Arithmetic:
matrix algebra with
applications,
matrix normalforms,
complex numbers,
elementary functions,
special functions,
computing with
arbitrary precision floating point numbers,
approximative methods.
Polynomial operations:
factorization,
decomposition,
polynomial real and complex roots,
real algebraic numbers,
Gröbner bases,
ideals ,
non-commutatve ideals,
global and local computations in
commutative algebra.
Calculus:
symbolic integration,
and definte integration,
limits,
formal summation,
Gosper's algorithm,
Zeilberger's algorithm,
Taylor series with lazy evaluation technique
multivariate,
formal power series,
residues,
exterior differential systems,
computation with differential forms
(exterior calculus),
Laplace transforms and
Z_transformations.
Symbolic Solving:
of
algebraic equations and equation systems
with rational solutions,
modular solve,
and ordinary differential equations.
Symmetry analysis for differential
equations in the packages
spde and crack.
Code Generation
of
programs in other languages and
their optimization.
REDUCE Logic Package:
REDLOG.
Geometry:
Geoprover and
Geometry packages.
For more examples please consult the documentation of the REDUCE packages.