Extensive Mathematics Capabilities of MuPAD Pro 4
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Library source included
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Powerful Simplify tool allows fine-tuning. Specify
time, designate a rule-base, obtain lists of rules applied and intermediate
expressions computed
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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
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Calculus: Limits; integration; differentiation; series
expansions; integral transforms; differential operators; orthogonal
polynomials; summation; piecewise defined functions
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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.
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Special Functions: Airy and
Whittaker functions, the KummerU confluent hypergeometric function, and the
surd function.
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Assumptions and Properties: Attach properties to identifiers
(properties are integers; reals; intervals; residue classes; relations); check
mathematical properties of identifiers
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Set Theory: Union; Intersection; Cartesian product; power set
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Polynomials: Over arbitrary rings; sparse representation;
gcd; lcm; factorization; Groebner bases
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Linear Optimization: Solve; minimize; maximize; plot linear
and mixed-integer programs
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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
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Combinatorics: Bell, Catalan, and Stirling numbers;
compositions; partitions of numbers; power sets; permutations of lists; subsets;
generators
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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 parameterized distributions; goodness-of-fit tests;
box plot representations of statistical samples
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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
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Lindenmayer Systems: Define and draw fractals by means of
context-free grammars
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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.
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