOrder without prefix and weight matrix.

toScriptPlain

public java.lang.String toScriptPlain()

Script representation of ExprTermOrder without prefix and weight matrix.

toScriptOrder

public java.lang.String toScriptOrder(int ev)

Script and String representation of ExprTermOrder name.

extend

public ExprTermOrder extend(int r,
                            int k)

Extend variables. Used e.g. in module embedding. Extend ExprTermOrder by k elements. Note: todo distinguish TOP and POT orders.

Parameters:

r - current number of variables.

k - number of variables to extend.

Returns:

extended ExprTermOrder.

extendLower

public ExprTermOrder extendLower(int r,
                                 int k)

Extend lower variables. Extend ExprTermOrder by k elements. Note: todo distinguish TOP and POT orders.

Parameters:

r - current number of variables.

k - number of variables to extend.

Returns:

extended ExprTermOrder.

contract

public ExprTermOrder contract(int k,
                              int len)

Contract variables. Used e.g. in module embedding. Contract ExprTermOrder to non split status.

Parameters:

k - position of first element to be copied.

len - new length.

Returns:

contracted ExprTermOrder.

reverse

public ExprTermOrder reverse()

Reverse variables. Used e.g. in opposite rings.

Returns:

ExprTermOrder for reversed variables.

reverse

public ExprTermOrder reverse(boolean partial)

Reverse variables. Used e.g. in opposite rings.

Parameters:

partial - true for partialy reversed term orders.

Returns:

ExprTermOrder for reversed variables.

revert

public static int revert(int evord)

Revert exponent order. Used e.g. in opposite rings.

Parameters:

evord - exponent order to be reverted.

Returns:

reverted exponent order.

longArrayPermutation

public static long[] longArrayPermutation(java.util.List<java.lang.Integer> P,
                                          long[] a)

Permutation of a long array.

Parameters:

a - array of long.

P - permutation.

Returns:

P(a).

permutation

public ExprTermOrder permutation(java.util.List<java.lang.Integer> P)

Permutation of the termorder.

Parameters:

P - permutation.

Returns:

P(a).

reverseWeight

public static ExprTermOrder reverseWeight(long[][] w)

Weight ExprTermOrder with reversed weight vectors.

Parameters:

w - weight matrix

Returns:

ExprTermOrder with reversed weight vectors