edu.jas.poly

Class 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.

Field Summary

Fields

Modifier and Type	Field and Description
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.

Method Summary

Methods

Modifier and Type	Method and Description
abstract ExpVector	abs() ExpVector absolute value.
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.
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	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 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	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(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	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 boolean	multipleOf(ExpVector V) ExpVector multiple test.
abstract ExpVector	negate() ExpVector negate.
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 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.
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.

Methods inherited from class java.lang.Object

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

Field Detail

hash

protected int hash

Stored hash code.

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 ExpVector create(int n)

Factory constructor for ExpVector.

Parameters:

n - length of exponent vector.

create

public static 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 ExpVector create(long[] v)

Internal factory constructor for ExpVector. Sets val.

Parameters:

v - internal representation array.

create

public static 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 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(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 j variables. Used e.g. in opposite rings. Reverses the first j-1 variables, the rest is unchanged.

Parameters:

j - index of first variable not 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.

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 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()

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 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 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 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 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 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 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.

EVSU

public static 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 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 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 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 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 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 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 long EVMDEG(ExpVector U)

ExpVector maximal degree.

Parameters:

U -

Returns:

maximal exponent.

maxDeg

public abstract long maxDeg()

ExpVector maximal degree.

Returns:

maximal exponent.

EVWDEG

public static 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.

EVLCM

public static 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 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 int[] EVDOV(ExpVector U)

ExpVector dependency on variables.

Parameters:

U -

Returns:

array of indices where U has positive exponents.

dependencyOnVariables

public abstract int[] dependencyOnVariables()

ExpVector dependency on variables.

Returns:

array of indices where val has positive exponents.

EVMT

public static 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 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 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 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 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 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 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 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 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.

EVIWLC

public static 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 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.