Package edu.jas.poly
Class TermOrderByName
java.lang.Object
edu.jas.poly.TermOrderByName
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
FieldsModifier and TypeFieldDescriptionstatic final TermOrder
Default TermOrder.static final TermOrder
TermOrder name deglex of Sage.static final TermOrder
TermOrder name DegreeLexicographic of Math like CAS.static final TermOrder
TermOrder name DegreeReverseLexicographic of Math like CAS.static final TermOrder
TermOrder name degrevlex of Sage.static final TermOrder
TermOrder name dp of Singular.static final TermOrder
TermOrder name Dp of Singular.static final TermOrder
TermOrder name ds of Singular.static final TermOrder
TermOrder name Ds of Singular.static final TermOrder
TermOrder named GRLEX.static final TermOrder
TermOrder named IGRLEX.static final TermOrder
TermOrder name invlex of Sage.static final TermOrder
TermOrder named INVLEX.static final TermOrder
TermOrder named ITDEGLEX.static final TermOrder
TermOrder name lex of Sage.static final TermOrder
TermOrder named LEX.static final TermOrder
TermOrder name Lexicographic of Math like CAS.private static final org.apache.logging.log4j.Logger
static final TermOrder
TermOrder name lp of Singular.static final TermOrder
TermOrder name ls of Singular.static final TermOrder
TermOrder name NegativeDegreeLexicographic of Math like CAS.static final TermOrder
TermOrder name NegativeDegreeReverseLexicographic of Math like CAS.static final TermOrder
TermOrder name NegativeLexicographic of Math like CAS.static final TermOrder
TermOrder name NegativeReverseLexicographic of Math like CAS.static final TermOrder
TermOrder name negdeglex of Sage.static final TermOrder
TermOrder name negdegrevlex of Sage.static final TermOrder
TermOrder name neglex of Sage.static final TermOrder
TermOrder name negrevlex of Sage.static final TermOrder
TermOrder name ReverseLexicographic of Math like CAS.static final TermOrder
TermOrder named REVILEX.static final TermOrder
TermOrder named REVITDEG.static final TermOrder
TermOrder named REVITDG.static final TermOrder
TermOrder named REVLEX.static final TermOrder
TermOrder named REVTDEG.static final TermOrder
TermOrder name rp of Singular. -
Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionstatic final TermOrder
blockOrder
(TermOrder t1, int s) Construct elimination block TermOrder.static final TermOrder
blockOrder
(TermOrder t1, ExpVector e, int s) Construct elimination block TermOrder.static final TermOrder
blockOrder
(TermOrder t1, TermOrder t2, int s) Construct elimination block TermOrder.static final TermOrder
blockOrder
(TermOrder t1, TermOrder t2, ExpVector e, int s) Construct elimination block TermOrder.(package private) static final long[][]
weightForOrder
(int to, int n) Construct weight for term order.static final long[][]
weightForOrder
(TermOrder to, int n) Construct weight for term order.(package private) static final long[][]
weightForSplitOrder
(int to, int to2, int n, int s) Construct weight for split term order.static final TermOrder
weightOrder
(long[] v) Construct weight TermOrder.static final TermOrder
weightOrder
(long[][] w) Construct weight TermOrder.static final TermOrder
weightOrder
(List<List<Long>> wa) Construct weight TermOrder.
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Field Details
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logger
private static final org.apache.logging.log4j.Logger logger -
LEX
TermOrder named LEX. -
INVLEX
TermOrder named INVLEX. -
GRLEX
TermOrder named GRLEX. -
IGRLEX
TermOrder named IGRLEX. -
REVLEX
TermOrder named REVLEX. -
REVILEX
TermOrder named REVILEX. -
REVTDEG
TermOrder named REVTDEG. -
REVITDG
TermOrder named REVITDG. -
ITDEGLEX
TermOrder named ITDEGLEX. -
REVITDEG
TermOrder named REVITDEG. -
DEFAULT
Default TermOrder. -
Lexicographic
TermOrder name Lexicographic of Math like CAS. -
NegativeLexicographic
TermOrder name NegativeLexicographic of Math like CAS. -
DegreeLexicographic
TermOrder name DegreeLexicographic of Math like CAS. -
NegativeDegreeLexicographic
TermOrder name NegativeDegreeLexicographic of Math like CAS. -
ReverseLexicographic
TermOrder name ReverseLexicographic of Math like CAS. -
DegreeReverseLexicographic
TermOrder name DegreeReverseLexicographic of Math like CAS. -
NegativeReverseLexicographic
TermOrder name NegativeReverseLexicographic of Math like CAS. -
NegativeDegreeReverseLexicographic
TermOrder name NegativeDegreeReverseLexicographic of Math like CAS. -
lex
TermOrder name lex of Sage. -
degrevlex
TermOrder name degrevlex of Sage. -
deglex
TermOrder name deglex of Sage. -
invlex
TermOrder name invlex of Sage. -
neglex
TermOrder name neglex of Sage. -
negdegrevlex
TermOrder name negdegrevlex of Sage. -
negdeglex
TermOrder name negdeglex of Sage. -
negrevlex
TermOrder name negrevlex of Sage. -
lp
TermOrder name lp of Singular. -
dp
TermOrder name dp of Singular. -
Dp
TermOrder name Dp of Singular. -
rp
TermOrder name rp of Singular. -
ls
TermOrder name ls of Singular. -
ds
TermOrder name ds of Singular. -
Ds
TermOrder name Ds of Singular.
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Constructor Details
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TermOrderByName
public TermOrderByName()
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Method Details
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blockOrder
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
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
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
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
Construct weight TermOrder.- Parameters:
v
- weight vector- Returns:
- constructed term order
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weightOrder
Construct weight TermOrder.- Parameters:
w
- weight matrix- Returns:
- constructed term order
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weightOrder
Construct weight TermOrder.- Parameters:
wa
- weight matrix as List- Returns:
- constructed term order
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weightForOrder
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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