go-symbolic documentation

go-symbolic is the planned home of computer algebra for go-scikit: expressions, polynomials, differentiation, integration, series, limits and solving, as Mathematica’s core offers them, and what Maple adds on top (code generation, algebraic numbers, ODE and PDE solving, triangular decomposition, differential algebra, symbolic random variables, groups and tensors). It is in wave 4, the last of the roadmap, because nearly everything in it waits for the core: the expression DAG, polynomials, GCD and factorisation.

Status: planned (wave 4). The organisation has no library and no release tag. These pages state the scope, the plan and the references each library will be validated against. The plan itself is PLAN.md of go-scikit/roadmap, and the state of each item is in STATUS.md.

Plan

In PLAN.md, wave 4:

• item 18: expression DAG, polynomials over Z, Q and F_p, GCD and factorisation, differentiation, LaTeX through go-tex; then Gröbner bases, integration, series and limits;
• item 19: codegen, right after the core (expression DAG and diff): expressions to Go source with common-subexpression elimination and pluggable targets, C and Fortran emitters as test oracles only;
• item 20: the Maple delta after the core: algnum, modular linear algebra, ode (verifier first) then pde, triangular (regular chains, CAD), diffalg and stats;
• item 21: group (Schreier-Sims) then tensor (index canonicalisation, curvature tensors, Lie algebras).

It builds on the number theory of go-bignum (wave 4, item 17), go-tex for rendering, and go-ndarray kernels for word-size prime-field linear algebra.

The libraries

Every library of the go-scikit family is pure Go (CGO_ENABLED=0), validated against the tool that is the reference of its domain, run as an oracle from Go, and measured against it on one core. None of that is claimed here yet: there is nothing to measure.

What each library’s pages hold