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.

Author:

Heinz Kredel

Field Summary

Fields

Modifier and Type	Field and 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	lex TermOrder name lex of Sage.
static TermOrder	LEX TermOrder named LEX.
static TermOrder	Lexicographic TermOrder name Lexicographic of Math like CAS.
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	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 and Description
TermOrderByName()

Method Summary

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

Methods inherited from class java.lang.Object

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

Field Detail

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.

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

weightForOrder

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

Construct weight for INVLEX.

Returns:

weight matrix