org.matheclipse.core.polynomials

Class ExprTermOrderByName

java.lang.Object

org.matheclipse.core.polynomials.ExprTermOrderByName

public class ExprTermOrderByName
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.

Author:

Heinz Kredel

Field Summary

Fields

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

Constructor Summary

Constructors

Constructor and Description
ExprTermOrderByName()

Method Summary

Modifier and Type	Method and Description
static ExprTermOrder	blockOrder(ExprTermOrder t1, ExprTermOrder t2, ExpVectorLong e, int s) Construct elimination block ExprTermOrder.
static ExprTermOrder	blockOrder(ExprTermOrder t1, ExprTermOrder t2, int s) Construct elimination block ExprTermOrder.
static ExprTermOrder	blockOrder(ExprTermOrder t1, ExpVectorLong e, int s) Construct elimination block ExprTermOrder.
static ExprTermOrder	blockOrder(ExprTermOrder t1, int s) Construct elimination block ExprTermOrder.
static long[][]	weightForOrder(int to, int n) Construct weight for INVLEX.
static ExprTermOrder	weightOrder(long[] v) Construct weight ExprTermOrder.
static ExprTermOrder	weightOrder(long[][] w) Construct weight ExprTermOrder.

Methods inherited from class java.lang.Object

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

Field Detail

LEX

public static final ExprTermOrder LEX

ExprTermOrder named LEX.

INVLEX

public static final ExprTermOrder INVLEX

ExprTermOrder named INVLEX.

GRLEX

public static final ExprTermOrder GRLEX

ExprTermOrder named GRLEX.

IGRLEX

public static final ExprTermOrder IGRLEX

ExprTermOrder named IGRLEX.

REVLEX

public static final ExprTermOrder REVLEX

ExprTermOrder named REVLEX.

REVILEX

public static final ExprTermOrder REVILEX

ExprTermOrder named REVILEX.

REVTDEG

public static final ExprTermOrder REVTDEG

ExprTermOrder named REVTDEG.

REVITDG

public static final ExprTermOrder REVITDG

ExprTermOrder named REVITDG.

ITDEGLEX

public static final ExprTermOrder ITDEGLEX

ExprTermOrder named ITDEGLEX.

REVITDEG

public static final ExprTermOrder REVITDEG

ExprTermOrder named REVITDEG.

DEFAULT

public static final ExprTermOrder DEFAULT

Default ExprTermOrder.

Lexicographic

public static final ExprTermOrder Lexicographic

ExprTermOrder name Lexicographic of Math like CAS.

NegativeLexicographic

public static final ExprTermOrder NegativeLexicographic

ExprTermOrder name NegativeLexicographic of Math like CAS.

DegreeLexicographic

public static final ExprTermOrder DegreeLexicographic

ExprTermOrder name DegreeLexicographic of Math like CAS.

NegativeDegreeLexicographic

public static final ExprTermOrder NegativeDegreeLexicographic

ExprTermOrder name NegativeDegreeLexicographic of Math like CAS.

ReverseLexicographic

public static final ExprTermOrder ReverseLexicographic

ExprTermOrder name ReverseLexicographic of Math like CAS.

DegreeReverseLexicographic

public static final ExprTermOrder DegreeReverseLexicographic

ExprTermOrder name DegreeReverseLexicographic of Math like CAS.

NegativeReverseLexicographic

public static final ExprTermOrder NegativeReverseLexicographic

ExprTermOrder name NegativeReverseLexicographic of Math like CAS.

NegativeDegreeReverseLexicographic

public static final ExprTermOrder NegativeDegreeReverseLexicographic

ExprTermOrder name NegativeDegreeReverseLexicographic of Math like CAS.

lex

public static final ExprTermOrder lex

ExprTermOrder name lex of Sage.

degrevlex

public static final ExprTermOrder degrevlex

ExprTermOrder name degrevlex of Sage.

deglex

public static final ExprTermOrder deglex

ExprTermOrder name deglex of Sage.

invlex

public static final ExprTermOrder invlex

ExprTermOrder name invlex of Sage.

neglex

public static final ExprTermOrder neglex

ExprTermOrder name neglex of Sage.

negdegrevlex

public static final ExprTermOrder negdegrevlex

ExprTermOrder name negdegrevlex of Sage.

negdeglex

public static final ExprTermOrder negdeglex

ExprTermOrder name negdeglex of Sage.

negrevlex

public static final ExprTermOrder negrevlex

ExprTermOrder name negrevlex of Sage.

lp

public static final ExprTermOrder lp

ExprTermOrder name lp of Singular.

dp

public static final ExprTermOrder dp

ExprTermOrder name dp of Singular.

Dp

public static final ExprTermOrder Dp

ExprTermOrder name Dp of Singular.

rp

public static final ExprTermOrder rp

ExprTermOrder name rp of Singular.

ls

public static final ExprTermOrder ls

ExprTermOrder name ls of Singular.

ds

public static final ExprTermOrder ds

ExprTermOrder name ds of Singular.

Ds

public static final ExprTermOrder Ds

ExprTermOrder name Ds of Singular.

Constructor Detail

ExprTermOrderByName

public ExprTermOrderByName()

Method Detail

blockOrder

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

Construct elimination block ExprTermOrder. 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 ExprTermOrder blockOrder(ExprTermOrder t1,
                                             ExpVectorLong e,
                                             int s)

Construct elimination block ExprTermOrder. 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 ExprTermOrder blockOrder(ExprTermOrder t1,
                                             ExprTermOrder t2,
                                             int s)

Construct elimination block ExprTermOrder. 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 ExprTermOrder blockOrder(ExprTermOrder t1,
                                             ExprTermOrder t2,
                                             ExpVectorLong e,
                                             int s)

Construct elimination block ExprTermOrder. 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 ExprTermOrder weightOrder(long[] v)

Construct weight ExprTermOrder.

Parameters:

v - weight vector

Returns:

constructed term order

weightOrder

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

Construct weight ExprTermOrder.

Parameters:

w - weight matrix

Returns:

constructed term order

weightForOrder

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

Construct weight for INVLEX.

Returns:

weight matrix