Timberlake Software - MuPAD

Library source included
New, more powerful Simplify tool allows fine-tuning. Specify time, designate a rule-base, obtain lists of rules applied and intermediate expressions computed
Solve: Equations and systems of equations; inequalities; ordinary and partial differential equations; linear recurrence relations; linear congruences; polynomial diophantine equations; equations over standard domains (integer; real; complex); equations over abstract algebraic structures
Calculus: Limits; integration; differentiation; series expansions; integral transforms; differential operators; orthogonal polynomials; piecewise defined functions
Linear Algebra: Extended linear algebra library includes Pascal and Vandermonde matrices and their inverses, Toepliz matrices, and linear Toepliz and Vandermonde system solutions, in addition to matrices over arbitrary coefficient rings; determinants; eigenvalues; eigenvectors; canonical forms; divergence; gradient; curl
Numerics: Solve equations and systems of equations; polynomial roots; integration; ODEs; functional calculus for matrices; eigenvalues; eigenvectors; singular value decomposition; FFT; polynomial interpolation; splines; optimization problems. Extended library when the Scilab numerical system is connected to MuPAD Pro 3.
Special Functions: New special functions include Airy and Whittaker functions, the KummerU confluent hypergeometric function, and the surd function.
Assumptions and Properties: Attach properties to identifiers (properties are integers; reals; intervals; residue classes; relations); check mathematical properties of identifiers
Set Theory: Union; Intersection; Cartesian product; power set
Polynomials: Over arbitrary rings; sparse representation; gcd; factorization; Groebner bases
Linear Optimization: Solve; minimize; maximize; plot linear and mixed-integer programs
Number Theory: Now includes Cornacchia's algorithm along with continued fractions; factorization using elliptic curves; Jacobi and Legendre symbol; Euler phi; Euler totient; Mangoldt's; Moebius and Carmichael functions; modular and primitive roots
Combinatorics: Bell, Catalan, and Stirling numbers; compositions; partitions of numbers; powerset; permutations of lists; subsets; generators
Statistics: Bravais-Pearson and Fechner correlation; continuous and discrete distributions; chi square, normal, and T distribution; arithmetic; geometric; harmonic and quadratic mean; linear and non-linear regression; standard and mean deviation; variance, covariance, kurtosis, and k-th moment; random number generators; quartiles; cumulative and probability densities for 16 types of parametrized distributions; goodness-of-fit tests; box plot representations of statistical samples
Networks and Graphs: A new, more general Graph library replaces the Version 2.5 Network library and contains over 60 functions for creating, modifying, and visualizing graphs; computing the maximal flow, minimal cost flow, shortest path, and more
Lindenmayer Systems: Define and draw fractals by means of context-free grammars
Algebraic Structures: Symmetric groups; polynomial rings; matrix rings and groups; product rings; algebraic field extensions; finite fields; and quotient fields. User-created domains extend these structures.