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 array 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 since not all are well-founded, so watch your step. This class does not 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 Description

static class TermOrder.EVComparator
Comparator for ExpVectors.

Field Summary

Fields
Modifier and Type	Field	Description
`static int`	`DEFAULT_EVORD`
`static int`	`GRLEX`
`static int`	`IGRLEX`
`static int`	`INVLEX`
`static int`	`ITDEGLEX`
`static int`	`LEX`
`static int`	`MAX_EVORD`
`static int`	`MIN_EVORD`
`static int`	`REVILEX`
`static int`	`REVITDEG`
`static int`	`REVITDG`
`static int`	`REVLEX`
`static int`	`REVTDEG`
`boolean`	`TOP`	Termorders for modules: TOP or POT.

Constructor Summary

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

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`TermOrder`	`blockOrder(int s)`	Create block term order at split index.
`TermOrder`	`blockOrder(int s, int len)`	Create block term order at split index.
`TermOrder`	`blockOrder(int s, TermOrder t)`	Create block term order at split index.
`TermOrder`	`blockOrder(int s, TermOrder t, int len)`	Create block term order at split index.
`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`	`extend(int r, int k, boolean top)`	Extend variables.
`TermOrder`	`extendLower(int r, int k)`	Extend lower variables.
`TermOrder`	`extendLower(int r, int k, boolean top)`	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`	`getSize()`	Get the exponent vector size.
`int`	`getSplit()`	Get the split index.
`TermOrder.EVComparator`	`getSugarComparator()`	Get the sugar order comparator.
`long[][]`	`getWeight()`	Get the weight array.
`int`	`hashCode()`	Hash code.
`boolean`	`isSplit()`	Test if this term order is a split order.
`static long[]`	`longArrayPermutation(java.util.List<java.lang.Integer> P, long[] a)`	Permutation of a long array.
`TermOrder`	`permutation(java.util.List<java.lang.Integer> P)`	Permutation of the termorder.
`TermOrder`	`reverse()`	Reverse variables.
`TermOrder`	`reverse(boolean partial)`	Reverse variables.
`static TermOrder`	`reverseWeight(long[][] w)`	Weight TermOrder with reversed weight vectors.
`static int`	`revert(int evord)`	Revert exponent order.
`java.lang.String`	`toScript()`	String representation of TermOrder.
`java.lang.String`	`toScriptOrder(int ev)`	Script and String representation of TermOrder name.
`java.lang.String`	`toScriptPlain()`	Script representation of TermOrder without prefix and weight matrix.
`java.lang.String`	`toString()`	String representation of TermOrder.
`java.lang.String`	`toStringPlain()`	String representation of TermOrder without prefix and weight matrix.
`java.lang.String`	`weightToScript()`	Script representation of weight matrix.
`java.lang.String`	`weightToString()`	String representation of weight matrix.

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
  - MIN_EVORD
```
public static final int MIN_EVORD
```
    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
  - ITDEGLEX
```
public static final int ITDEGLEX
```
    See Also:
    
    Constant Field Values
  - REVITDEG
```
public static final int REVITDEG
```
    See Also:
    
    Constant Field Values
  - MAX_EVORD
```
public static final int MAX_EVORD
```
    See Also:
    
    Constant Field Values
  - DEFAULT_EVORD
```
public static final int DEFAULT_EVORD
```
    See Also:
    
    Constant Field Values
  - TOP
```
public final boolean TOP
```
    Termorders for modules: TOP or POT. POT: position over term (default) TOP: term over position (new)
- 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 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.
  - TermOrder
```
public TermOrder(int ev1,
                 int ev2,
                 int r,
                 int split,
                 boolean top)
```
    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.
    
    top - module termorder, if true, default false.
- Method Detail
  - isSplit
```
public boolean isSplit()
```
    Test if this term order is a split order.
    
    Returns:
    
    true if this is a split term order, else false.
  - blockOrder
```
public TermOrder blockOrder(int s)
```
    Create block term order at split index.
    
    Parameters:
    
    s - split index.
    
    Returns:
    
    block TermOrder with split index.
  - blockOrder
```
public TermOrder blockOrder(int s,
                            int len)
```
    Create block term order at split index.
    
    Parameters:
    
    s - split index.
    
    len - length of ExpVectors to compare
    
    Returns:
    
    block TermOrder with split index.
  - blockOrder
```
public TermOrder blockOrder(int s,
                            TermOrder t)
```
    Create block term order at split index.
    
    Parameters:
    
    s - split index.
    
    t - second term order.
    
    Returns:
    
    block TermOrder with split index.
  - blockOrder
```
public TermOrder blockOrder(int s,
                            TermOrder t,
                            int len)
```
    Create block term order at split index.
    
    Parameters:
    
    s - split index.
    
    t - second term order.
    
    len - length of ExpVectors to compare
    
    Returns:
    
    block TermOrder with split index.
  - 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.
  - getSize
```
public int getSize()
```
    Get the exponent vector size. Note: can be INTEGER.MAX_VALUE.
    
    Returns:
    
    size.
  - 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 matrix.
    
    Returns:
    
    string representation of weight matrix.
  - weightToScript
```
public java.lang.String weightToScript()
```
    Script representation of weight matrix.
    
    Returns:
    
    script representation of weight matrix.
  - toScript
```
public java.lang.String toScript()
```
    String representation of TermOrder.
    
    Returns:
    
    script representation of TermOrder.
  - toString
```
public java.lang.String toString()
```
    String representation of TermOrder.
    
    Overrides:
    
    toString in class java.lang.Object
    
    See Also:
    
    Object.toString()
  - toStringPlain
```
public java.lang.String toStringPlain()
```
    String representation of TermOrder without prefix and weight matrix.
  - toScriptPlain
```
public java.lang.String toScriptPlain()
```
    Script representation of TermOrder without prefix and weight matrix.
  - toScriptOrder
```
public java.lang.String toScriptOrder(int ev)
```
    Script and String representation of TermOrder name.
  - extend
```
public TermOrder extend(int r,
                        int k)
```
    Extend variables. Used e.g. in module embedding. Extend TermOrder by k elements. Note: Use POT module term order.
    
    Parameters:
    
    r - current number of variables.
    
    k - number of variables to extend.
    
    Returns:
    
    extended TermOrder.
  - extend
```
public TermOrder extend(int r,
                        int k,
                        boolean top)
```
    Extend variables. Used e.g. in module embedding. Extend TermOrder by k elements. Note: Now TOP and POT orders are distinguished.
    
    Parameters:
    
    r - current number of variables.
    
    k - number of variables to extend.
    
    top - true for TOP term order, false for POT term order.
    
    Returns:
    
    extended TermOrder.
  - extendLower
```
public TermOrder extendLower(int r,
                             int k)
```
    Extend lower variables. Extend TermOrder by k elements. Note: Use POT module term order.
    
    Parameters:
    
    r - current number of variables.
    
    k - number of variables to extend.
    
    Returns:
    
    extended TermOrder.
  - extendLower
```
public TermOrder extendLower(int r,
                             int k,
                             boolean top)
```
    Extend lower variables. Extend TermOrder by k elements. Note: Now TOP and POT orders are distinguished.
    
    Parameters:
    
    r - current number of variables.
    
    k - number of variables to extend.
    
    top - true for TOP term order, false for POT term order.
    
    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 partially 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.
  - longArrayPermutation
```
public static long[] longArrayPermutation(java.util.List<java.lang.Integer> P,
                                          long[] a)
```
    Permutation of a long array.
    
    Parameters:
    
    a - array of long.
    
    P - permutation.
    
    Returns:
    
    P(a).
  - permutation
```
public TermOrder permutation(java.util.List<java.lang.Integer> P)
```
    Permutation of the termorder.
    
    Parameters:
    
    P - permutation.
    
    Returns:
    
    P(a).
  - reverseWeight
```
public static TermOrder reverseWeight(long[][] w)
```
    Weight TermOrder with reversed weight vectors.
    
    Parameters:
    
    w - weight matrix
    
    Returns:
    
    TermOrder with reversed weight vectors

Class TermOrder

Nested Class Summary

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

LEX

MIN_EVORD

INVLEX

GRLEX

IGRLEX

REVLEX

REVILEX

REVTDEG

REVITDG

ITDEGLEX

REVITDEG

MAX_EVORD

DEFAULT_EVORD

TOP

Constructor Detail

TermOrder

TermOrder

TermOrder

TermOrder

TermOrder

TermOrder

Method Detail

isSplit

blockOrder

blockOrder

blockOrder

blockOrder

getEvord

getEvord2

getSplit

getSize

getWeight

getDescendComparator

getAscendComparator

getSugarComparator

equals

hashCode

weightToString

weightToScript

toScript

toString

toStringPlain

toScriptPlain

toScriptOrder

extend

extend

extendLower

extendLower

contract

reverse

reverse

revert

longArrayPermutation

permutation

reverseWeight