MathForge v0.8.0 - The speed release

MathForge v0.8.0 is the speed release. Exact computation is many times cheaper, and an independent checker still confirms every answer before it is returned. The core remains pure Python with zero runtime dependencies.

Faster, with every check intact

Call	Input	v0.7.0	v0.8.0	Faster
mf.rref	16 × 16 integer matrix	117 ms	306 µs	383×
mf.det	8 × 8 integer matrix	5.4 ms	114 µs	48×
mf.real_roots	x⁵ − 4x + 2	63 ms	1.3 ms	50×
mf.factor	x¹² − 1	21 ms	1.1 ms	20×
mf.evaluate_algebraic	x³ + 2x at x = ∛2	47 ms	5.1 ms	9.3×
mf.factor_integer	2³² + 1	2.1 ms	55 µs	37×
mf.integer_gcd	1071 and 462	238 µs	2.8 µs	85×
mf.binomial	C(100, 50)	317 µs	6.6 µs	48×
mf.complex_sqrt	√(3 + 4i)	2.7 ms	32 µs	84×
mf.expectation	Binomial(20, 1/3)	2.1 ms	222 µs	9.3×
mf.median	101 integers	15 ms	35 µs	427×
mf.taylor	sin(x)·eˣ to order 6	152 ms	23 ms	6.6×

Medians of three alternating rounds of nine calls on one Windows machine with Python 3.14.6, with MathForge's result caches cleared before every call. Both versions check every answer they return. Timings depend on the machine and the input; they are not guarantees.

What's new

• Exact kernels with their own checkers: integer linear algebra, dense integer polynomials, an integer kernel for factorization and primality, and complex and quadratic-surd arithmetic. Separate checkers in mathforge.certify confirm their answers without rerunning the producer: modular certificates, prime certificates, truncated power series and a counting certificate for medians.
• A lean value path: a value function such as mf.det calls the kernel and its checker directly. Any call it does not handle takes the structured path, so values and errors stay the same.
• A cheaper structured pipeline: Rational fast paths, an inline computation budget, and mathforge.operations inspecting arguments, value and evidence once. Records and bytes are unchanged.
• Area modules from one registry: lazily loaded modules such as mf.ntheory, mf.linalg and mf.stats, generated with the rest of the API from a declarative operation registry.
• Mathematical JSON v6: a packaged schema that rejects a crafted document in milliseconds, and a generic Unevaluated(kind, request, reason) record for a request without a verified answer.
• MCP area tools and mathforge.catalog: 37 tools in total. The thirty v0.7 tools keep their names and input schemas, and mathforge.verify accepts JSON versions 1 through 6.
• Continued fractions: mf.ntheory.continued_fraction, the first v6 operation.

Compatibility

Python 3.11–3.14 and the dependency-free core remain. Every v0.7 operation keeps its name, signature and result. v1–v5 documents keep their bytes and get the same verdicts, except that some checks that ran out of budget in v0.7 now complete. Some inputs just past a resource limit may now succeed, never with a different value. Rational now uses slots, so vars() of one raises TypeError. MathForge 0.7 does not read v6 documents.

Known limitations

integer_gcd and integer_lcm on very large integers, from about 2,000 bits (RSA size) upward, remain comparatively slow, because every result carries an independently checked Bézout certificate. solve_system still uses the v0.7 structured pipeline and will be accelerated in a later version, as will solve on the smallest equations, where that pipeline's fixed cost dominates.

Install

MathForge is not published on PyPI. Install the wheel attached below:

python -m pip install https://github.com/U-C4N/MathForge/releases/download/v0.8.0/mathforge-0.8.0-py3-none-any.whl

The wheel and source distribution are built from the v0.8.0 tag; SHA-256 checksums are included. See the README, the user guide and the changelog.

Validation includes 1,262 automated tests, executable documentation, typing and layering checks, and isolated wheel and sdist installations. CI passed on Linux and Windows with Python 3.11–3.14, with distribution checks also passing on macOS/Python 3.14.