Accumath™

Complete capability lists

Every item is numbered in one continuous list. Items 1–109 are already built. Items 110–230 are still being built for version 1.

109 built · 121 remaining · 230 total 47% of version 1 · updated 2026-09-19

Estimated ship date: January 2, 2027, if early-supporter sales fund the remaining work.

Already built (1–109)

Grouped by area. Numbering is continuous across groups.

Algebra

  1. Polynomial arithmetic
  2. Polynomial factorization
  3. Resultants
  4. Discriminants
  5. Groebner bases
  6. Minimal polynomials
  7. Sparse polynomials
  8. Periodic trig solution families

Matrices (SoftFloat)

  1. Matrix exponential
  2. Matrix logarithm
  3. Matrix square root
  4. Matrix power
  5. Schur form

Calculus

  1. Symbolic differentiation
  2. Differentiation of user-defined functions
  3. Curvilinear gradient
  4. Divergence
  5. Curl
  6. Laplacian
  7. Non-conservative line integrals
  8. Integrating factors
  9. Rational integration (Risch)
  10. Algebraic integration (Risch)
  11. Transcendental integration (Risch)
  12. Heuristic integration
  13. Definite integrals
  14. Contour integrals
  15. Laplace transforms
  16. Fourier transforms
  17. Z transforms
  18. Mellin transforms
  19. Hankel transforms
  20. Distributional transform forms
  21. Convolution
  22. Gosper summation
  23. Zeilberger algorithm
  24. q-Zeilberger
  25. Sister Celine / WZ method
  26. Exact products
  27. Generating functions
  28. Lagrange inversion
  29. Gruntz limits
  30. Oscillatory limits
  31. Taylor series
  32. Laurent series
  33. Asymptotic series
  34. Stirling series
  35. WKB

Differential equations

  1. First-order ODEs
  2. Constant-coefficient second-order ODEs
  3. Kovacic algorithm
  4. Frobenius method
  5. Magnus expansion
  6. Abel equations
  7. Lie symmetries for ODEs
  8. PDE separation of variables
  9. Modal drumhead
  10. One-dimensional method of lines
  11. Linear recurrence solving (Petkovšek)

Special functions

  1. Error function (erf)
  2. Exponential integral
  3. Gamma function
  4. Digamma
  5. Polygamma
  6. Hypergeometric 2F1
  7. Hypergeometric pFq
  8. Bessel J
  9. Bessel Y
  10. Bessel I
  11. Bessel K
  12. Elliptic K
  13. Elliptic E
  14. Elliptic Pi
  15. Riemann zeta
  16. Hurwitz zeta
  17. Polylogarithm
  18. Meijer G

Real algebra

  1. Cylindrical algebraic decomposition (seeded)
  2. Quantifier elimination for closed sentences
  3. Quantifier elimination with one free variable

Numbers and statistics

  1. SoftFloat virtual machine
  2. Parallel SoftFloat batch evaluation
  3. One-dimensional Monte Carlo
  4. Normal distribution (PDF/CDF/quantile/moments)
  5. Exponential distribution
  6. Poisson distribution
  7. Binomial distribution
  8. Gamma distribution
  9. Beta distribution
  10. Uniform distribution
  11. Chi-squared distribution
  12. Student t distribution
  13. F distribution
  14. Numeric descriptive statistics
  15. Welch t-test
  16. ANOVA
  17. Ordinary least squares (OLS)
  18. Robust regression errors
  19. Newey-West errors
  20. Logistic regression
  21. Poisson regression
  22. Probit regression
  23. Exact rational linear regression
  24. Exact rational polynomial regression

Language and intake

  1. Math parser
  2. Expression simplifier
  3. Basic assumptions engine
  4. LaTeX intake / equation library loader
  5. Half a million unique parsed equations in the product library

Still being built (110–230)

Grouped by area. Numbering continues from the built list with no restart.

Language, notebook, and units

  1. Assumption / domain system (real/complex/integer predicates driving simplify/solve)
  2. Piecewise / Abs/Sign complete calculus (diff/int/limit/solve)
  3. accu_book notebook core (document/state/DAG/jobs; display shell follow-on)
  4. LaTeX emitter for matrix (pmatrix), ODEs, assumption annotations
  5. Unit/quantity system with dimensional analysis + offline CODATA conversion tables
  6. Units depth (uncertain quantities, temperature affine, industrial unit packs — offline)
  7. Parallel SoftFloat array evaluation (CPU)

Differential equations and PDEs

  1. 2nd-order linear ODEs with non-UC forcing
  2. Mathieu full functions (ce_n, se_n, characteristic exponent)
  3. 2nd-order linear ODEs with irregular singular points
  4. General time-varying linear ODE systems (dimension greater than 3)
  5. Sturm-Liouville BVPs with variable coefficients; more eigenvalues
  6. Zeilberger order ≥ 4; Franel/Apéry closed forms from telescopers
  7. Multi-index WZ beyond 2 indices
  8. Charpit methods for first-order PDEs
  9. Nonlinear PDEs (Burgers, KdV, Hamilton-Jacobi, eikonal)
  10. Mixed boundary conditions on 2nd-order PDEs
  11. Circular drumhead azimuthal modes m > 0
  12. 2D Method of Lines (parabolic + hyperbolic PDEs)
  13. Multi-dimensional Green's functions and 2D convolution
  14. Higher-order Euler-Lagrange equations
  15. Automated trajectory solving from Euler-Lagrange equations
  16. Kepler two-body solver with anomaly equations
  17. DAE index-0/1 solvers
  18. Stiff / adaptive ODE suites
  19. Delay differential equations
  20. Summation / product algorithms completeness
  21. Risch / heuristic integrator completeness pass

Plotting, notebook desktop, and documents

  1. 2D plotting core (functions, parametric, implicit, contour, density; SoftFloat sampling)
  2. Desktop notebook local-only IPC
  3. OS clipboard + headless PDF/LaTeX generation
  4. 3D plotting (surfaces, parametric, level sets, mesh)
  5. Vector field / stream / quiver + phase-portrait plotting
  6. Plot themes, annotations, dual axes, export (PNG/SVG/PDF via Rust)
  7. Discrete/data plots (scatter, line, bar, histogram)
  8. Region / inequality shading plots
  9. Complex-plane plots (Abs/Arg coloring)
  10. Interactive Manipulate/Dynamic with parameter sliders + real-time plotting
  11. CDF portable interactive documents

Algebra, groups, and geometry

  1. Nullstellensatz Groebner combination matrix recovery
  2. Noncommutative algebra (free algebras, NC polynomials, NC Groebner)
  3. Permutation and matrix groups (actions, orbits, stabilizers)
  4. Finite groups: character tables, homomorphisms, quotients
  5. Lie algebras / representation basics
  6. Algebraic geometry limb (ideals, varieties, primary decomposition hooks)
  7. Puiseux series / plane-curve desingularization
  8. Tensor algebra / index gymnastics
  9. Curved Geometry Engine (v1)
  10. Differential geometry extras (forms, Hodge, exterior calculus)
  11. CAD / real quantifier elimination completeness

Special functions

  1. Clausen functions Cl₂(θ), Cl₃(θ)
  2. Barnes G-function G(z)
  3. ₂F₁ analytic continuation outside the unit disk
  4. Complete elliptic Π (3rd kind) with analytic continuation
  5. Analytic continuation of incomplete elliptic integrals
  6. Inverse Jacobi elliptic functions
  7. Fox H-function
  8. Special-function identity automation
  9. Orthogonal polynomials completeness (Jacobi/Laguerre/Hermite/Chebyshev)
  10. Bessel / Airy / Scorer / Kelvin / Struve / Anger–Weber SoftFloat limbs
  11. Wright ω, generalized Lambert, polylog multi-valued branches
  12. Heun / Lamé / spheroidal wave special ODE functions

Control, signals, and communications

  1. Bilinear transform (s→z plane)
  2. LP→HP, LP→BP, LP→BS frequency transformations
  3. Discrete-time Lyapunov certificate
  4. Classical control depth (root locus, Nichols, Bode/Nyquist, margins, lead/lag)
  5. Kautsky-Nichols robust eigenstructure assignment
  6. Full MIMO state-space design for high-dimensional models
  7. Realistic aircraft dynamics G(s) state space
  8. LQR/LQG/H₂/H∞ synthesis (native SoftFloat)
  9. Model reduction (balanced truncation, Hankel singular values)
  10. System identification (ARX/OE/BJ, subspace ID)
  11. STFT + spectrograms; CWT + DWT wavelets
  12. Signal processing depth (FIR/IIR, resampling, filter banks, Hilbert, cepstrum)
  13. Communications primitives offline (constellations, sync, matched filters)

Physics, geometry computing, and FEM

  1. Lane-Emden polytrope solver
  2. Kerr spinning geodesic integration + Forest-Ruth symplectic integrator
  3. Linearized gravitational waves + metric perturbations
  4. Functional path integrals and measures
  5. Dirac bra-ket operator algebra
  6. Computational geometry (convex hulls, Delaunay/Voronoi, Boolean polygons)
  7. FEM: mesh generation, adaptive refinement, unstructured Poisson/heat/wave/elasticity
  8. PDE method library expansion (spectral, finite-volume, operator splitting)
  9. Moving-boundary / Stefan / free-boundary PDE helpers
  10. Sensitivity / adjoint ODE-PDE
  11. FEM depth (vector elements, mixed methods, nonlinear materials, modal analysis)
  12. FEM multiphysics coupling (thermal–structural, basic Stokes/Poisson)

Statistics, optimization, and learning

  1. More distributions + MLE fitting (Beta, Gamma, Weibull, LogNormal, MVN, Dirichlet, Wishart)
  2. Goodness-of-fit: KS, Anderson-Darling, Shapiro-Wilk
  3. Non-parametric tests: Wilcoxon, Mann-Whitney, Kruskal-Wallis
  4. Survival analysis: Kaplan-Meier, log-rank, Cox
  5. Time series: ARIMA/ARMA + ACF/PACF + STL + Kalman / state-space
  6. Bayesian MCMC: Metropolis-Hastings, Gibbs, HMC/NUTS, ADVI
  7. GLM / nonlinear regression / mixed models
  8. PCA / SVD-stats / clustering / Gaussian mixtures
  9. Design of experiments + ANOVA depth
  10. Nonlinear inequality KKT optimization
  11. Global optimization (simulated annealing, basin-hopping)
  12. Convex optimization (QP/SOCP/SDP — SoftFloat native)
  13. Multiobjective / constrained global optimization
  14. ML framework: neural network primitives + reverse-mode autodiff
  15. 3D tensor product cubature rules
  16. Sparse grid cubature (Smolyak)
  17. Multi-dimensional Monte Carlo with importance sampling

Number theory, graphs, and local data

  1. BSGS discrete logarithm for non-generators
  2. Integer factorization and primality toolkit
  3. Number fields, rings of integers, ideal arithmetic
  4. Algebraic number theory extras
  5. Full secp256k1 scalar point multiplication
  6. Modular forms + elliptic curve arithmetic
  7. L-functions / Dirichlet characters / modular arithmetic toolkit
  8. Diophantine solvers (linear, Pell, selected elliptic Thue)
  9. Graph data structures + algorithms
  10. Graph spectra, Laplacians, random walks, centrality, matching, flows
  11. Combinatorial graph generation + isomorphism helpers
  12. Offline natural-language math parser (local only)
  13. Local offline entity / data store
  14. Local entity store depth (physics/chem/math tables, user ontologies)
  15. Image + audio processing primitives
  16. GPU acceleration for dense SoftFloat arrays (bit-identical only)
  17. Code generation (Rust emission of SoftFloat-evaluated expressions)
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