596
Comment:

857
removed selfadvertising, added some brief nodes about linear/commutative algebra

Deletions are marked like this.  Additions are marked like this. 
Line 6:  Line 6: 
* Computing a Groebner basis is fast because of the SINGULAR computer algebra system.  
Line 13:  Line 14: 
* 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. 
Line 16:  Line 17: 
* Basic arithmetic over finite extension fields is fast because of the Givaro library. 

Line 22:  Line 25: 
* 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
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