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public interface Polynomial
Polynomial p∈R[S] := R^{(S)}.
R^{(S)} := ⊕_{s∈S} R is the Ralgebra of the magma S over R.
With S=N^{n} these are the multivariate polynomials in n variables. Of course, the multivariate polynomials are polynomials over polynomial rings:
ValueFactory.polynomial(Object)
,
ValueFactory.asPolynomial(Tensor)
,
"N. Bourbaki, Algebra III.2.6: Algebra of a magma, a monoid, a group.",
"N. Bourbaki, Algebra III.2.7: Free algebras."Nested Class Summary 

Nested classes/interfaces inherited from interface orbital.math.functional.Function 

Function.Composite 
Nested classes/interfaces inherited from interface orbital.logic.functor.Functor 

Functor.Specification 
Nested classes/interfaces inherited from interface orbital.logic.functor.Functor 

Functor.Specification 
Field Summary 

Fields inherited from interface orbital.logic.functor.Function 

callTypeDeclaration 
Method Summary  

Polynomial 
add(Polynomial b)

java.lang.Object 
apply(java.lang.Object a)
Evaluate this polynomial at a. 
Integer 
degree()
Get the total degree of this polynomial. 
int[] 
degrees()
Returns the multidegree, i.e., the vector of partial degrees of this polynomial for the individual variables X_{i}. 
int 
degreeValue()
Get the (int value of the) degree of this polynomial. 
Arithmetic 
get(Arithmetic i)
Get the ith coefficient. 
java.lang.Object 
indexSet()
Describes the index magma S of our polynomial ring R[S]. 
java.util.Iterator 
indices()
Returns an iterator over the (relevant) indices. 
java.util.ListIterator 
iterator()
Returns an iterator over all coefficients (up to degree). 
java.util.Iterator 
monomials()
Returns an iterator over our (relevant) monomials, i.e., pairs of (exponent, coefficient). 
Polynomial 
multiply(Polynomial b)
Multiplies two polynomials. 
int 
rank()
Get the rank of this polynomial, i.e., the number of distinct variables. 
Polynomial 
subtract(Polynomial b)

Methods inherited from interface orbital.math.functional.Function 

derive, integrate 
Methods inherited from interface orbital.logic.functor.Functor 

equals, hashCode, toString 
Methods inherited from interface orbital.logic.functor.Functor 

equals, hashCode, toString 
Method Detail 

java.lang.Object indexSet()
The index set specifies what form indices of coefficients have.
Since there usually is no computer representation of the full
index set, this method will only return a description object
that can be compared to other index sets via Object.equals(Object)
.
The precise structure of this object is not defined but, for example, for the polynomial ring R[N^{n}]=R[X_{0},...,X_{n1}] in n variables, it may simply be the integer n.
java.util.Iterator indices()
The order of this iterator is not generally defined, but should be deterministic. Particularly, the iterator may  but need not  be restricted to occurring indices with coefficients ≠0.
java.util.Iterator monomials()
The order of this iterator is not generally defined, but should be deterministic. Particularly, the iterator may  but need not  be restricted to occurring indices with coefficients ≠0.
Arithmetic get(Arithmetic i)
0
if i>deg(this).
S
int rank()
java.lang.UnsupportedOperationException
 if R[S] is not a ring with a meaningful finite rank.Tensor.rank()
Integer degree()
For example, if S=N^{n} then this method returns the total degree deg(this) := max {i := ∑_{j=0,...,n1} i_{j} ¦ i∈N^{n} ∧ a_{i}≠0}. Further, deg(0) < 0
java.lang.UnsupportedOperationException
 if R[S] is not a graded ring with a very meaningful graduation.
By providing this option, implementations are not forced to use trivial graduations if no
meaningful graduation exists.int degreeValue()
degreeValue()
int[] degrees()
For example, if S=N^{n} then this method returns the vector of partial degrees deg_{p}(this) := (max {j ¦ there is an i∈N^{n} with i_{k}=j ∧ a_{i}≠0})_{k=0,...,n1}. Further, deg_p(f)_{k} < 0 iff X_{k} does not occur in f.
java.lang.UnsupportedOperationException
 if R[S] is not a ring with a meaningful finite rank.Tensor.dimensions()
java.util.ListIterator iterator()
java.lang.Object apply(java.lang.Object a)
apply
in interface Function
a
 the index embedding a
:S→(E,⋅), encoded as a Function<S,E>
,
that determines to which element a
(s) to map the index s∈S.a
can also be encoded as a Vector<E>
a
∈E^{n}≅E^{Nn}.
Polynomial add(Polynomial b)
Polynomial subtract(Polynomial b)
Polynomial multiply(Polynomial b)

Orbital library 1.3.0: 11 Apr 2009 

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