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 and Description

protected int hash
Stored hash code.

WordFactory mono
Defining alphabet in WordFactory.

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

Constructor Summary

Constructors
Constructor and 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

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and 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 Element<Word>
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<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.

Class Word

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface edu.jas.structure.MonoidElem

Field Detail

mono

hash

Constructor Detail

Word

Word

Word

Method Detail

factory

copy

getVal

length

toString

toScript

toScriptFactory

equals

hashCode

isONE

isUnit

multiply

divide

divideLeft

divideRight

divideWord

divideWord

remainder

quotientRemainder

inverse

signum

degree

dependencyOnVariables

histogram

leadingExpVector

reductum

multipleOf

divides

compareTo

gradCompareTo

gradInvlexCompareTo

isOverlap

overlap

lcm