orbital.math
Interface Symbol

All Superinterfaces:

Arithmetic, Normed, Variable

public interface Symbol
extends Arithmetic, Variable

Represents an algebraic or transcendental symbol.

Algebraic or transcendental symbols behave like arithmetic objects, with the exception that the result of an operation may not have a numeric value but require a symbolic representation again.

Variables and constants are symbols, for example. Roots of radicals can sometimes be represented as symbols.

Formally, symbols are elements of a term algebra, which is essentially the free symbolic algebra without relations, see, e.g., ValueFactory.quotient(Arithmetic,orbital.logic.functor.Function) or AlgebraicAlgorithms.reduce(Polynomial,java.util.Collection,java.util.Comparator) for generating relations.

Author:

André Platzer

See Also:

ValueFactory.symbol(String)

Field Summary

static Predicate

isa Checks whether the given arithmetic object is a symbol.

Fields inherited from interface orbital.math.Arithmetic

numerical

Method Summary

boolean	equals(java.lang.Object o)
boolean	equals(java.lang.Object o, Real tolerance) Compares for tolerant equality.
java.lang.String	getSignifier() Get the signifier representing this symbol (the symbol's name).
int	hashCode()

Methods inherited from interface orbital.math.Arithmetic

add, divide, inverse, isOne, isZero, minus, multiply, one, power, scale, subtract, toString, valueFactory, zero

Methods inherited from interface orbital.math.Normed

norm

Methods inherited from interface orbital.logic.trs.Variable

isVariable

Field Detail

isa

static final Predicate isa

Checks whether the given arithmetic object is a symbol.

Method Detail

getSignifier

java.lang.String getSignifier()

Get the signifier representing this symbol (the symbol's name).

See Also:

Symbol.getSignifier()

Preconditions:

true

equals

boolean equals(java.lang.Object o,
               Real tolerance)

Compares for tolerant equality.

Specified by:

equals in interface Arithmetic

tolerance - specifies how much the arithmetic objects may differ to be treated as equal.

Returns:

true if this.equals(o), or if tolerance=∞.

equals

boolean equals(java.lang.Object o)

Overrides:

equals in class java.lang.Object

hashCode

int hashCode()

Overrides:

hashCode in class java.lang.Object

Returns:

getSignifier().hashCode().