edu.jas.poly

Class TermOrder

java.lang.Object

edu.jas.poly.TermOrder

All Implemented Interfaces:

java.io.Serializable

public final class TermOrder
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, so watch your step. This class does not jet 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	TermOrder.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	LEX
static int	REVILEX
static int	REVITDG
static int	REVLEX
static int	REVTDEG

Constructor Summary

Constructors

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

Method Summary

Methods

Modifier and Type	Method and Description
TermOrder	contract(int k, int len) Contract variables.
boolean	equals(java.lang.Object B) Comparison with any other object.
TermOrder	extend(int r, int k) Extend variables.
TermOrder	extendLower(int r, int k) Extend lower variables.
TermOrder.EVComparator	getAscendComparator() Get the ascending order comparator.
TermOrder.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.
TermOrder.EVComparator	getSugarComparator() Get the sugar order comparator.
long[][]	getWeight() Get the weight array.
int	hashCode() Hash code.
TermOrder	reverse() Reverse variables.
TermOrder	reverse(boolean partial) Reverse variables.
static int	revert(int evord) Revert exponent order.
java.lang.String	toString() String representation of TermOrder.
java.lang.String	weightToString() String representation of weight vector.

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

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

DEFAULT_EVORD

public static final int DEFAULT_EVORD

See Also:

Constant Field Values

Constructor Detail

TermOrder

public TermOrder()

Constructor for default term order.

TermOrder

public TermOrder(int evord)

Constructor for given term order.

Parameters:

evord - requested term order indicator / enumerator.

TermOrder

public TermOrder(long[] w)

Constructor for given exponent weights.

Parameters:

w - weight vector of longs.

TermOrder

public TermOrder(long[][] w)

Constructor for given exponent weights.

Parameters:

w - weight array of longs.

TermOrder

public TermOrder(int r,
         int split)

Constructor for default split order.

Parameters:

r - max number of exponents to compare.

split - index.

TermOrder

public TermOrder(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

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 TermOrder.EVComparator getDescendComparator()

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

Returns:

horder.

getAscendComparator

public TermOrder.EVComparator getAscendComparator()

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

Returns:

lorder.

getSugarComparator

public TermOrder.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 vector.

See Also:

Object.toString()

toString

public java.lang.String toString()

String representation of TermOrder.

Overrides:

toString in class java.lang.Object

See Also:

Object.toString()

extend

public TermOrder extend(int r,
               int k)

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

Parameters:

r - current number of variables.

k - number of variables to extend.

Returns:

extended TermOrder.

extendLower

public TermOrder extendLower(int r,
                    int k)

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

Parameters:

r - current number of variables.

k - number of variables to extend.

Returns:

extended TermOrder.

contract

public TermOrder contract(int k,
                 int len)

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

Parameters:

k - position of first element to be copied.

len - new length.

Returns:

contracted TermOrder.

reverse

public TermOrder reverse()

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

Returns:

TermOrder for reversed variables.

reverse

public TermOrder reverse(boolean partial)

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

Parameters:

partial - true for partialy reversed term orders.

Returns:

TermOrder 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.