Future plans

· Fix known bugs and limitations

· Bessel K and Y functions for integer n (high priority)

· Update GMP stuff for AMS 2.07/2.08

· More experimental GMP functions

· Nonlinear multivariate local and global optimization

· Merge nSeries and CmplxMap into MathTools

· Include E.W.’s UniWrite in MathTools, and add feature requested by user

· Improved speed for BesselJ for complex arguments

· Return symbolic result for Psi(1,n/4) in terms of çatalan

· IncGamma(n/2,x) and RegGamma(n/2,x), in terms of the error function

· Cosine integral Ci(z), and hyperbolic counterparts for Ci(z) and Si(z)

· Elliptic integrals

· Polylog({n,p},z) should return the Nielsen polylogarithm S_n,p(z)

· More statistical distributions; some inferential and non-parametric statistics

· Exponential smoothing for data

· Higher-order non-homogeneous constant-coefficient recurrence equations

· Systems of recurrence equations

· Most-rapidly-varying (MRV) algorithm for computing limits

· Asymptotic expansions

· Tensor analysis functions for multidimensional arrays

· Series convergence tests

· Roots of polynomials modulo a composite integer using Hensel lifting and the CRT

· Improved support for congruence systems and nonlinear Diophantine equations

· Quantifier elimination using cylindrical algebraic decomposition (CAD)

· Improve RTInt and Horowitz so that they can integrate all rational functions

· Complete Risch and Minimize functions

· Allow ChinRem to take univariate polynomials as arguments

· Generalize PolyQ for multivariate polynomials

· Implement PSLQ with multiple precision to find integer relations
(I implemented it in TI-Basic, but the 14-digit precision is too low)

· Sugarcube selection strategy and basis reduction for Groebner

· Support for trig functions in iSolve

· Series solution of ordinary differential equations

· Multivariate limits

· Inflection points of a function

· LQ, Schur (using QR iteration) and Hessenberg matrix decompositions

· Hermite and Smith normal form for matrices

· Matrix scaling

· More list operations, such as list convolution and correlation

· Linear algebra functions MatDet(), MatInv() and LinSolve() with modulus argument

· Derivatives of special functions

· Multidimensional interpolation

· More filters and discrete transforms for signal processing

· Trigonometric fits for data with regular spacing (using Fourier transform)

· Spline fits

· 3D parametric plots

· 3D vector plots

· 3D matrix plots

· Support for error bars in ListPlot

· Computational geometry

· Lattice reduction to give a reduced basis for a set of vectors (LLL algorithm)

· Improve Hadamard matrix function

· Rosser and Wilkinson matrices

· Default values for MatchQ; function Replace for pattern-based substitution

· Complexity analysis for various types of simplification
(this would work only if the auto-simplification of the AMS were disabled)

· Second-order or higher PDEs and PDE systems, using Lie symmetry analysis, integral transforms, and separation of variables

· Support for integral and integro-differential equations

· Multidimensional finite differences

· More functions for numerical solution of PDEs

· Solvers for stochastic and delay differential equations

· More integral transforms such as the Mellin transform

· Symbolic Laurent series expansions and symbolic residues

· Closed-form n^th derivative, e.g. d(sin(x),x,n) is

· Graph theory

· Differential geometry

· Coulomb wave functions

· StruveL and Weber functions

· Euler numbers

· Lucas polynomials

· Derivatives of the Airy functions

· Improve speed for PermSig

· PowerSet function (combinatorics)

· Sum-of-products and product-of-sums forms (logic)

· Surface, volume and contour integrals

· Implicit representations of parametric curves and surfaces
(transform to a polynomial form, do trig expansion, and use trig identities)

· Wigner 6-j and 9-j symbols for couplings of quantum momentum states

· PolyGCD(poly1,poly2,prime) [multivariate polynomial GCD modulo a prime]

· Heuristic polynomial GCD

· Arithmetic and squarefree factorization over finite fields, such as Galois fields

· Berlekamp factorization (implement nullspace computation mod a prime)

· More finance functions (cash flows, bonds, interest rates, etc.)

· Add some basics on computer algebra to the documentation (ongoing process)

· Optimization of methods used (for speed and size)

· Any suggestions?