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| * Computing a Groebner basis is fast because of the SINGULAR computer algebra system. | |
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| * Using the notebook, Timothy Clemans has made an app that shows the calculation of the GCD of a list of numbers using cancellation and an app that given a factorable trinomial where A = 1 a visualization of finding the solution is given. | * The notebook is a useful tool for basic math education because of its flexible visualization/output capabilities. |
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* Basic arithmetic over finite extension fields is fast because of the Givaro library. |
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| == Interfaces == * SAGE provides interfaces to the mathematical software Axiom, CoCoA, GAP, KASH, Macaulay2, Magma, Maple, Mathematica, Matlab, Maxima, MuPAD, Octave, and Singular. * SAGE provides C/C++-library interfaces to NTL, PARI, Linbox, and mwrank. |
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* The reduced row echelon form of e.g. dense 20,000x20,000 matrices over GF(2) can be computed in seconds and 50MB of RAM. * Computation of reduced row echelon forms of sparse matrices is supported. |
What SAGE Can Do
Calculus
Commutative Algebra
- Computing a Groebner basis is fast because of the SINGULAR computer algebra system.
Crypto
- Classical ciphers are well supported.
Elementary Education
- The notebook is a useful tool for basic math education because of its flexible visualization/output capabilities.
Finite Fields
- Basic arithmetic over finite extension fields is fast because of the Givaro library.
Graphical Interface
Group Theory
Interfaces
- SAGE provides interfaces to the mathematical software Axiom, CoCoA, GAP, KASH, Macaulay2, Magma, Maple, Mathematica, Matlab, Maxima, MuPAD, Octave, and Singular.
- SAGE provides C/C++-library interfaces to NTL, PARI, Linbox, and mwrank.
Linear Algebra
- The reduced row echelon form of e.g. dense 20,000x20,000 matrices over GF(2) can be computed in seconds and 50MB of RAM.
- Computation of reduced row echelon forms of sparse matrices is supported.
Number Theory
Numerical Computation
p-adic Numbers