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Indefinite and definite integration of rational functions,
elementary functions (Risch), algebraic functions (Trager),
and special functions.
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Laplace, Fourier, Mellin, and Z transforms and inverse transforms,
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Definite and indefinite summation, infinite products, solution
of recurrence equations, Taylor series, asymptotic expansions, symbolic limits,
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Polynomial arithmetic over finite and algebraic number fields,
including GCDs, resultants, decomposition, factorization, root finding,
Galois groups,
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Symbolic linear algebra: matrix determinant and inverse,
eigenvalues and eigenvectors, Row echelon, Smith, Hermite,
and Jordan canonical forms,
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Solving equations: linear systems, polynomial systems, Grobner bases,
ODE's,
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Specialized packages: finite Groups, number theory, Tensors,
generating functions, geometry, orthogonal polynomials, differential forms,
symmetric functions, graph theory, statistics, etc.