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Native Python API

Jacobian provides a deliberately small native-value API for deterministic mathematical computations. It is independent of the MCP transport and does not construct a capability runtime.

from fractions import Fraction

import networkx as nx
import sympy

from jacobian.math import arithmetic, graphs, matrices, polynomials

half = arithmetic.sum_rationals(Fraction(1, 3), Fraction(1, 6))
inverse = matrices.inverse(sympy.Matrix([[1, 2], [3, 4]]))
triangles = graphs.triangle_count(nx.cycle_graph(3))
derivative = polynomials.derivative(sympy.Poly(sympy.Symbol("x") ** 2, sympy.Symbol("x")))

The supported modules and symbols are:

  • jacobian.math.arithmetic: absolute_value, sign, reciprocal, sum_rationals, and quotient;
  • jacobian.math.matrices: rref, inverse, and trace; and
  • jacobian.math.graphs: triangle_count, diameter, and is_eulerian; and
  • jacobian.math.polynomials: derivative, gcdex, and resultant.

Arithmetic functions return Python int or fractions.Fraction values. Matrix functions accept and return SymPy matrices and exact SymPy scalar values. Graph functions accept undirected simple NetworkX Graph objects. Polynomial functions accept and return exact SymPy Poly values or their exact scalar results. Each module's __all__ is the authoritative public symbol manifest; other implementation modules remain internal.

This API shares typed mathematical kernels with the corresponding capability implementations, but it is not a facade over math.run. Capability requests, result contracts, artifacts, provenance, completeness, and verification remain available through the capability runtime and retain their existing wire semantics.