Computational software
From MSCF
There are an enormous number of high quality software systems which can help with mathematical computations and investigations. Many of these systems are available on the windows machines and on the t-machines. In addition, there are some high performance computers available for longer running calculations. Currently, these are available in a manner similar to the t-machine through Dr. Robert Molzon and Dr. Ruriko Yoshida.
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Maple
Maple is a commercial, general computer algebra system. It is quite suited to speeding up preparation for MA1xx courses, and can solve simple systems of equations, differentiate and integrate standard functions, and solve standard differential equations. It typically solves a problem symbolically, but does not remember exceptions to the symbolic solution, so remember to check its answers. Dr. Russell Brown and Dr. Ken Kubota are fond of finding obviously incorrect results from maple (such as integrating a positive function from 0 to 1 and getting a negative answer).
Matlab
Matlab is commercial software designed especially around problems that can be solved with numerical linear algebra. Virtually everything is stored as a sequence of floating point numbers, so there are no exact answers, and no symbolic manipulation. However, there are proven and useful bounds for the error in the answers, so that in many ways the answers returned by matlab are quite reliable.
R
R is open source software for working with statistics and is probably the most highly regarded and most often used piece of software for statistical research. It can also be used for basic statistical calculations as in the STA2xx service courses. Social sciences typically use less powerful, but more friendly software such as SAS and SPSS. Our licensing arrangement for these other packages changes frequently, and usually only applies to the statistics department (and occasionally some social science departments).
GAP
gap is open source software especially suited to working with finite groups, an area of algebra. It has methods for working with lie algebras, graphs, finite geometries, and other algebraic and combinatoric structures.
Singular
Singular is open source software for commutative algebra. Its multivariate polynomial algorithms and implementations are quite often the best available. Singular also allows working with some non-commutative infinite dimensional associative algebras called PBW-algebras, which includes Weyl algebras.
Maculay2
M2 is another open source software package for commutative algebra. It has algorithms in place for many current fads in algebra, and has relatively transparent module and homological algebra support.
Pari/Gp
gp is open source number theory software. It virtually defined the cutting edge of computational algebraic number theory for many years, and has good support for elliptic curves and quadratic forms. It is designed for speed, and so some of its more advanced features are not wrapped in pretty ways. For basic number theory over the rational integers it is very easy to use.
KANT
kash is proprietary number theory software. It provides nicer wrappers for computational algebraic number theory, and makes it easy to work with ideals in number rings and orders. It has some support for function fields as well.
Maxima
Maxima is an open source general computer algebra system. It can be used for much the same purposes as maple, and you can be comfortable publishing scripts and code for it since your audience will also have access to it.
Other software
Some other software can be made available upon request:
