Mathematics Capabilities of MuPAD Pro 2.5
  • Library source included
  • 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: 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 2.5.
  • 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: 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: Define, edit, and plot; find shortest paths or maximal flows
  • 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.