Package edu.jas.poly

Class Word

java.lang.Object

edu.jas.poly.Word

All Implemented Interfaces:

Element<Word>, MonoidElem<Word>, java.io.Serializable, java.lang.Comparable<Word>

public final class Word
extends java.lang.Object
implements MonoidElem<Word>

Word implements strings of letters for polynomials.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected int	hash	Stored hash code.
WordFactory	mono	Defining alphabet in WordFactory.

Constructor Summary

Constructors

Constructor	Description
Word(WordFactory m)	Constructor for Word.
Word(WordFactory m, java.lang.String s)	Constructor for Word.
Word(WordFactory m, java.lang.String s, boolean translate)	Constructor for Word.

Method Summary

Modifier and Type	Method	Description
int	compareTo(Word V)	Word compareTo.
Word	copy()	Copy this.
long	degree()	Word degree.
java.util.SortedMap<java.lang.String,java.lang.Integer>	dependencyOnVariables()	Word dependency on letters.
Word	divide(Word V)	Word divide.
Word	divideLeft(Word V)	Word divide left.
Word	divideRight(Word V)	Word divide right.
boolean	divides(Word V)	Word divides test.
Word[]	divideWord(Word V)	Word divide with prefix and suffix.
Word[]	divideWord(Word V, boolean first)	Word divide with prefix and suffix.
boolean	equals(java.lang.Object B)	Comparison with any other object.
MonoidFactory<Word>	factory()	Get the corresponding element factory.
char	getVal(int i)	Get the letter at position i.
int	gradCompareTo(Word V)	Word graded comparison.
int	gradInvlexCompareTo(Word V)	Word graded comparison.
int	hashCode()	hashCode.
static java.util.SortedMap<java.lang.String,java.lang.Integer>	histogram(java.lang.String v)	String dependency on letters.
Word	inverse()	Word inverse.
boolean	isONE()	Is Word one.
boolean	isOverlap(Overlap ol, Word V)	Is word overlap.
boolean	isUnit()	Is Word unit.
Word	lcm(Word V)	Word pseudo least common multiple.
ExpVector	leadingExpVector()	Word leading exponent vector.
int	length()	Get the length of this word.
boolean	multipleOf(Word V)	Word multiple test.
Word	multiply(Word V)	Word multiplication.
OverlapList	overlap(Word V)	Word overlap list.
Word[]	quotientRemainder(Word S)	Quotient and remainder by division of this by S.
Word	reductum()	Word without leading exponent vector.
Word	remainder(Word V)	Word remainder.
int	signum()	Word signum.
java.lang.String	toScript()	Get a scripting compatible string representation.
java.lang.String	toScriptFactory()	Get a scripting compatible string representation of the factory.
java.lang.String	toString()	Get the string representation.

Methods inherited from class java.lang.Object

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

Methods inherited from interface edu.jas.structure.MonoidElem

leftDivide, leftRemainder, power, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

Field Detail

mono

public final WordFactory mono

Defining alphabet in WordFactory.

hash

protected int hash

Stored hash code.

Constructor Detail

Word

public Word(WordFactory m)

Constructor for Word.

Parameters:

m - factory for words.

Word

public Word(WordFactory m,
            java.lang.String s)

Constructor for Word.

Parameters:

m - factory for words.

s - String

Word

public Word(WordFactory m,
            java.lang.String s,
            boolean translate)

Constructor for Word.

Parameters:

m - factory for words.

s - String

translate - indicator if s needs translation

Method Detail

factory

public MonoidFactory<Word> factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<Word>

Returns:

factory for this Element.

See Also:

Element.factory()

copy

public Word copy()

Copy this.

Specified by:

copy in interface Element<Word>

Returns:

copy of this.

getVal

public char getVal(int i)

Get the letter at position i.

Parameters:

i - position.

Returns:

val[i].

length

public int length()

Get the length of this word.

Returns:

val.length.

toString

public java.lang.String toString()

Get the string representation.

Overrides:

toString in class java.lang.Object

See Also:

Object.toString()

toScript

public java.lang.String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface Element<Word>

Returns:

script compatible representation for this Element.

See Also:

Element.toScript()

toScriptFactory

public java.lang.String toScriptFactory()

Get a scripting compatible string representation of the factory.

Specified by:

toScriptFactory in interface Element<Word>

Returns:

script compatible representation for this ElemFactory.

See Also:

Element.toScriptFactory()

equals

public boolean equals(java.lang.Object B)

Comparison with any other object.

Specified by:

equals in interface Element<Word>

Overrides:

equals in class java.lang.Object

Returns:

true if this is equal to b, else false.

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

hashCode.

Specified by:

hashCode in interface Element<Word>

Overrides:

hashCode in class java.lang.Object

Returns:

the hashCode.

See Also:

Object.hashCode()

isONE

public boolean isONE()

Is Word one.

Specified by:

isONE in interface MonoidElem<Word>

Returns:

If this is the empty word then true is returned, else false.

isUnit

public boolean isUnit()

Is Word unit.

Specified by:

isUnit in interface MonoidElem<Word>

Returns:

If this is a unit then true is returned, else false.

multiply

public Word multiply(Word V)

Word multiplication.

Specified by:

multiply in interface MonoidElem<Word>

Parameters:

V - other word.

Returns:

this * V.

divide

public Word divide(Word V)

Word divide.

Specified by:

divide in interface MonoidElem<Word>

Parameters:

V - other word.

Returns:

this / V.

divideLeft

public Word divideLeft(Word V)

Word divide left.

Parameters:

V - other word.

Returns:

this / V = left, with left * V = this.

divideRight

public Word divideRight(Word V)

Word divide right.

Parameters:

V - other word.

Returns:

this / V = right, with V * right = this.

divideWord

public Word[] divideWord(Word V)

Word divide with prefix and suffix.

Parameters:

V - other word.

Returns:

[left,right] with left * V * right = this.

divideWord

public Word[] divideWord(Word V,
                         boolean first)

Word divide with prefix and suffix.

Parameters:

V - other word.

first - is true for first index, false for last index.

Returns:

[left,right] with left * V * right = this.

remainder

public Word remainder(Word V)

Word remainder.

Specified by:

remainder in interface MonoidElem<Word>

Parameters:

V - other word.

Returns:

this (this/V). Note: not useful.

quotientRemainder

public Word[] quotientRemainder(Word S)

Quotient and remainder by division of this by S.

Specified by:

quotientRemainder in interface MonoidElem<Word>

Parameters:

S - a Word

Returns:

[this/S, this - (this/S)*S]. Note: not useful.

inverse

public Word inverse()

Word inverse.

Specified by:

inverse in interface MonoidElem<Word>

Returns:

1 / this.

signum

public int signum()

Word signum.

Returns:

0 if this is one, 1 if it is non empty.

degree

public long degree()

Word degree.

Returns:

total degree of all letters.

dependencyOnVariables

public java.util.SortedMap<java.lang.String,java.lang.Integer> dependencyOnVariables()

Word dependency on letters.

Returns:

sorted map of letters and the number of its occurences.

histogram

public static java.util.SortedMap<java.lang.String,java.lang.Integer> histogram(java.lang.String v)

String dependency on letters.

Parameters:

v - string.

Returns:

sorted map of letters and the number of its occurences.

leadingExpVector

public ExpVector leadingExpVector()

Word leading exponent vector.

Returns:

an ExpVector for the first power of a letter.

reductum

public Word reductum()

Word without leading exponent vector.

Returns:

an Word without the first power of a letter.

multipleOf

public boolean multipleOf(Word V)

Word multiple test.

Parameters:

V - other word.

Returns:

true if this is a multiple of V, else false.

divides

public boolean divides(Word V)

Word divides test.

Parameters:

V - other word.

Returns:

true if this divides V, else false.

compareTo

public int compareTo(Word V)

Word compareTo. Uses String.compareTo.

Specified by:

compareTo in interface java.lang.Comparable<Word>

Specified by:

compareTo in interface Element<Word>

Parameters:

V - other word.

Returns:

0 if U == V, -1 if U < V, 1 if U > V.

gradCompareTo

public int gradCompareTo(Word V)

Word graded comparison. Compares first be degree, then lexicographical.

Parameters:

V - other word.

Returns:

0 if U == V, -1 if U < V, 1 if U > V.

gradInvlexCompareTo

public int gradInvlexCompareTo(Word V)

Word graded comparison. Compares first be degree, then inverse lexicographical.

Parameters:

V - other word.

Returns:

0 if U == V, -1 if U < V, 1 if U > V.

isOverlap

public boolean isOverlap(Overlap ol,
                         Word V)

Is word overlap.

Parameters:

ol - = [l1,r1,l2,r2] an Overlap container of four words

V - word

Returns:

true if l1 * this * r1 = l2 * V * r2, else false.

overlap

public OverlapList overlap(Word V)

Word overlap list.

Parameters:

V - other word.

Returns:

list of overlaps [l1,r1,l2,r2] with l1 * this * r1 = l2 * V * r2. If no such overlaps exist the empty overlap list is returned.

lcm

public Word lcm(Word V)

Word pseudo least common multiple.

Parameters:

V - other word.

Returns:

w = l1*this*r1, with l1*this*r1 == l2*V*r2, if l1, r1, l2, r2 exist, else null is returned.