JMathematics

A symbolic mathematics library for Java. JMathematics represents mathematical entities exactly and performs formal operations on them — no floating-point approximation unless explicitly requested.

Features

Number types

Complete number hierarchy with exact representations:

Type	Set	Description
NaturalNumber	N	Non-negative integers
IntegerNumber	Z	Strictly negative integers
DecimalNumber	D	Exact decimals (e.g. 3.14)
RationalNumber	Q	Irreducible fractions (e.g. 1/3)
NamedConstant	R	Pi, e
PowerNumber	R	a^b, covers roots
LogarithmNumber	R	log_a(b), ln
TrigonometricNumber	R	sin, cos, tan, arcsin, arccos, arctan
RealExpression	R	Composite expressions (e.g. 2 + sqrt(3))
ComplexNumber	C	a + bi

Every number simplifies to its canonical form at construction: IntegerNumber.of(5) returns a NaturalNumber, RationalNumber.of(1, 4) returns a DecimalNumber (0.25), PowerNumber.of(4, 1/2) returns NaturalNumber(2).

Arithmetic

Cross-type arithmetic via RealNumbers:

RealNumbers.add(NaturalNumber.of(1), RationalNumber.of(1, 3))  // -> 4/3
RealNumbers.multiply(RationalNumber.of(2, 3), RationalNumber.of(3, 4))  // -> 0.5
RealNumbers.negate(NaturalNumber.of(5))  // -> -5
RealNumbers.divide(NaturalNumber.of(7), NaturalNumber.of(3))  // -> 7/3

Rational arithmetic is exact (via BigInteger). Operations with irrationals produce RealExpression when they cannot be simplified further.

Sets

Mathematical sets as first-class objects:

• ClassicalNumberSet — N, Z, D, Q, R, C with sign and zero restrictions (26 predefined variants via NumberSets)
• EnumerationSet — finite sets by enumeration
• IntervalSet — bounded intervals with open/closed bounds
• UnionSet / IntersectionSet — n-ary, with flattening and deduplication
• DifferenceSet — binary (A \ B)

Operations via Sets facade:

Sets.union(setA, setB, setC)
Sets.intersection(setA, setB)
Sets.difference(universe, excluded)  // complement

Formal comparison

Exact comparison between real numbers via RealNumbers.compare():

• Rational vs Rational: cross-multiplication (always decidable)
• PowerNumber vs Rational: raising to a common power

Conventions

• French mathematical convention: positive means >= 0, negative means <= 0
• Formal mathematics: approximate() is only for display purposes, never for mathematical operations

Requirements

• Java 25
• Maven

Build

mvn compile

Test

mvn test

639 tests covering all number types and set operations.

License

LGPL v3