This page will survey open source computer algebra systems (OSCAS's). Some of this may appear as columns in CCA.
A computer algebra system (CAS) is a mathematical software package capable of symbolic manipulation. The commercial CAS industry is big business. Few people know more about the CAS industry than Darren McIntyre, VP of Worldwide Sales at Maplesoft. He estimates the worldwide yearly expenditures on computer algebra (buying licenses, employee salaries, and so on) is at least $ 600 million. Clients include not just students and universities, but diverse industries who often find that a CAS is a convenient programming environment to model industrial problems.
For a list maintained by sigsam, see here.
For the list by Oberwolfach, see here.
Another list by the AMS here.
The terrain
Axiom 

CADABRA 
GPL 

open source 

FriCAS 

GAP 
GPL 

GIAC 
GPL 

GINAC 
GPL 

GTYBALT 
GPL 

JScience 
BSD 

LiDIA 
"open source" 

Macaulay2 
GPL 

Magnus 
GPL 

MAS 
"open source" 

Mathemagix 
GPL 

Mathomatic 
LGPL 

Maxima 
GPL 

NTL 
GPL 

Pari 
GPL 

GPL 

Scilab 
"open source" 

Singular 
GPL 

Symmetrica 
public domain 
http://www.algorithm.unibayreuth.de/en/research/SYMMETRICA/ 
SymPy 
BSD 

Yacas 
GPL 
Omitted is CAFE (Computer Algebra and Functional Equations), a group writing a collection of CAS libraries (see CAFE). They appear to be written in Aldor and Maple by (the late) Manuel Bronstein. I (=David Joyner) cannot determine the license (if any) they are released under. (Note added by Marc Mezzarobba: most of them have since been released under free software licenses, as part of the Aldor library and/or of the bronsteincodes archive.) I am also unsure if the "open source" licenses of LiDIA, MAS, and Scilab are compatible with the abovementioned open source definition. Several of these are under very active development and some of these are essentially dead. Two other sources of information are the Computer algebra handbook GKW] and the internet sites CA].
In any case, we see from this table that there are a lot of open source computer algebra systems out there. Some of these are special purpose (such as Symmetrica) and others are general purpose (such as Axiom).