Package edu.jas.poly
Class TermOrderByName
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- edu.jas.poly.TermOrderByName
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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, ..., xr it is assumed in JAS that x1 < ... < xr in other CAS it means x1 > ... > xr.
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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.
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Constructor Summary
Constructors Constructor Description TermOrderByName()
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Method Summary
All Methods Static Methods Concrete Methods 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.
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Field Detail
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logger
private static final org.apache.logging.log4j.Logger logger
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LEX
public static final TermOrder LEX
TermOrder named LEX.
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INVLEX
public static final TermOrder INVLEX
TermOrder named INVLEX.
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GRLEX
public static final TermOrder GRLEX
TermOrder named GRLEX.
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IGRLEX
public static final TermOrder IGRLEX
TermOrder named IGRLEX.
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REVLEX
public static final TermOrder REVLEX
TermOrder named REVLEX.
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REVILEX
public static final TermOrder REVILEX
TermOrder named REVILEX.
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REVTDEG
public static final TermOrder REVTDEG
TermOrder named REVTDEG.
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REVITDG
public static final TermOrder REVITDG
TermOrder named REVITDG.
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ITDEGLEX
public static final TermOrder ITDEGLEX
TermOrder named ITDEGLEX.
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REVITDEG
public static final TermOrder REVITDEG
TermOrder named REVITDEG.
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DEFAULT
public static final TermOrder DEFAULT
Default TermOrder.
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Lexicographic
public static final TermOrder Lexicographic
TermOrder name Lexicographic of Math like CAS.
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NegativeLexicographic
public static final TermOrder NegativeLexicographic
TermOrder name NegativeLexicographic of Math like CAS.
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DegreeLexicographic
public static final TermOrder DegreeLexicographic
TermOrder name DegreeLexicographic of Math like CAS.
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NegativeDegreeLexicographic
public static final TermOrder NegativeDegreeLexicographic
TermOrder name NegativeDegreeLexicographic of Math like CAS.
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ReverseLexicographic
public static final TermOrder ReverseLexicographic
TermOrder name ReverseLexicographic of Math like CAS.
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DegreeReverseLexicographic
public static final TermOrder DegreeReverseLexicographic
TermOrder name DegreeReverseLexicographic of Math like CAS.
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NegativeReverseLexicographic
public static final TermOrder NegativeReverseLexicographic
TermOrder name NegativeReverseLexicographic of Math like CAS.
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NegativeDegreeReverseLexicographic
public static final TermOrder NegativeDegreeReverseLexicographic
TermOrder name NegativeDegreeReverseLexicographic of Math like CAS.
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lex
public static final TermOrder lex
TermOrder name lex of Sage.
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degrevlex
public static final TermOrder degrevlex
TermOrder name degrevlex of Sage.
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deglex
public static final TermOrder deglex
TermOrder name deglex of Sage.
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invlex
public static final TermOrder invlex
TermOrder name invlex of Sage.
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neglex
public static final TermOrder neglex
TermOrder name neglex of Sage.
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negdegrevlex
public static final TermOrder negdegrevlex
TermOrder name negdegrevlex of Sage.
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negdeglex
public static final TermOrder negdeglex
TermOrder name negdeglex of Sage.
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negrevlex
public static final TermOrder negrevlex
TermOrder name negrevlex of Sage.
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lp
public static final TermOrder lp
TermOrder name lp of Singular.
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dp
public static final TermOrder dp
TermOrder name dp of Singular.
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Dp
public static final TermOrder Dp
TermOrder name Dp of Singular.
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rp
public static final TermOrder rp
TermOrder name rp of Singular.
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ls
public static final TermOrder ls
TermOrder name ls of Singular.
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ds
public static final TermOrder ds
TermOrder name ds of Singular.
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Ds
public static final TermOrder Ds
TermOrder name Ds of Singular.
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Method Detail
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blockOrder
public static final TermOrder blockOrder(TermOrder t1, int s)
Construct elimination block TermOrder. Variables {x1, ..., x s-1} < {xs, ..., xr}- Parameters:
t1
- term order for both blockss
- split index- Returns:
- constructed term order
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blockOrder
public static final TermOrder blockOrder(TermOrder t1, ExpVector e, int s)
Construct elimination block TermOrder. Variables {x1, ..., x s-1} < {xs, ..., xr}- Parameters:
t1
- term order for both blockse
- exponent vector of desired length, r = length(e)s
- split index- Returns:
- constructed term order
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blockOrder
public static final TermOrder blockOrder(TermOrder t1, TermOrder t2, int s)
Construct elimination block TermOrder. Variables {x1, ..., x s-1} < {xs, ..., xr}- Parameters:
t1
- term order for lower valiablest2
- term order for higher variabless
- split index- Returns:
- constructed term order
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blockOrder
public static final TermOrder blockOrder(TermOrder t1, TermOrder t2, ExpVector e, int s)
Construct elimination block TermOrder. Variables {x1, ..., x s-1} < {xs, ..., xr}- Parameters:
t1
- term order for lower valiablest2
- term order for higher variablese
- exponent vector of desired length, r = length(e)s
- split index- Returns:
- constructed term order
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weightOrder
public static final TermOrder weightOrder(long[] v)
Construct weight TermOrder.- Parameters:
v
- weight vector- Returns:
- constructed term order
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weightOrder
public static final TermOrder weightOrder(long[][] w)
Construct weight TermOrder.- Parameters:
w
- weight matrix- Returns:
- constructed term order
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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
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weightForOrder
public static final long[][] weightForOrder(TermOrder to, int n)
Construct weight for term order.- Parameters:
to
- term ordern
- exponent vector size- Returns:
- weight matrix
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weightForOrder
static final long[][] weightForOrder(int to, int n)
Construct weight for term order.- Parameters:
to
- term order indicatorn
- exponent vector size- Returns:
- weight matrix
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weightForSplitOrder
static final long[][] weightForSplitOrder(int to, int to2, int n, int s)
Construct weight for split term order.- Parameters:
to
- first term order indicatorto2
- second term order indicatorn
- exponent vector sizes
- slpit index- Returns:
- weight matrix
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