Detailed Description

kernels, forms, exterior calculus, Hamiltonian flow.

Copyright: 2026 The Dedekind Authors Licensed under the Apache License, Version 2.0.

analysis__Description

Public facade for the current analysis layer.

Exported partitions:

:dual – Dual numbers 𝔻 = a + bε (ε² = 0); forward-mode AD carrier (moved from :numbers at PR #513).
:forms – differential one-forms and covector conversion.
:exterior – wedge products and alternating two-forms.
:hamilton – Poisson brackets and Hamiltonian witnesses.
:kernels – Gaussian and reproducing-kernel primitives.
:ftc – Fundamental Theorem of Calculus bridge hooks.

Note: "L'analyse, ce n'est pas seulement calculer; c'est organiser les structures qui rendent le calcul intelligible." ("Analysis is not only about calculating; it is about organizing the structures that make calculation intelligible.") – Laurent Schwartz, paraphrase

#286 undergraduate calculus: present in part are sequence limits and series, the central-difference derivative, the trapezoidal integral and the FTC as numerical hypotheses; still open are limits and continuity of functions, a differentiability concept, Taylor series, the integral theorems of vector calculus, initial-value problems and the differential algebra.
#272 Denotational Automatic Differentiation: forward-mode AD by Dual (a ring, ε² = 0); still open are DualVector with a directional seed, Jacobians computed from it and their chain rule, the OneForm bridge and nonsmooth derivatives.
#273 Kernel Functions and Feature Maps: the Gaussian kernel; still open are the positive-definiteness witness, the Gabor kernel and the kernel rig (sums and products).