Symbolica Computer Algebra System

Original Article ↗ Hacker News Discussion ↗

Use cases and capabilities

  • Strong focus on huge symbolic expressions, especially rational polynomials with hundreds of MB to ~1 TB size and >100M terms.
  • Key real-world domain: high‑precision quantum field theory / collider physics (Feynman diagrams, QCD beta function), where intermediate expressions blow up then collapse to compact results.
  • Supports streaming large expressions from disk and combining terms via external mergesort, echoing “tape drive” algorithms for big data.
  • Also used for complex but comparatively small systems (e.g., 6 linear equations leading to ~80KB expressions), where simplification speed is the differentiator.
  • Provides polynomial tools (Groebner bases, GCD, elimination via lex order/resultants), pattern matching, series expansion, numerical integration, and a general expression system; ODE solving is missing.

Performance and comparisons

  • Multiple reports that it is significantly faster and more compact than SymPy and Maxima on some tasks; a referenced paper claims ~10× speed and ~60× less memory than Maxima for certain polynomial problems.
  • Some users note similarities in motivation to earlier CAS efforts that replaced slower systems in physics research.
  • Compared to Mathematica/Sage, Symbolica aims to be a fast embeddable library rather than a full ecosystem; some claim it outperforms Mathematica on pattern matching and rational polynomial manipulation.

API, language, and UX

  • Python API seen as straightforward but requires explicit variable/function creation; some compare this unfavorably to Mathematica’s very terse syntax.
  • C/C++ interface is currently thin and C‑like; some want idiomatic modern C++ wrappers.
  • Documentation examples had minor issues (typos, missing variable declarations) but were quickly fixed.

Licensing, pricing, and source availability

  • Source‑available but proprietary; students and hobbyists can use it free, professional/academic use requires a license.
  • Current emphasis is on institution‑wide academic licenses; indicative price mentioned around several thousand EUR per year per site.
  • Online license checks and 24‑hour offline keys drew strong criticism, especially from people needing long offline runs; author indicates willingness to relax this.
  • Some argue depending on a proprietary CAS is risky; others say source availability plus small‑author responsiveness mitigates this.
  • Confusion and debate around “open source” vs “source‑available” is explicitly noted.

Naming and ecosystem concerns

  • Name clashes with an unrelated AI startup and general frustration about namespace conflicts in the AI/ML world.