What SAGE Can Do
- Computing a Groebner basis is fast because of the SINGULAR computer algebra system.
- Classical ciphers are well supported.
- The notebook is a useful tool for basic math education because of its flexible visualization/output capabilities.
- Basic arithmetic over finite extension fields is fast because of the Givaro library.
- 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.
- 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.