jgb: Java Gröbner Basis Computation Library

jgb is a Java-based symbolic algebra library focused on polynomial computation. It includes several algorithms for computing Gröbner bases, various monomial orderings, polynomial ring operations, and polynomial generation tools.

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Requirements

• Java 21 or later
• No external dependencies (pure Java)

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Installing

Maven

Add the following dependency to your pom.xml:

<dependency>
  <groupId>io.github.ola-jed.jgb</groupId>
  <artifactId>lib</artifactId>
  <version>0.0.3</version>
</dependency>

Gradle

Add the following to your build.gradle dependencies :

implementation 'io.github.ola-jed.jgb:lib:0.0.3'

Or for the Kotlin DSL (build.gradle.kts):

implementation("io.github.ola-jed.jgb:lib:0.0.3")

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Features

• Polynomial rings over different fields
  • Galois Fields
  • Rationals
  • Reals
  • Complex numbers
• Generation of benchmark polynomial systems (Katsura, Reimer)
• Multiple Gröbner basis algorithms:
  • Buchberger’s Algorithm (with multiple selection strategies)
  • F4 Algorithm
  • Improved F4 Algorithm
  • M4GB Algorithm
• Basis reduction support
• Ordering change with FGLM
• Monomial orderings:
  • Lexicographic
  • Graded Lexicographic
  • Graded Reverse Lexicographic
  • Elimination Ordering
  • Weighted Ordering
• Dense and Sparse polynomial support

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Usage

var ring = new PolynomialRing(GaloisFieldElement.class, new String[]{"x1", "x2", "x3", "x4", "x5"});
var polynomials = KatsuraGenerator.get(4);

// Print input polynomials
for (var poly : polynomials) {
    System.out.println(ring.format(poly));
}

// Compute Gröbner bases using Buchberger’s algorithm with different strategies
var gb = BuchbergerAlgorithm.compute(polynomials, PairSelectionStrategy.DEGREE);

// Reduce the basis
var reduced = GrobnerBasisAlgorithms.reduceGrobnerBasis(gb);

// Use other algorithms
gb = F4Algorithm.compute(polynomials);
gb = ImprovedF4Algorithm.compute(polynomials);
gb = M4GBAlgorithm.compute(polynomials);

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Selection Strategies

When using Buchberger’s algorithm, select the S-pair processing strategy via:

PairSelectionStrategy.FIRST
PairSelectionStrategy.DEGREE
PairSelectionStrategy.NORMAL
PairSelectionStrategy.SUGAR

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Monomial Ordering Setup

Monomial orderings can be configured using:

MonomialOrdering<Real> ordering = new LexOrdering<>();
ordering = new GrlexOrdering<>();
ordering = new GrevlexOrdering<>();
ordering = new EliminationOrdering<>(block1, block2, new GrlexOrdering<>());
ordering = new WeightedOrdering<>(weights);

Each ordering influences how terms are compared and can significantly affect algorithm performance.

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