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* SAGE provides interfaces to the mathematical software Axiom, CoCoA, GAP, KASH, Macaulay2, Magma, Maple, Mathematica, Matlab, Maxima, MuPAD, Octave, and Singular.  * SAGE provides interpreter interfaces to Axiom, CoCoA, GAP, KASH, Macaulay2, Magma, Maple, Mathematica, Matlab, Maxima, MuPAD, Octave, and Singular. 
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 interpreter interfaces to 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
padic Numbers