ExpVector

java.lang.Object
- edu.jas.poly.ExpVector

All Implemented Interfaces:

AbelianGroupElem<ExpVector>, Element<ExpVector>, java.io.Serializable, java.lang.Comparable<ExpVector>

Direct Known Subclasses:

ExpVectorByte, ExpVectorInteger, ExpVectorLong, ExpVectorShort
```
public abstract class ExpVector
extends java.lang.Object
implements AbelianGroupElem<ExpVector>
```
ExpVector implements exponent vectors for polynomials. Exponent vectors are implemented as arrays of Java elementary types, like long, int, short and byte. ExpVector provides also the familiar MAS static method names. The implementation is only tested for nonnegative exponents but should work also for negative exponents. Objects of this class are intended to be immutable, but exponents can be set (during construction); also the hash code is only computed once, when needed. The different storage unit implementations are ExpVectorLong ExpVectorInteger, ExpVectorShort and ExpVectorByte. The static factory methods create() of ExpVector select the respective storage unit. The selection of the desired storage unit is internally done via the static variable storunit. This varaible should not be changed dynamically.

Author:

Heinz Kredel

See Also:

Serialized Form

Nested Class Summary

Nested Classes
Modifier and Type Class and Description

static class ExpVector.StorUnit
Storage representation of exponent arrays.

Nested Classes
Modifier and Type	Class and Description
`static class`	`ExpVector.StorUnit` Storage representation of exponent arrays.

Field Summary

Fields
Modifier and Type	Field and Description
`protected long`	`blen` Stored bitLength.
`protected int`	`hash` Stored hash code.
`static ExpVector.StorUnit`	`storunit` Used storage representation of exponent arrays.

Constructor Summary

Constructors
Constructor and Description

ExpVector()
Constructor for ExpVector.

Constructors
Constructor and Description
`ExpVector()` Constructor for ExpVector.

Method Summary

All Methods Static Methods Instance Methods Abstract Methods Concrete Methods
Modifier and Type	Method and Description
`abstract ExpVector`	`abs()` ExpVector absolute value.
`long`	`bitLength()` Returns the number of bits in the representation of this exponent vector.
`abstract ExpVector`	`combine(ExpVector V)` Combine with ExpVector.
`int`	`compareTo(ExpVector V)` ExpVector compareTo.
`abstract ExpVector`	`contract(int i, int len)` Contract variables.
`abstract ExpVector`	`copy()` Clone this.
`static ExpVector`	`create(java.util.Collection<java.lang.Long> v)` Factory constructor for ExpVector.
`static ExpVector`	`create(int n)` Factory constructor for ExpVector.
`static ExpVector`	`create(int n, int i, long e)` Factory constructor for ExpVector.
`static ExpVector`	`create(long[] v)` Internal factory constructor for ExpVector.
`static ExpVector`	`create(java.lang.String s)` Factory constructor for ExpVector.
`long`	`degree()` ExpVector degree.
`abstract int[]`	`dependencyOnVariables()` ExpVector dependency on variables.
`abstract int`	`dependentVariables()` ExpVector dependent variables.
`boolean`	`divides(ExpVector V)` ExpVector divides test.
`boolean`	`equals(java.lang.Object B)` Comparison with any other object.
`static ExpVector`	`EVABS(ExpVector U)` ExpVector absolute value.
`<C extends RingElem<C>> C`	`evaluate(RingFactory<C> cf, java.util.List<C> a)` Evaluate.
`static ExpVector`	`EVDIF(ExpVector U, ExpVector V)` ExpVector difference.
`static int[]`	`EVDOV(ExpVector U)` ExpVector dependency on variables.
`static ExpVector`	`EVGCD(ExpVector U, ExpVector V)` ExpVector greatest common divisor.
`static int`	`EVIGLC(ExpVector U, ExpVector V)` Inverse graded lexicographical compare.
`static int`	`EVIGLC(ExpVector U, ExpVector V, int begin, int end)` Inverse graded lexicographical compare part.
`static int`	`EVILCP(ExpVector U, ExpVector V)` Inverse lexicographical compare.
`static int`	`EVILCP(ExpVector U, ExpVector V, int begin, int end)` Inverse lexicographical compare part.
`static int`	`EVITDEGLC(ExpVector U, ExpVector V)` Inverse total degree lexicographical compare.
`static int`	`EVIWLC(long[][] w, ExpVector U, ExpVector V)` Inverse weighted lexicographical compare.
`static int`	`EVIWLC(long[][] w, ExpVector U, ExpVector V, int begin, int end)` Inverse weighted lexicographical compare part.
`static ExpVector`	`EVLCM(ExpVector U, ExpVector V)` ExpVector least common multiple.
`static long`	`EVMDEG(ExpVector U)` ExpVector maximal degree.
`static long`	`EVMINDEG(ExpVector U)` ExpVector minimal degree.
`static boolean`	`EVMT(ExpVector U, ExpVector V)` ExpVector multiple test.
`static ExpVector`	`EVNEG(ExpVector U)` ExpVector negate.
`static ExpVector`	`EVRAND(int r, long k, float q)` Generate a random ExpVector.
`static ExpVector`	`EVRAND(int r, long k, float q, java.util.Random rnd)` Generate a random ExpVector.
`static int`	`EVRIGLC(ExpVector U, ExpVector V)` Reverse inverse graded lexicographical compare.
`static int`	`EVRIGLC(ExpVector U, ExpVector V, int begin, int end)` Reverse inverse graded lexicographical compare part.
`static int`	`EVRILCP(ExpVector U, ExpVector V)` Reverse inverse lexicographical compare.
`static int`	`EVRILCP(ExpVector U, ExpVector V, int begin, int end)` Reverse inverse lexicographical compare part.
`static int`	`EVRLITDEGC(ExpVector U, ExpVector V)` Reverse lexicographical inverse total degree compare.
`static int`	`EVSIGN(ExpVector U)` ExpVector sign.
`static ExpVector`	`EVSU(ExpVector U, int i, long d)` ExpVector substitution.
`static ExpVector`	`EVSUM(ExpVector U, ExpVector V)` ExpVector summation.
`static long`	`EVTDEG(ExpVector U)` ExpVector total degree.
`static long`	`EVWDEG(long[][] w, ExpVector U)` ExpVector weighted degree.
`abstract ExpVector`	`extend(int i, int j, long e)` Extend variables.
`abstract ExpVector`	`extendLower(int i, int j, long e)` Extend lower variables.
`AbelianGroupFactory<ExpVector>`	`factory()` Get the corresponding element factory.
`abstract ExpVector`	`gcd(ExpVector V)` ExpVector greatest common divisor.
`abstract long[]`	`getVal()` Get the exponent vector.
`abstract long`	`getVal(int i)` Get the exponent at position i.
`int`	`hashCode()` hashCode.
`int`	`indexVar(java.lang.String x, java.lang.String... vars)` Get the index of a variable.
`java.lang.String`	`indexVarName(int idx, java.lang.String... vars)` Get the variable name at index.
`abstract int`	`invGradCompareTo(ExpVector V)` ExpVector inverse graded lexicographical compareTo.
`abstract int`	`invGradCompareTo(ExpVector V, int begin, int end)` ExpVector inverse graded lexicographical compareTo.
`abstract int`	`invLexCompareTo(ExpVector V)` ExpVector inverse lexicographical compareTo.
`abstract int`	`invLexCompareTo(ExpVector V, int begin, int end)` ExpVector inverse lexicographical compareTo.
`abstract int`	`invTdegCompareTo(ExpVector V)` ExpVector inverse total degree lexicographical compareTo.
`abstract int`	`invWeightCompareTo(long[][] w, ExpVector V)` ExpVector inverse weighted lexicographical compareTo.
`abstract int`	`invWeightCompareTo(long[][] w, ExpVector V, int begin, int end)` ExpVector inverse weighted lexicographical compareTo.
`boolean`	`isFinite()` Is this structure finite or infinite.
`boolean`	`isZERO()` Is ExpVector zero.
`abstract ExpVector`	`lcm(ExpVector V)` ExpVector least common multiple.
`abstract int`	`length()` Get the length of this exponent vector.
`abstract long`	`maxDeg()` ExpVector maximal degree.
`abstract long`	`minDeg()` ExpVector minimal degree.
`abstract boolean`	`multipleOf(ExpVector V)` ExpVector multiple test.
`abstract ExpVector`	`negate()` ExpVector negate.
`abstract ExpVector`	`permutation(java.util.List<java.lang.Integer> P)` Permutation of exponent vector.
`static ExpVector`	`random(int r, long k, float q)` Generate a random ExpVector.
`static ExpVector`	`random(int r, long k, float q, java.util.Random rnd)` Generate a random ExpVector.
`abstract ExpVector`	`reverse()` Reverse variables.
`abstract ExpVector`	`reverse(int j)` Reverse lower j variables.
`abstract int`	`revInvGradCompareTo(ExpVector V)` ExpVector reverse inverse graded compareTo.
`abstract int`	`revInvGradCompareTo(ExpVector V, int begin, int end)` ExpVector reverse inverse graded compareTo.
`abstract int`	`revInvLexCompareTo(ExpVector V)` ExpVector reverse inverse lexicographical compareTo.
`abstract int`	`revInvLexCompareTo(ExpVector V, int begin, int end)` ExpVector reverse inverse lexicographical compareTo.
`abstract int`	`revLexInvTdegCompareTo(ExpVector V)` ExpVector reverse lexicographical inverse total degree compareTo.
`abstract ExpVector`	`scalarMultiply(long s)` ExpVector multiply by scalar.
`protected abstract long`	`setVal(int i, long e)` Set the exponent at position i to e.
`abstract int`	`signum()` ExpVector signum.
`java.lang.String[]`	`stdVars()` Standard variable names.
`static java.lang.String[]`	`STDVARS(int n)` Standard variable names.
`java.lang.String[]`	`stdVars(java.lang.String prefix)` Generate variable names.
`static java.lang.String[]`	`STDVARS(java.lang.String prefix, int n)` Generate variable names.
`ExpVector`	`subst(int i, long d)` ExpVector substitution.
`abstract ExpVector`	`subtract(ExpVector V)` ExpVector subtract.
`abstract ExpVector`	`sum(ExpVector V)` ExpVector summation.
`java.lang.String`	`toScript()` Get a scripting compatible string representation.
`java.lang.String`	`toScript(java.lang.String[] vars)` 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.
`java.lang.String`	`toString(java.lang.String[] vars)` Get the string representation with variable names.
`abstract long`	`totalDeg()` ExpVector total degree.
`int`	`varIndex(int idx)` Get the array index of a variable at index.
`static java.lang.String`	`varsToString(java.lang.String[] vars)` Get the string representation of the variables.
`abstract long`	`weightDeg(long[] w)` ExpVector weighted degree.
`abstract long`	`weightDeg(long[][] w)` ExpVector weighted degree.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

- Field Detail
  - hash
```
protected transient int hash
```
    Stored hash code.
  - blen
```
protected transient long blen
```
    Stored bitLength.
  - storunit
```
public static final ExpVector.StorUnit storunit
```
    Used storage representation of exponent arrays. Note: Set this only statically and not dynamically.
- Constructor Detail
  - ExpVector
```
public ExpVector()
```
    Constructor for ExpVector.
- Method Detail
  - create
```
public static final ExpVector create(int n)
```
    Factory constructor for ExpVector.
    
    Parameters:
    
    n - length of exponent vector.
  - create
```
public static final ExpVector create(int n,
                                     int i,
                                     long e)
```
    Factory constructor for ExpVector. Sets exponent i to e.
    
    Parameters:
    
    n - length of exponent vector.
    
    i - index of exponent to be set.
    
    e - exponent to be set.
  - create
```
public static final ExpVector create(long[] v)
```
    Internal factory constructor for ExpVector. Sets val.
    
    Parameters:
    
    v - internal representation array.
  - create
```
public static final ExpVector create(java.lang.String s)
```
    Factory constructor for ExpVector. Converts a String representation to an ExpVector. Accepted format = (1,2,3,4,5,6,7).
    
    Parameters:
    
    s - String representation.
  - create
```
public static final ExpVector create(java.util.Collection<java.lang.Long> v)
```
    Factory constructor for ExpVector. Sets val.
    
    Parameters:
    
    v - collection of exponents.
  - factory
```
public AbelianGroupFactory<ExpVector> factory()
```
    Get the corresponding element factory.
    
    Specified by:
    
    factory in interface Element<ExpVector>
    
    Returns:
    
    factory for this Element.
    
    See Also:
    
    Element.factory()
  - isFinite
```
public boolean isFinite()
```
    Is this structure finite or infinite.
    
    Returns:
    
    true if this structure is finite, else false.
    
    See Also:
    
    Note: returns true because of finite set of values in each index.
  - copy
```
public abstract ExpVector copy()
```
    Clone this.
    
    Specified by:
    
    copy in interface Element<ExpVector>
    
    Returns:
    
    Creates and returns a copy of this Element.
    
    See Also:
    
    Object.clone()
  - getVal
```
public abstract long[] getVal()
```
    Get the exponent vector.
    
    Returns:
    
    val.
  - getVal
```
public abstract long getVal(int i)
```
    Get the exponent at position i.
    
    Parameters:
    
    i - position.
    
    Returns:
    
    val[i].
  - setVal
```
protected abstract long setVal(int i,
                               long e)
```
    Set the exponent at position i to e.
    
    Parameters:
    
    i -
    
    e -
    
    Returns:
    
    old val[i].
  - length
```
public abstract int length()
```
    Get the length of this exponent vector.
    
    Returns:
    
    val.length.
  - extend
```
public abstract ExpVector extend(int i,
                                 int j,
                                 long e)
```
    Extend variables. Used e.g. in module embedding. Extend this by i elements and set val[j] to e.
    
    Parameters:
    
    i - number of elements to extend.
    
    j - index of element to be set.
    
    e - new exponent for val[j].
    
    Returns:
    
    extended exponent vector.
  - extendLower
```
public abstract ExpVector extendLower(int i,
                                      int j,
                                      long e)
```
    Extend lower variables. Extend this by i lower elements and set val[j] to e.
    
    Parameters:
    
    i - number of elements to extend.
    
    j - index of element to be set.
    
    e - new exponent for val[j].
    
    Returns:
    
    extended exponent vector.
  - contract
```
public abstract ExpVector contract(int i,
                                   int len)
```
    Contract variables. Used e.g. in module embedding. Contract this to len elements.
    
    Parameters:
    
    i - position of first element to be copied.
    
    len - new length.
    
    Returns:
    
    contracted exponent vector.
  - reverse
```
public abstract ExpVector reverse()
```
    Reverse variables. Used e.g. in opposite rings.
    
    Returns:
    
    reversed exponent vector.
  - reverse
```
public abstract ExpVector reverse(int j)
```
    Reverse lower j variables. Used e.g. in opposite rings. Reverses the first j-1 variables, the rest is unchanged.
    
    Parameters:
    
    j - index of first variable reversed.
    
    Returns:
    
    reversed exponent vector.
  - combine
```
public abstract ExpVector combine(ExpVector V)
```
    Combine with ExpVector. Combine this with the other ExpVector V.
    
    Parameters:
    
    V - the other exponent vector.
    
    Returns:
    
    combined exponent vector.
  - permutation
```
public abstract ExpVector permutation(java.util.List<java.lang.Integer> P)
```
    Permutation of exponent vector.
    
    Parameters:
    
    P - permutation.
    
    Returns:
    
    P(e).
  - toString
```
public java.lang.String toString()
```
    Get the string representation.
    
    Overrides:
    
    toString in class java.lang.Object
    
    See Also:
    
    Object.toString()
  - toString
```
public java.lang.String toString(java.lang.String[] vars)
```
    Get the string representation with variable names.
    
    Parameters:
    
    vars - names of variables.
    
    See Also:
    
    Object.toString()
  - varsToString
```
public static final java.lang.String varsToString(java.lang.String[] vars)
```
    Get the string representation of the variables.
    
    Parameters:
    
    vars - names of variables.
    
    Returns:
    
    string representation of the variables.
    
    See Also:
    
    Object.toString()
  - toScript
```
public java.lang.String toScript()
```
    Get a scripting compatible string representation.
    
    Specified by:
    
    toScript in interface Element<ExpVector>
    
    Returns:
    
    script compatible representation for this Element.
    
    See Also:
    
    Element.toScript()
  - toScript
```
public java.lang.String toScript(java.lang.String[] vars)
```
    Get a scripting compatible string representation.
    
    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<ExpVector>
    
    Returns:
    
    script compatible representation for this ElemFactory.
    
    See Also:
    
    Element.toScriptFactory()
  - indexVarName
```
public java.lang.String indexVarName(int idx,
                                     java.lang.String... vars)
```
    Get the variable name at index.
    
    Parameters:
    
    idx - index of the variable
    
    vars - array of names of variables
    
    Returns:
    
    name of variable at the given index.
  - varIndex
```
public int varIndex(int idx)
```
    Get the array index of a variable at index.
    
    Parameters:
    
    idx - index of the variable
    
    Returns:
    
    array index of the variable.
  - indexVar
```
public int indexVar(java.lang.String x,
                    java.lang.String... vars)
```
    Get the index of a variable.
    
    Parameters:
    
    x - variable name to be searched.
    
    vars - array of names of variables
    
    Returns:
    
    index of x in vars.
  - evaluate
```
public <C extends RingElem<C>> C evaluate(RingFactory<C> cf,
                                          java.util.List<C> a)
```
    Evaluate.
    
    Parameters:
    
    cf - ring factory for elements of a.
    
    a - list of values.
    
    Returns:
    
    a_1^{e_1} * ... * a_n^{e_n}.
  - equals
```
public boolean equals(java.lang.Object B)
```
    Comparison with any other object.
    
    Specified by:
    
    equals in interface Element<ExpVector>
    
    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. Optimized for small exponents, i.e. ≤ 2⁴ and small number of variables, i.e. ≤ 8.
    
    Specified by:
    
    hashCode in interface Element<ExpVector>
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    
    the hashCode.
    
    See Also:
    
    Object.hashCode()
  - bitLength
```
public long bitLength()
```
    Returns the number of bits in the representation of this exponent vector.
    
    Returns:
    
    number of bits in the representation of this ExpVector, including sign bits.
  - isZERO
```
public boolean isZERO()
```
    Is ExpVector zero.
    
    Specified by:
    
    isZERO in interface AbelianGroupElem<ExpVector>
    
    Returns:
    
    If this has all elements 0 then true is returned, else false.
  - stdVars
```
public java.lang.String[] stdVars()
```
    Standard variable names. Generate standard names for variables, i.e. x0 to x(n-1).
    
    Returns:
    
    standard names.
  - stdVars
```
public java.lang.String[] stdVars(java.lang.String prefix)
```
    Generate variable names. Generate names for variables, i.e. prefix0 to prefix(n-1).
    
    Parameters:
    
    prefix - name prefix.
    
    Returns:
    
    standard names.
  - STDVARS
```
public static final java.lang.String[] STDVARS(int n)
```
    Standard variable names. Generate standard names for variables, i.e. x0 to x(n-1).
    
    Parameters:
    
    n - size of names array
    
    Returns:
    
    standard names.
  - STDVARS
```
public static final java.lang.String[] STDVARS(java.lang.String prefix,
                                               int n)
```
    Generate variable names. Generate names for variables from given prefix. i.e. prefix0 to prefix(n-1).
    
    Parameters:
    
    n - size of names array.
    
    prefix - name prefix.
    
    Returns:
    
    vatiable names.
  - EVABS
```
public static final ExpVector EVABS(ExpVector U)
```
    ExpVector absolute value.
    
    Parameters:
    
    U -
    
    Returns:
    
    abs(U).
  - abs
```
public abstract ExpVector abs()
```
    ExpVector absolute value.
    
    Specified by:
    
    abs in interface AbelianGroupElem<ExpVector>
    
    Returns:
    
    abs(this).
  - EVNEG
```
public static final ExpVector EVNEG(ExpVector U)
```
    ExpVector negate.
    
    Parameters:
    
    U -
    
    Returns:
    
    -U.
  - negate
```
public abstract ExpVector negate()
```
    ExpVector negate.
    
    Specified by:
    
    negate in interface AbelianGroupElem<ExpVector>
    
    Returns:
    
    -this.
  - EVSUM
```
public static final ExpVector EVSUM(ExpVector U,
                                    ExpVector V)
```
    ExpVector summation.
    
    Parameters:
    
    U -
    
    V -
    
    Returns:
    
    U+V.
  - sum
```
public abstract ExpVector sum(ExpVector V)
```
    ExpVector summation.
    
    Specified by:
    
    sum in interface AbelianGroupElem<ExpVector>
    
    Parameters:
    
    V -
    
    Returns:
    
    this+V.
  - EVDIF
```
public static final ExpVector EVDIF(ExpVector U,
                                    ExpVector V)
```
    ExpVector difference. Result may have negative entries.
    
    Parameters:
    
    U -
    
    V -
    
    Returns:
    
    U-V.
  - subtract
```
public abstract ExpVector subtract(ExpVector V)
```
    ExpVector subtract. Result may have negative entries.
    
    Specified by:
    
    subtract in interface AbelianGroupElem<ExpVector>
    
    Parameters:
    
    V -
    
    Returns:
    
    this-V.
  - scalarMultiply
```
public abstract ExpVector scalarMultiply(long s)
```
    ExpVector multiply by scalar.
    
    Parameters:
    
    s - scalar
    
    Returns:
    
    s*this.
  - EVSU
```
public static final ExpVector EVSU(ExpVector U,
                                   int i,
                                   long d)
```
    ExpVector substitution. Clone and set exponent to d at position i.
    
    Parameters:
    
    U -
    
    i - position.
    
    d - new exponent.
    
    Returns:
    
    substituted ExpVector.
  - subst
```
public ExpVector subst(int i,
                       long d)
```
    ExpVector substitution. Clone and set exponent to d at position i.
    
    Parameters:
    
    i - position.
    
    d - new exponent.
    
    Returns:
    
    substituted ExpVector.
  - EVRAND
```
public static final ExpVector EVRAND(int r,
                                     long k,
                                     float q)
```
    Generate a random ExpVector.
    
    Parameters:
    
    r - length of new ExpVector.
    
    k - maximal degree in each exponent.
    
    q - density of nozero exponents.
    
    Returns:
    
    random ExpVector.
  - EVRAND
```
public static final ExpVector EVRAND(int r,
                                     long k,
                                     float q,
                                     java.util.Random rnd)
```
    Generate a random ExpVector.
    
    Parameters:
    
    r - length of new ExpVector.
    
    k - maximal degree in each exponent.
    
    q - density of nozero exponents.
    
    rnd - is a source for random bits.
    
    Returns:
    
    random ExpVector.
  - random
```
public static final ExpVector random(int r,
                                     long k,
                                     float q)
```
    Generate a random ExpVector.
    
    Parameters:
    
    r - length of new ExpVector.
    
    k - maximal degree in each exponent.
    
    q - density of nozero exponents.
    
    Returns:
    
    random ExpVector.
  - random
```
public static final ExpVector random(int r,
                                     long k,
                                     float q,
                                     java.util.Random rnd)
```
    Generate a random ExpVector.
    
    Parameters:
    
    r - length of new ExpVector.
    
    k - maximal degree in each exponent.
    
    q - density of nozero exponents.
    
    rnd - is a source for random bits.
    
    Returns:
    
    random ExpVector.
  - EVSIGN
```
public static final int EVSIGN(ExpVector U)
```
    ExpVector sign.
    
    Parameters:
    
    U -
    
    Returns:
    
    0 if U is zero, -1 if some entry is negative, 1 if no entry is negativ and at least one entry is positive.
  - signum
```
public abstract int signum()
```
    ExpVector signum.
    
    Specified by:
    
    signum in interface AbelianGroupElem<ExpVector>
    
    Returns:
    
    0 if this is zero, -1 if some entry is negative, 1 if no entry is negative and at least one entry is positive.
  - EVTDEG
```
public static final long EVTDEG(ExpVector U)
```
    ExpVector total degree.
    
    Parameters:
    
    U -
    
    Returns:
    
    sum of all exponents.
  - degree
```
public long degree()
```
    ExpVector degree.
    
    Returns:
    
    total degree of all exponents.
  - totalDeg
```
public abstract long totalDeg()
```
    ExpVector total degree.
    
    Returns:
    
    sum of all exponents.
  - EVMDEG
```
public static final long EVMDEG(ExpVector U)
```
    ExpVector maximal degree.
    
    Parameters:
    
    U -
    
    Returns:
    
    maximal exponent.
  - maxDeg
```
public abstract long maxDeg()
```
    ExpVector maximal degree.
    
    Returns:
    
    maximal exponent.
  - EVMINDEG
```
public static final long EVMINDEG(ExpVector U)
```
    ExpVector minimal degree.
    
    Parameters:
    
    U -
    
    Returns:
    
    minimal exponent.
  - minDeg
```
public abstract long minDeg()
```
    ExpVector minimal degree.
    
    Returns:
    
    minimal exponent.
  - EVWDEG
```
public static final long EVWDEG(long[][] w,
                                ExpVector U)
```
    ExpVector weighted degree.
    
    Parameters:
    
    w - weights.
    
    U -
    
    Returns:
    
    weighted sum of all exponents.
  - weightDeg
```
public abstract long weightDeg(long[][] w)
```
    ExpVector weighted degree.
    
    Parameters:
    
    w - weights.
    
    Returns:
    
    weighted sum of all exponents.
  - weightDeg
```
public abstract long weightDeg(long[] w)
```
    ExpVector weighted degree.
    
    Parameters:
    
    w - weights.
    
    Returns:
    
    weighted sum of all exponents.
  - EVLCM
```
public static final ExpVector EVLCM(ExpVector U,
                                    ExpVector V)
```
    ExpVector least common multiple.
    
    Parameters:
    
    U -
    
    V -
    
    Returns:
    
    component wise maximum of U and V.
  - lcm
```
public abstract ExpVector lcm(ExpVector V)
```
    ExpVector least common multiple.
    
    Parameters:
    
    V -
    
    Returns:
    
    component wise maximum of this and V.
  - EVGCD
```
public static final ExpVector EVGCD(ExpVector U,
                                    ExpVector V)
```
    ExpVector greatest common divisor.
    
    Parameters:
    
    U -
    
    V -
    
    Returns:
    
    component wise minimum of U and V.
  - gcd
```
public abstract ExpVector gcd(ExpVector V)
```
    ExpVector greatest common divisor.
    
    Parameters:
    
    V -
    
    Returns:
    
    component wise minimum of this and V.
  - EVDOV
```
public static final int[] EVDOV(ExpVector U)
```
    ExpVector dependency on variables.
    
    Parameters:
    
    U -
    
    Returns:
    
    array of indices where U has positive exponents.
  - dependentVariables
```
public abstract int dependentVariables()
```
    ExpVector dependent variables.
    
    Returns:
    
    number of indices where val has positive exponents.
  - dependencyOnVariables
```
public abstract int[] dependencyOnVariables()
```
    ExpVector dependency on variables.
    
    Returns:
    
    array of indices where val has positive exponents.
  - EVMT
```
public static final boolean EVMT(ExpVector U,
                                 ExpVector V)
```
    ExpVector multiple test. Test if U is component wise greater or equal to V.
    
    Parameters:
    
    U -
    
    V -
    
    Returns:
    
    true if U is a multiple of V, else false.
  - multipleOf
```
public abstract boolean multipleOf(ExpVector V)
```
    ExpVector multiple test. Test if this is component wise greater or equal to V.
    
    Parameters:
    
    V -
    
    Returns:
    
    true if this is a multiple of V, else false.
  - divides
```
public boolean divides(ExpVector V)
```
    ExpVector divides test. Test if V is component wise greater or equal to this.
    
    Parameters:
    
    V -
    
    Returns:
    
    true if this divides V, else false.
  - compareTo
```
public int compareTo(ExpVector V)
```
    ExpVector compareTo.
    
    Specified by:
    
    compareTo in interface Element<ExpVector>
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<ExpVector>
    
    Parameters:
    
    V -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - EVILCP
```
public static final int EVILCP(ExpVector U,
                               ExpVector V)
```
    Inverse lexicographical compare.
    
    Parameters:
    
    U -
    
    V -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - invLexCompareTo
```
public abstract int invLexCompareTo(ExpVector V)
```
    ExpVector inverse lexicographical compareTo.
    
    Parameters:
    
    V -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - EVILCP
```
public static final int EVILCP(ExpVector U,
                               ExpVector V,
                               int begin,
                               int end)
```
    Inverse lexicographical compare part. Compare entries between begin and end (-1).
    
    Parameters:
    
    U -
    
    V -
    
    begin -
    
    end -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - invLexCompareTo
```
public abstract int invLexCompareTo(ExpVector V,
                                    int begin,
                                    int end)
```
    ExpVector inverse lexicographical compareTo.
    
    Parameters:
    
    V -
    
    begin -
    
    end -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - EVIGLC
```
public static final int EVIGLC(ExpVector U,
                               ExpVector V)
```
    Inverse graded lexicographical compare.
    
    Parameters:
    
    U -
    
    V -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - invGradCompareTo
```
public abstract int invGradCompareTo(ExpVector V)
```
    ExpVector inverse graded lexicographical compareTo.
    
    Parameters:
    
    V -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - EVIGLC
```
public static final int EVIGLC(ExpVector U,
                               ExpVector V,
                               int begin,
                               int end)
```
    Inverse graded lexicographical compare part. Compare entries between begin and end (-1).
    
    Parameters:
    
    U -
    
    V -
    
    begin -
    
    end -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - invGradCompareTo
```
public abstract int invGradCompareTo(ExpVector V,
                                     int begin,
                                     int end)
```
    ExpVector inverse graded lexicographical compareTo.
    
    Parameters:
    
    V -
    
    begin -
    
    end -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - EVRILCP
```
public static final int EVRILCP(ExpVector U,
                                ExpVector V)
```
    Reverse inverse lexicographical compare.
    
    Parameters:
    
    U -
    
    V -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - revInvLexCompareTo
```
public abstract int revInvLexCompareTo(ExpVector V)
```
    ExpVector reverse inverse lexicographical compareTo.
    
    Parameters:
    
    V -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - EVRILCP
```
public static final int EVRILCP(ExpVector U,
                                ExpVector V,
                                int begin,
                                int end)
```
    Reverse inverse lexicographical compare part. Compare entries between begin and end (-1).
    
    Parameters:
    
    U -
    
    V -
    
    begin -
    
    end -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - revInvLexCompareTo
```
public abstract int revInvLexCompareTo(ExpVector V,
                                       int begin,
                                       int end)
```
    ExpVector reverse inverse lexicographical compareTo.
    
    Parameters:
    
    V -
    
    begin -
    
    end -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - EVRIGLC
```
public static final int EVRIGLC(ExpVector U,
                                ExpVector V)
```
    Reverse inverse graded lexicographical compare.
    
    Parameters:
    
    U -
    
    V -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - revInvGradCompareTo
```
public abstract int revInvGradCompareTo(ExpVector V)
```
    ExpVector reverse inverse graded compareTo.
    
    Parameters:
    
    V -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - EVRIGLC
```
public static final int EVRIGLC(ExpVector U,
                                ExpVector V,
                                int begin,
                                int end)
```
    Reverse inverse graded lexicographical compare part. Compare entries between begin and end (-1).
    
    Parameters:
    
    U -
    
    V -
    
    begin -
    
    end -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - revInvGradCompareTo
```
public abstract int revInvGradCompareTo(ExpVector V,
                                        int begin,
                                        int end)
```
    ExpVector reverse inverse graded compareTo.
    
    Parameters:
    
    V -
    
    begin -
    
    end -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - EVITDEGLC
```
public static final int EVITDEGLC(ExpVector U,
                                  ExpVector V)
```
    Inverse total degree lexicographical compare.
    
    Parameters:
    
    U -
    
    V -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - invTdegCompareTo
```
public abstract int invTdegCompareTo(ExpVector V)
```
    ExpVector inverse total degree lexicographical compareTo.
    
    Parameters:
    
    V -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - EVRLITDEGC
```
public static final int EVRLITDEGC(ExpVector U,
                                   ExpVector V)
```
    Reverse lexicographical inverse total degree compare.
    
    Parameters:
    
    U -
    
    V -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - revLexInvTdegCompareTo
```
public abstract int revLexInvTdegCompareTo(ExpVector V)
```
    ExpVector reverse lexicographical inverse total degree compareTo.
    
    Parameters:
    
    V -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - EVIWLC
```
public static final int EVIWLC(long[][] w,
                               ExpVector U,
                               ExpVector V)
```
    Inverse weighted lexicographical compare.
    
    Parameters:
    
    w - weight array.
    
    U -
    
    V -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - invWeightCompareTo
```
public abstract int invWeightCompareTo(long[][] w,
                                       ExpVector V)
```
    ExpVector inverse weighted lexicographical compareTo.
    
    Parameters:
    
    w - weight array.
    
    V -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - EVIWLC
```
public static final int EVIWLC(long[][] w,
                               ExpVector U,
                               ExpVector V,
                               int begin,
                               int end)
```
    Inverse weighted lexicographical compare part. Compare entries between begin and end (-1).
    
    Parameters:
    
    w - weight array.
    
    U -
    
    V -
    
    begin -
    
    end -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.
  - invWeightCompareTo
```
public abstract int invWeightCompareTo(long[][] w,
                                       ExpVector V,
                                       int begin,
                                       int end)
```
    ExpVector inverse weighted lexicographical compareTo.
    
    Parameters:
    
    w - weight array.
    
    V -
    
    begin -
    
    end -
    
    Returns:
    
    0 if U == V, -1 if U < V, 1 if U > V.

Class ExpVector

Nested Class Summary

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

hash

blen

storunit

Constructor Detail

ExpVector

Method Detail

create

create

create

create

create

factory

isFinite

copy

getVal

getVal

setVal

length

extend

extendLower

contract

reverse

reverse

combine

permutation

toString

toString

varsToString

toScript

toScript

toScriptFactory

indexVarName

varIndex

indexVar

evaluate

equals

hashCode

bitLength

isZERO

stdVars

stdVars

STDVARS

STDVARS

EVABS

abs

EVNEG

negate

EVSUM

sum

EVDIF

subtract

scalarMultiply

EVSU

subst

EVRAND

EVRAND

random

random

EVSIGN

signum

EVTDEG

degree

totalDeg

EVMDEG

maxDeg

EVMINDEG

minDeg

EVWDEG

weightDeg

weightDeg

EVLCM

lcm

EVGCD