Overview
The PACE project provides a comprehensive software ecosystem for algebraic computations in engineering applications.
Our software combines high-performance C libraries with user-friendly Julia packages to deliver both efficiency and ease of use. The Julia ecosystem is designed with a two-layer architecture to provide both core functionality and domain-specific applications. The LACE library is also available as a Maple package, and our Julia packages are interfaced with Maple and MATLAB:
- Julia Core Packages - Main integration package and core components
- Julia Application Packages - Domain-specific applications
- Maple Package - LACE for Maple
- Maple/MATLAB Interface - Integration of Julia packages with Maple and MATLAB
- C Libraries - High-performance core libraries
Julia Core Packages
PACE.jl serves as the main integration package that brings together these core components:
Julia interface to the LACE C library - RUR and real solutions of zero-dimensional systems, real root isolation, bivariate systems, interval Newton method and Kantorovich test, elimination ideals, ideals at infinity and saturations for discriminant varieties. It also provides the functions of RS.jl and RS4.jl.
RUR computation of zero-dimensional polynomial systems
Julia Application Packages
Specialized tools for control theory applications leveraging core PACE algorithms
Specialized tools for robotics applications leveraging core PACE algorithms
Maple Package
Maple package for the LACE library - certified real roots of univariate polynomials, RUR and real solutions of zero-dimensional systems, bivariate systems, interval Newton and Kantorovich tests, elimination ideals, ideals at infinity and saturations for discriminant varieties. Also available under the names RealSolving and RS4. Maple 2026, macOS (Apple silicon).
Maple/MATLAB Interface for PACE.jl
C Libraries
Certified solving of polynomial systems - Rational Univariate Representation and real solutions of zero-dimensional systems, isolation and refinement of real roots, bivariate systems - and Newton's method in interval arithmetic, Kantorovich uniqueness test and interval polynomial evaluation, in multiple precision. Used by LACE.jl and LACE for Maple.