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 Sn,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 nth 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?

 

 

MathTools and its documentation copyright © Bhuvanesh Bhatt (bbhatt1@towson.edu)