Package edu.jas.poly

Class TermOrderByName

java.lang.Object

edu.jas.poly.TermOrderByName

public class TermOrderByName
extends java.lang.Object

Term order names for ordered polynomials. Defines names for the most used term orders: graded and lexicographical 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. Not all algorithms may work with all term orders since not all are well-founded, so watch your step. Note: Variables in printed JAS polynomial (low, ..., medium, ..., high) Variables in other CAS polynomial (high, ..., medium, ..., low) with low < medium < high. Example: for variables x₁, ..., x_r it is assumed in JAS that x₁ < ... < x_r in other CAS it means x₁ > ... > x_r.

Field Summary

Fields

Modifier and Type	Field	Description
static TermOrder	DEFAULT	Default TermOrder.
static TermOrder	deglex	TermOrder name deglex of Sage.
static TermOrder	DegreeLexicographic	TermOrder name DegreeLexicographic of Math like CAS.
static TermOrder	DegreeReverseLexicographic	TermOrder name DegreeReverseLexicographic of Math like CAS.
static TermOrder	degrevlex	TermOrder name degrevlex of Sage.
static TermOrder	dp	TermOrder name dp of Singular.
static TermOrder	Dp	TermOrder name Dp of Singular.
static TermOrder	ds	TermOrder name ds of Singular.
static TermOrder	Ds	TermOrder name Ds of Singular.
static TermOrder	GRLEX	TermOrder named GRLEX.
static TermOrder	IGRLEX	TermOrder named IGRLEX.
static TermOrder	invlex	TermOrder name invlex of Sage.
static TermOrder	INVLEX	TermOrder named INVLEX.
static TermOrder	ITDEGLEX	TermOrder named ITDEGLEX.
static TermOrder	lex	TermOrder name lex of Sage.
static TermOrder	LEX	TermOrder named LEX.
static TermOrder	Lexicographic	TermOrder name Lexicographic of Math like CAS.
private static org.apache.logging.log4j.Logger	logger
static TermOrder	lp	TermOrder name lp of Singular.
static TermOrder	ls	TermOrder name ls of Singular.
static TermOrder	NegativeDegreeLexicographic	TermOrder name NegativeDegreeLexicographic of Math like CAS.
static TermOrder	NegativeDegreeReverseLexicographic	TermOrder name NegativeDegreeReverseLexicographic of Math like CAS.
static TermOrder	NegativeLexicographic	TermOrder name NegativeLexicographic of Math like CAS.
static TermOrder	NegativeReverseLexicographic	TermOrder name NegativeReverseLexicographic of Math like CAS.
static TermOrder	negdeglex	TermOrder name negdeglex of Sage.
static TermOrder	negdegrevlex	TermOrder name negdegrevlex of Sage.
static TermOrder	neglex	TermOrder name neglex of Sage.
static TermOrder	negrevlex	TermOrder name negrevlex of Sage.
static TermOrder	ReverseLexicographic	TermOrder name ReverseLexicographic of Math like CAS.
static TermOrder	REVILEX	TermOrder named REVILEX.
static TermOrder	REVITDEG	TermOrder named REVITDEG.
static TermOrder	REVITDG	TermOrder named REVITDG.
static TermOrder	REVLEX	TermOrder named REVLEX.
static TermOrder	REVTDEG	TermOrder named REVTDEG.
static TermOrder	rp	TermOrder name rp of Singular.

Constructor Summary

Constructors

Constructor	Description
TermOrderByName()

Method Summary

Modifier and Type	Method	Description
static TermOrder	blockOrder(TermOrder t1, int s)	Construct elimination block TermOrder.
static TermOrder	blockOrder(TermOrder t1, ExpVector e, int s)	Construct elimination block TermOrder.
static TermOrder	blockOrder(TermOrder t1, TermOrder t2, int s)	Construct elimination block TermOrder.
static TermOrder	blockOrder(TermOrder t1, TermOrder t2, ExpVector e, int s)	Construct elimination block TermOrder.
(package private) static long[][]	weightForOrder(int to, int n)	Construct weight for term order.
static long[][]	weightForOrder(TermOrder to, int n)	Construct weight for term order.
(package private) static long[][]	weightForSplitOrder(int to, int to2, int n, int s)	Construct weight for split term order.
static TermOrder	weightOrder(long[] v)	Construct weight TermOrder.
static TermOrder	weightOrder(long[][] w)	Construct weight TermOrder.
static TermOrder	weightOrder(java.util.List<java.util.List<java.lang.Long>> wa)	Construct weight TermOrder.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

logger

private static final org.apache.logging.log4j.Logger logger

LEX

public static final TermOrder LEX

TermOrder named LEX.

INVLEX

public static final TermOrder INVLEX

TermOrder named INVLEX.

GRLEX

public static final TermOrder GRLEX

TermOrder named GRLEX.

IGRLEX

public static final TermOrder IGRLEX

TermOrder named IGRLEX.

REVLEX

public static final TermOrder REVLEX

TermOrder named REVLEX.

REVILEX

public static final TermOrder REVILEX

TermOrder named REVILEX.

REVTDEG

public static final TermOrder REVTDEG

TermOrder named REVTDEG.

REVITDG

public static final TermOrder REVITDG

TermOrder named REVITDG.

ITDEGLEX

public static final TermOrder ITDEGLEX

TermOrder named ITDEGLEX.

REVITDEG

public static final TermOrder REVITDEG

TermOrder named REVITDEG.

DEFAULT

public static final TermOrder DEFAULT

Default TermOrder.

Lexicographic

public static final TermOrder Lexicographic

TermOrder name Lexicographic of Math like CAS.

NegativeLexicographic

public static final TermOrder NegativeLexicographic

TermOrder name NegativeLexicographic of Math like CAS.

DegreeLexicographic

public static final TermOrder DegreeLexicographic

TermOrder name DegreeLexicographic of Math like CAS.

NegativeDegreeLexicographic

public static final TermOrder NegativeDegreeLexicographic

TermOrder name NegativeDegreeLexicographic of Math like CAS.

ReverseLexicographic

public static final TermOrder ReverseLexicographic

TermOrder name ReverseLexicographic of Math like CAS.

DegreeReverseLexicographic

public static final TermOrder DegreeReverseLexicographic

TermOrder name DegreeReverseLexicographic of Math like CAS.

NegativeReverseLexicographic

public static final TermOrder NegativeReverseLexicographic

TermOrder name NegativeReverseLexicographic of Math like CAS.

NegativeDegreeReverseLexicographic

public static final TermOrder NegativeDegreeReverseLexicographic

TermOrder name NegativeDegreeReverseLexicographic of Math like CAS.

lex

public static final TermOrder lex

TermOrder name lex of Sage.

degrevlex

public static final TermOrder degrevlex

TermOrder name degrevlex of Sage.

deglex

public static final TermOrder deglex

TermOrder name deglex of Sage.

invlex

public static final TermOrder invlex

TermOrder name invlex of Sage.

neglex

public static final TermOrder neglex

TermOrder name neglex of Sage.

negdegrevlex

public static final TermOrder negdegrevlex

TermOrder name negdegrevlex of Sage.

negdeglex

public static final TermOrder negdeglex

TermOrder name negdeglex of Sage.

negrevlex

public static final TermOrder negrevlex

TermOrder name negrevlex of Sage.

lp

public static final TermOrder lp

TermOrder name lp of Singular.

dp

public static final TermOrder dp

TermOrder name dp of Singular.

Dp

public static final TermOrder Dp

TermOrder name Dp of Singular.

rp

public static final TermOrder rp

TermOrder name rp of Singular.

ls

public static final TermOrder ls

TermOrder name ls of Singular.

ds

public static final TermOrder ds

TermOrder name ds of Singular.

Ds

public static final TermOrder Ds

TermOrder name Ds of Singular.

Constructor Detail

TermOrderByName

public TermOrderByName()

Method Detail

blockOrder

public static final TermOrder blockOrder(TermOrder t1,
                                         int s)

Construct elimination block TermOrder. Variables {x₁, ..., x _s-1} < {x_s, ..., x_r}

Parameters:

t1 - term order for both blocks

s - split index

Returns:

constructed term order

blockOrder

public static final TermOrder blockOrder(TermOrder t1,
                                         ExpVector e,
                                         int s)

Construct elimination block TermOrder. Variables {x₁, ..., x _s-1} < {x_s, ..., x_r}

Parameters:

t1 - term order for both blocks

e - exponent vector of desired length, r = length(e)

s - split index

Returns:

constructed term order

blockOrder

public static final TermOrder blockOrder(TermOrder t1,
                                         TermOrder t2,
                                         int s)

Construct elimination block TermOrder. Variables {x₁, ..., x _s-1} < {x_s, ..., x_r}

Parameters:

t1 - term order for lower valiables

t2 - term order for higher variables

s - split index

Returns:

constructed term order

blockOrder

public static final TermOrder blockOrder(TermOrder t1,
                                         TermOrder t2,
                                         ExpVector e,
                                         int s)

Construct elimination block TermOrder. Variables {x₁, ..., x _s-1} < {x_s, ..., x_r}

Parameters:

t1 - term order for lower valiables

t2 - term order for higher variables

e - exponent vector of desired length, r = length(e)

s - split index

Returns:

constructed term order

weightOrder

public static final TermOrder weightOrder(long[] v)

Construct weight TermOrder.

Parameters:

v - weight vector

Returns:

constructed term order

weightOrder

public static final TermOrder weightOrder(long[][] w)

Construct weight TermOrder.

Parameters:

w - weight matrix

Returns:

constructed term order

weightOrder

public static final TermOrder weightOrder(java.util.List<java.util.List<java.lang.Long>> wa)

Construct weight TermOrder.

Parameters:

wa - weight matrix as List

Returns:

constructed term order

weightForOrder

public static final long[][] weightForOrder(TermOrder to,
                                            int n)

Construct weight for term order.

Parameters:

to - term order

n - exponent vector size

Returns:

weight matrix

weightForOrder

static final long[][] weightForOrder(int to,
                                     int n)

Construct weight for term order.

Parameters:

to - term order indicator

n - exponent vector size

Returns:

weight matrix

weightForSplitOrder

static final long[][] weightForSplitOrder(int to,
                                          int to2,
                                          int n,
                                          int s)

Construct weight for split term order.

Parameters:

to - first term order indicator

to2 - second term order indicator

n - exponent vector size

s - slpit index

Returns:

weight matrix