Package orbital.math

Defines arithmetic objects and provides mathematical algorithms.

See:
Description

Interface Summary

Arithmetic	Arithmetic is implemented by all arithmetic objects that behave like algebraic numbers in terms of their compositional laws.
Complex	Representation of a complex number a + i*b∈C.
Euclidean	Euclidean ring interface.
Fraction	Representation of a fraction a⁄s ∈ S-1M = MS.
Integer	Representation of an integer number k∈Z.
Matrix	Represents a matrix of any dimension n×m.
Metric	This interface imposes a metric on the objects supported by it.
Normed	This interface imposes a norm on the objects of each class that implements it.
Polynomial	Polynomial p∈R[S] := R(S).
Quotient	Quotient represents an (algebraic) equivalence class ā=ã=[a]∈M/~.
Rational	Representation of a rational number a⁄s ∈ Q.
Real	Representation of a real number a∈R.
Scalar	Abstraction of all scalar arithmetic number objects.
Symbol	Represents an algebraic or transcendental symbol.
Tensor	Represents a tensor t∈Rn0×n1×…×nr-1 of dimensions n0×n1×…×nr-1 and rank r.
UnivariatePolynomial	(Univariate) polynomial p∈R[X].
ValueFactory	Scalar value and arithmetic object value constructor factory.
Vector	Represents a mathematical vector of any dimension n.

Class Summary

AlgebraicAlgorithms	Algebraic algorithms and computer algebra.
ArithmeticFormat	ArithmeticFormat is responsible for formatting and parsing arithmetic objects.
Evaluations	Deprecated. since Orbital1.1 This class is deprecated since its (simple) methods are mere facades for convenience.
LUDecomposition	LUDecomposition class, decomposing A into P∙A = L∙U.
MathUtilities	This class contains basic mathematical utilities.
NumericalAlgorithms	This class contains numerical algorithms.
Stat	This class contains algorithms and utilities for stochastics and statistical mathematics.
Values	Manager for scalar value and arithmetic object value constructor factories.

Error Summary

FactoryConfigurationError

Thrown when a problem with configuration of the factories exists.

Package orbital.math Description

Defines arithmetic objects and provides mathematical algorithms.

Arithmetic objects contained in this package are:

Types of arithmetic objects (or algebraic objects) provided

Group	Class	Value Representation
scalar types	Integer	k ∈ Z
	Rational	a⁄s ∈ Q
	Real	a∈R
	Complex	a + i*b ∈ C
vector space types	Vector<A>	v ∈ An
	Matrix<A>	M ∈ Am×n
	Tensor<A>	t ∈ An1×n2×…×nr
polynomial types	UnivariatePolynomial<R>	p ∈ R[X]
	Polynomial<R,Vector<Integer>>	p ∈ R[X0,...,Xn-1]
	Polynomial<R,S>	p ∈ R[S]
special	Symbol	"x"
	Quotient<A>	ā ∈ A/~
	Fraction<A,S>	a⁄s ∈ S-1A

Here A denotes a set of arbitrary arithmetic objects, R is a ring. Z is the set of integers, Q is the set of rational numers, R is the set of real values, and C is the set of complex numbers. Then the type hierarchy of the arithmetic objects realize the mathematical inclusion Z ⊂ Q ⊂ R ⊂ C

Since our general arithmetic objects are modelled as interfaces to provide a maximum of flexibility, you need factory methods to create an arithmetic object value. The interface ValueFactory is that central factory class which can create arithmetic object values from all kinds of primitive types. And Values is its manager class which also provides a "pluggable value factory implementation" that allow other vendor's implementation of arithmetic objects to be used. Especially, this makes it possible to switch to an implementation with different numerical properties or differing levels of integration of symbolic mathematics. Even switching to implementations with lazy evaluation would be possible.

Mathematical function types are provided in a sub package orbital.math.functional.

See Also:

ValueFactory, orbital.math.functional, orbital.moon.logic.MathExpressionSyntax, Algebraic Structures