Package edu.jas.poly
Class RecSolvablePolynomialRing<C extends RingElem<C>>
- Type Parameters:
C
- coefficient type.
- All Implemented Interfaces:
AbelianGroupFactory<GenPolynomial<GenPolynomial<C>>>
,ElemFactory<GenPolynomial<GenPolynomial<C>>>
,MonoidFactory<GenPolynomial<GenPolynomial<C>>>
,RingFactory<GenPolynomial<GenPolynomial<C>>>
,Serializable
,Iterable<GenPolynomial<GenPolynomial<C>>>
public class RecSolvablePolynomialRing<C extends RingElem<C>>
extends GenSolvablePolynomialRing<GenPolynomial<C>>
RecSolvablePolynomialRing generic recursive solvable polynomial factory
implementing RingFactory and extending GenSolvablePolynomialRing factory.
Factory for n-variate ordered solvable polynomials over solvable polynomial
coefficients. The non-commutative multiplication relations are maintained in
a relation table and the non-commutative multiplication relations between the
coefficients and the variables are maintained in a coefficient-polynomial
relation table. Almost immutable object, except variable names and relation
table contents.
- See Also:
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Field Summary
FieldsModifier and TypeFieldDescriptionfinal RelationTable
<GenPolynomial<C>> The solvable multiplication relations between variables and coefficients.private static final org.apache.logging.log4j.Logger
The constant polynomial 1 for this ring.The constant polynomial 0 for this ring.Fields inherited from class edu.jas.poly.GenSolvablePolynomialRing
table
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Constructor Summary
ConstructorsConstructorDescriptionRecSolvablePolynomialRing
(RingFactory<GenPolynomial<C>> cf, int n) The constructor creates a solvable polynomial factory object with the default term order and commutative relations.RecSolvablePolynomialRing
(RingFactory<GenPolynomial<C>> cf, int n, RelationTable<GenPolynomial<C>> rt) The constructor creates a solvable polynomial factory object with the default term order.RecSolvablePolynomialRing
(RingFactory<GenPolynomial<C>> cf, int n, TermOrder t) The constructor creates a solvable polynomial factory object with the given term order and commutative relations.RecSolvablePolynomialRing
(RingFactory<GenPolynomial<C>> cf, int n, TermOrder t, RelationTable<GenPolynomial<C>> rt) The constructor creates a solvable polynomial factory object with the given term order.RecSolvablePolynomialRing
(RingFactory<GenPolynomial<C>> cf, int n, TermOrder t, String[] v) The constructor creates a solvable polynomial factory object with the given term order and commutative relations.RecSolvablePolynomialRing
(RingFactory<GenPolynomial<C>> cf, int n, TermOrder t, String[] v, RelationTable<GenPolynomial<C>> rt) The constructor creates a solvable polynomial factory object with the given term order.The constructor creates a solvable polynomial factory object with the the same term order, number of variables and variable names as the given polynomial factory, only the coefficient factories differ and the solvable multiplication relations are empty.RecSolvablePolynomialRing
(RingFactory<GenPolynomial<C>> cf, TermOrder t, String[] v) The constructor creates a solvable polynomial factory object with the given term order and commutative relations.RecSolvablePolynomialRing
(RingFactory<GenPolynomial<C>> cf, String[] v) The constructor creates a solvable polynomial factory object with the default term order. -
Method Summary
Modifier and TypeMethodDescriptionvoid
addCoeffRelations
(List<GenPolynomial<GenPolynomial<C>>> rel) Generate the coefficient relation table of the solvable polynomial ring from a polynomial list of relations.void
Generate the coefficient relation table of the solvable polynomial ring from a solvable polynomial list of relations.contract
(int i) Contract variables.Copy polynomial c.static <C extends RingElem<C>>
GenSolvablePolynomialRing<C> Distributive representation as polynomial with all main variables.boolean
Comparison with any other object.extend
(int i) Extend variables.extend
(int i, boolean top) Extend variables.Extend variables.Extend variables.fromInteger
(long a) Get a (constant) RecSolvablePolynomial<C> element from a long valueGet a (constant) RecSolvablePolynomial<C> element from a BigInteger value.getONE()
Get the one element.getZERO()
Get the zero element.int
hashCode()
Hash code for this polynomial ring.boolean
Query if this ring is associative.boolean
Query if this ring is commutative.Parse a solvable polynomial with the use of GenPolynomialTokenizerParse a solvable polynomial with the use of GenPolynomialTokenizerpermutation
(List<Integer> P) Permutation of polynomial ring variables.random
(int n) Random solvable polynomial.random
(int k, int l, int d, float q) Generate a random solvable polynomial.Random solvable polynomial.Random solvable polynomial.reverse()
Reverse variables.reverse
(boolean partial) Reverse variables.toScript()
Get a scripting compatible string representation.toString()
Get the String representation.univariate
(int i) Generate univariate solvable polynomial in a given variable.univariate
(int modv, int i, long e) Generate univariate solvable polynomial in a given variable with given exponent.univariate
(int i, long e) Generate univariate solvable polynomial in a given variable with given exponent.Generate list of univariate polynomials in all variables.univariateList
(int modv) Generate list of univariate polynomials in all variables.univariateList
(int modv, long e) Generate list of univariate polynomials in all variables with given exponent.Get a RecSolvablePolynomial<C> element from an exponent vector.valueOf
(GenPolynomial<C> a) Get a (constant) RecSolvablePolynomial<C> element from a coefficient value.valueOf
(GenPolynomial<C> a, ExpVector e) Get a RecSolvablePolynomial<C> element from a coefficient and an exponent vector.Methods inherited from class edu.jas.poly.GenSolvablePolynomialRing
addRelations, addRelations, addSolvRelations, copy, distribute, recursive
Methods inherited from class edu.jas.poly.GenPolynomialRing
characteristic, charPolynomial, copy, copy, copy, determinant, determinantFromCharPol, extendLower, extendLower, extendLower, fromVector, generators, generators, getComparator, getComparator, getCreations, getGenerators, getONECoefficient, getVars, getZEROCoefficient, isField, isFinite, iterator, newVars, newVars, newVars, newVars, permuteVars, setVars, toScript, traceFromCharPol, univariate, univariate, valueOf, valueOf, varsToString
Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait
Methods inherited from interface edu.jas.structure.ElemFactory
valueOf
Methods inherited from interface java.lang.Iterable
forEach, spliterator
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Field Details
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coeffTable
The solvable multiplication relations between variables and coefficients. -
ZERO
The constant polynomial 0 for this ring. Hides super ZERO. -
ONE
The constant polynomial 1 for this ring. Hides super ONE. -
logger
private static final org.apache.logging.log4j.Logger logger
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Constructor Details
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RecSolvablePolynomialRing
The constructor creates a solvable polynomial factory object with the default term order and commutative relations.- Parameters:
cf
- factory for coefficients of type C.n
- number of variables.
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RecSolvablePolynomialRing
public RecSolvablePolynomialRing(RingFactory<GenPolynomial<C>> cf, int n, RelationTable<GenPolynomial<C>> rt) The constructor creates a solvable polynomial factory object with the default term order.- Parameters:
cf
- factory for coefficients of type C.n
- number of variables.rt
- solvable multiplication relations.
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RecSolvablePolynomialRing
The constructor creates a solvable polynomial factory object with the given term order and commutative relations.- Parameters:
cf
- factory for coefficients of type C.n
- number of variables.t
- a term order.
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RecSolvablePolynomialRing
public RecSolvablePolynomialRing(RingFactory<GenPolynomial<C>> cf, int n, TermOrder t, RelationTable<GenPolynomial<C>> rt) The constructor creates a solvable polynomial factory object with the given term order.- Parameters:
cf
- factory for coefficients of type C.n
- number of variables.t
- a term order.rt
- solvable multiplication relations.
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RecSolvablePolynomialRing
The constructor creates a solvable polynomial factory object with the given term order and commutative relations.- Parameters:
cf
- factory for coefficients of type C.n
- number of variables.t
- a term order.v
- names for the variables.
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RecSolvablePolynomialRing
The constructor creates a solvable polynomial factory object with the given term order and commutative relations.- Parameters:
cf
- factory for coefficients of type C.t
- a term order.v
- names for the variables.
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RecSolvablePolynomialRing
The constructor creates a solvable polynomial factory object with the default term order.- Parameters:
cf
- factory for coefficients of type C.v
- names for the variables.
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RecSolvablePolynomialRing
public RecSolvablePolynomialRing(RingFactory<GenPolynomial<C>> cf, int n, TermOrder t, String[] v, RelationTable<GenPolynomial<C>> rt) The constructor creates a solvable polynomial factory object with the given term order.- Parameters:
cf
- factory for coefficients of type C.n
- number of variables.t
- a term order.v
- names for the variables.rt
- solvable multiplication relations.
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RecSolvablePolynomialRing
The constructor creates a solvable polynomial factory object with the the same term order, number of variables and variable names as the given polynomial factory, only the coefficient factories differ and the solvable multiplication relations are empty.- Parameters:
cf
- factory for coefficients of type C.o
- other solvable polynomial ring.
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Method Details
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addCoeffRelations
Generate the coefficient relation table of the solvable polynomial ring from a polynomial list of relations.- Parameters:
rel
- polynomial list of relations [..., ei, fj, pij, ... ] with ei * fj = pij.
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addSolvCoeffRelations
Generate the coefficient relation table of the solvable polynomial ring from a solvable polynomial list of relations.- Parameters:
rel
- solvable polynomial list of relations [..., ei, fj, pij, ... ] with ei * fj = pij.
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toString
Get the String representation.- Overrides:
toString
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- See Also:
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toScript
Get a scripting compatible string representation.- Specified by:
toScript
in interfaceElemFactory<C extends RingElem<C>>
- Overrides:
toScript
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Returns:
- script compatible representation for this Element.
- See Also:
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equals
Comparison with any other object.- Overrides:
equals
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- See Also:
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hashCode
public int hashCode()Hash code for this polynomial ring.- Overrides:
hashCode
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- See Also:
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getZERO
Get the zero element.- Specified by:
getZERO
in interfaceAbelianGroupFactory<C extends RingElem<C>>
- Overrides:
getZERO
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Returns:
- 0 as RecSolvablePolynomial
.
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getONE
Get the one element.- Specified by:
getONE
in interfaceMonoidFactory<C extends RingElem<C>>
- Overrides:
getONE
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Returns:
- 1 as RecSolvablePolynomial
.
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isCommutative
public boolean isCommutative()Query if this ring is commutative.- Specified by:
isCommutative
in interfaceMonoidFactory<C extends RingElem<C>>
- Overrides:
isCommutative
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Returns:
- true if this ring is commutative, else false.
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isAssociative
public boolean isAssociative()Query if this ring is associative. Test if the relations between the mian variables and the coefficient generators define an associative solvable ring.- Specified by:
isAssociative
in interfaceMonoidFactory<C extends RingElem<C>>
- Overrides:
isAssociative
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Returns:
- true, if this ring is associative, else false.
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valueOf
Get a (constant) RecSolvablePolynomial<C> element from a coefficient value.- Overrides:
valueOf
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
a
- coefficient.- Returns:
- a RecSolvablePolynomial<C>.
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valueOf
Get a RecSolvablePolynomial<C> element from an exponent vector.- Overrides:
valueOf
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
e
- exponent vector.- Returns:
- a RecSolvablePolynomial<C>.
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valueOf
Get a RecSolvablePolynomial<C> element from a coefficient and an exponent vector.- Overrides:
valueOf
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
a
- coefficient.e
- exponent vector.- Returns:
- a RecSolvablePolynomial<C>.
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fromInteger
Get a (constant) RecSolvablePolynomial<C> element from a long value- Specified by:
fromInteger
in interfaceElemFactory<C extends RingElem<C>>
- Overrides:
fromInteger
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
a
- long.- Returns:
- a RecSolvablePolynomial<C>.
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fromInteger
Get a (constant) RecSolvablePolynomial<C> element from a BigInteger value.- Specified by:
fromInteger
in interfaceElemFactory<C extends RingElem<C>>
- Overrides:
fromInteger
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
a
- BigInteger.- Returns:
- a RecSolvablePolynomial<C>.
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random
Random solvable polynomial. Generates a random solvable polynomial with k = 5, l = n, d = (nvar == 1) ? n : 3, q = (nvar == 1) ? 0.7 : 0.3.- Specified by:
random
in interfaceElemFactory<C extends RingElem<C>>
- Overrides:
random
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
n
- number of terms.- Returns:
- a random solvable polynomial.
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random
Random solvable polynomial. Generates a random solvable polynomial with k = 5, l = n, d = (nvar == 1) ? n : 3, q = (nvar == 1) ? 0.7 : 0.3.- Specified by:
random
in interfaceElemFactory<C extends RingElem<C>>
- Overrides:
random
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
n
- number of terms.rnd
- is a source for random bits.- Returns:
- a random solvable polynomial.
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random
Generate a random solvable polynomial.- Overrides:
random
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
k
- bitsize of random coefficients.l
- number of terms.d
- maximal degree in each variable.q
- density of nozero exponents.- Returns:
- a random solvable polynomial.
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random
Random solvable polynomial.- Overrides:
random
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
k
- size of random coefficients.l
- number of terms.d
- maximal degree in each variable.q
- density of nozero exponents.rnd
- is a source for random bits.- Returns:
- a random solvable polynomial.
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copy
Copy polynomial c.- Parameters:
c
-- Returns:
- a copy of c.
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parse
Parse a solvable polynomial with the use of GenPolynomialTokenizer- Specified by:
parse
in interfaceElemFactory<C extends RingElem<C>>
- Overrides:
parse
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
s
- String.- Returns:
- RecSolvablePolynomial from s.
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parse
Parse a solvable polynomial with the use of GenPolynomialTokenizer- Specified by:
parse
in interfaceElemFactory<C extends RingElem<C>>
- Overrides:
parse
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
r
- Reader.- Returns:
- next RecSolvablePolynomial from r.
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univariate
Generate univariate solvable polynomial in a given variable.- Overrides:
univariate
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
i
- the index of the variable.- Returns:
- X_i as solvable univariate polynomial.
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univariate
Generate univariate solvable polynomial in a given variable with given exponent.- Overrides:
univariate
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
i
- the index of the variable.e
- the exponent of the variable.- Returns:
- X_i^e as solvable univariate polynomial.
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univariate
Generate univariate solvable polynomial in a given variable with given exponent.- Overrides:
univariate
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
modv
- number of module variables.i
- the index of the variable.e
- the exponent of the variable.- Returns:
- X_i^e as solvable univariate polynomial.
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univariateList
Generate list of univariate polynomials in all variables.- Overrides:
univariateList
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Returns:
- List(X_1,...,X_n) a list of univariate polynomials.
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univariateList
Generate list of univariate polynomials in all variables.- Overrides:
univariateList
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
modv
- number of module variables.- Returns:
- List(X_1,...,X_n) a list of univariate polynomials.
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univariateList
Generate list of univariate polynomials in all variables with given exponent.- Overrides:
univariateList
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
modv
- number of module variables.e
- the exponent of the variables.- Returns:
- List(X_1^e,...,X_n^e) a list of univariate polynomials.
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extend
Extend variables. Used e.g. in module embedding. Extend number of variables by i.- Overrides:
extend
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
i
- number of variables to extend.- Returns:
- extended solvable polynomial ring factory.
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extend
Extend variables. Used e.g. in module embedding. Extend number of variables by i.- Overrides:
extend
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
i
- number of variables to extend.top
- true for TOP term order, false for POT term order.- Returns:
- extended solvable polynomial ring factory.
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extend
Extend variables. Used e.g. in module embedding. Extend number of variables by length(vn). New variables commute with the exiting variables.- Overrides:
extend
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
vs
- names for extended variables.- Returns:
- extended polynomial ring factory.
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extend
Extend variables. Used e.g. in module embedding. Extend number of variables by length(vn). New variables commute with the exiting variables.- Overrides:
extend
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
vs
- names for extended variables.top
- true for TOP term order, false for POT term order.- Returns:
- extended polynomial ring factory.
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contract
Contract variables. Used e.g. in module embedding. Contract number of variables by i.- Overrides:
contract
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
i
- number of variables to remove.- Returns:
- contracted solvable polynomial ring factory.
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reverse
Reverse variables. Used e.g. in opposite rings.- Overrides:
reverse
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Returns:
- solvable polynomial ring factory with reversed variables.
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reverse
Reverse variables. Used e.g. in opposite rings.- Overrides:
reverse
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
partial
- true for partially reversed term orders.- Returns:
- solvable polynomial ring factory with reversed variables.
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distribute
public static <C extends RingElem<C>> GenSolvablePolynomialRing<C> distribute(RecSolvablePolynomialRing<C> rf) Distributive representation as polynomial with all main variables.- Returns:
- distributive polynomial ring factory.
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permutation
Permutation of polynomial ring variables.- Overrides:
permutation
in classGenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
- Parameters:
P
- permutation.- Returns:
- P(this).
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