Differences between revisions 9 and 10
 ⇤ ← Revision 9 as of 2007-04-16 21:24:47 → Size: 596 Editor: c-67-183-64-183 Comment: ← Revision 10 as of 2007-04-17 08:10:48 → ⇥ Size: 857 Editor: MartinAlbrecht Comment: removed self-advertising, 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

## 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.

## 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.