<s>
This	O
is	O
a	O
list	O
of	O
open-source	B-Application
software	I-Application
to	O
be	O
used	O
for	O
high-order	O
mathematical	O
calculations	O
.	O
</s>
<s>
Open-source	B-Application
software	I-Application
in	O
mathematics	O
has	O
become	O
pivotal	O
in	O
education	O
because	O
of	O
the	O
high	O
cost	O
of	O
textbooks	O
.	O
</s>
<s>
A	O
computer	B-General_Concept
algebra	I-General_Concept
system	I-General_Concept
is	O
a	O
type	O
of	O
software	O
set	O
that	O
is	O
used	O
in	O
manipulation	O
of	O
mathematical	O
formulae	O
.	O
</s>
<s>
The	O
principal	O
objective	O
of	O
a	O
computer	B-General_Concept
algebra	I-General_Concept
system	I-General_Concept
is	O
to	O
systematize	O
monotonous	O
and	O
sometimes	O
problematic	O
algebraic	O
manipulation	O
tasks	O
.	O
</s>
<s>
The	O
primary	O
difference	O
between	O
a	O
computer	B-General_Concept
algebra	I-General_Concept
system	I-General_Concept
and	O
a	O
traditional	O
calculator	B-Application
is	O
the	O
ability	O
to	O
deal	O
with	O
equations	O
symbolically	B-Algorithm
rather	O
than	O
numerically	B-General_Concept
.	O
</s>
<s>
The	O
precise	O
uses	O
and	O
capabilities	O
of	O
these	O
systems	O
differ	O
greatly	O
from	O
one	O
system	O
to	O
another	O
,	O
yet	O
their	O
purpose	O
remains	O
the	O
same	O
:	O
manipulation	O
of	O
symbolic	B-Algorithm
equations	I-Algorithm
.	O
</s>
<s>
Computer	B-General_Concept
algebra	I-General_Concept
system	I-General_Concept
often	O
include	O
facilities	O
for	O
graphing	O
equations	O
and	O
provide	O
a	O
programming	O
language	O
for	O
the	O
users	O
 '	O
own	O
procedures	O
.	O
</s>
<s>
Axiom	B-Language
is	O
a	O
general-purpose	O
computer	B-General_Concept
algebra	I-General_Concept
system	I-General_Concept
.	O
</s>
<s>
It	O
has	O
been	O
in	O
development	O
since	O
1971	O
by	O
IBM	O
,	O
and	O
was	O
originally	O
named	O
scratchpad	B-Language
.	O
</s>
<s>
Richard	O
Jenks	O
originally	O
headed	O
it	O
but	O
over	O
the	O
years	O
Barry	O
Trager	O
who	O
then	O
shaped	O
the	O
direction	O
of	O
the	O
scratchpad	B-Language
project	O
took	O
over	O
the	O
project	O
.	O
</s>
<s>
It	O
was	O
eventually	O
sold	O
to	O
the	O
Numerical	B-General_Concept
Algorithms	I-General_Concept
Group	O
(	O
NAG	O
)	O
and	O
was	O
renamed	O
Axiom	B-Language
.	O
</s>
<s>
After	O
a	O
failure	O
to	O
launch	O
as	O
a	O
product	O
,	O
NAG	O
decided	O
to	O
release	O
it	O
as	O
a	O
free	B-Application
software	I-Application
in	O
2001	O
with	O
more	O
than	O
300	O
man-years	O
worth	O
of	O
research	O
involved	O
.	O
</s>
<s>
Axiom	B-Language
is	O
licensed	O
under	O
a	O
Modified	O
BSD	B-Operating_System
license	I-Operating_System
.	O
</s>
<s>
A	O
Computer	B-General_Concept
Algebra	I-General_Concept
System	I-General_Concept
designed	O
for	O
the	O
solution	O
of	O
problems	O
in	O
field	O
theory	O
.	O
</s>
<s>
An	O
unpublished	O
computational	O
program	O
written	O
in	O
Pascal	B-Application
called	O
Abra	O
inspired	O
this	O
open-source	B-Application
software	I-Application
.	O
</s>
<s>
Kespers	O
Peeters	O
then	O
decided	O
to	O
write	O
a	O
similar	O
program	O
in	O
C	B-Language
computing	I-Language
language	I-Language
rather	O
than	O
Pascal	B-Application
,	O
which	O
he	O
renamed	O
Cadabra	B-Language
.	O
</s>
<s>
However	O
,	O
Cadabra	B-Language
has	O
been	O
expanded	O
for	O
a	O
wider	O
range	O
of	O
uses	O
,	O
it	O
is	O
no	O
longer	O
restricted	O
to	O
physicists	O
.	O
</s>
<s>
CoCoA	B-Language
(	O
COmputations	O
in	O
COmmutative	O
Algebra	O
)	O
is	O
open-source	B-Application
software	I-Application
used	O
for	O
computing	O
multivariate	O
polynomials	O
and	O
initiated	O
in	O
1987	O
.	O
</s>
<s>
Originally	O
written	O
in	O
Pascal	B-Application
,	O
CoCoA	B-Language
was	O
later	O
translated	O
into	O
C	B-Language
.	O
</s>
<s>
GAP	B-General_Concept
was	O
initiated	O
by	O
RWTH	O
Aachen	O
University	O
in	O
1986	O
.	O
</s>
<s>
This	O
was	O
the	O
case	O
until	O
in	O
1997	O
when	O
they	O
decided	O
to	O
co-develop	O
GAP	B-General_Concept
further	O
with	O
CIRCA	O
(	O
Centre	O
for	O
Research	O
in	O
Computational	B-Algorithm
Algebra	I-Algorithm
)	O
.	O
</s>
<s>
Unlike	O
MAXIMA	B-Language
and	O
Axiom	B-Language
,	O
GAP	B-General_Concept
is	O
a	O
system	O
for	O
computational	O
discrete	O
algebra	O
with	O
particular	O
emphasis	O
on	O
computational	O
group	O
theory	O
.	O
</s>
<s>
In	O
March	O
2005	O
the	O
GAP	B-General_Concept
Council	O
and	O
the	O
GAP	B-General_Concept
developers	O
have	O
agreed	O
that	O
status	O
and	O
responsibilities	O
of	O
"	O
GAP	B-General_Concept
Headquarters	O
"	O
should	O
be	O
passed	O
to	O
an	O
equal	O
collaboration	O
of	O
a	O
number	O
of	O
"	O
GAP	B-General_Concept
Centres	O
"	O
,	O
where	O
there	O
is	O
permanent	O
staff	O
involvement	O
and	O
an	O
element	O
of	O
collective	O
or	O
organizational	O
commitment	O
,	O
while	O
fully	O
recognizing	O
the	O
vital	O
contributions	O
of	O
many	O
individuals	O
outside	O
those	O
centers	O
.	O
</s>
<s>
Mathics	O
is	O
an	O
open-source	B-Application
GPL3	O
license	O
version	O
of	O
the	O
Wolfram	B-Language
Language	I-Language
.	O
</s>
<s>
This	O
free	B-Application
software	I-Application
had	O
an	O
earlier	O
incarnation	O
,	O
Macsyma	B-Language
.	O
</s>
<s>
In	O
1998	O
,	O
Schelter	O
obtained	O
the	O
permission	O
to	O
release	O
Maxima	B-Language
as	O
open-source	B-Application
software	I-Application
under	O
the	O
GNU	B-License
General	I-License
Public	I-License
license	I-License
and	O
the	O
source	O
code	O
was	O
released	O
later	O
that	O
year	O
.	O
</s>
<s>
Since	O
his	O
passing	O
in	O
2001	O
,	O
a	O
group	O
of	O
Maxima	B-Language
enthusiasts	O
have	O
continued	O
to	O
provide	O
technical	O
support	O
.	O
</s>
<s>
PARI/GP	B-Language
is	O
a	O
computer	B-General_Concept
algebra	I-General_Concept
system	I-General_Concept
that	O
facilitates	O
number-theory	O
computation	O
.	O
</s>
<s>
Originally	O
developed	O
by	O
Henri	O
Cohen	O
et	O
al	O
at	O
Université	O
Bordeaux	O
I	O
,	O
France	O
,	O
it	O
now	O
is	O
GPL	B-License
software	O
.	O
</s>
<s>
The	O
gp	O
interactive	O
shell	O
allows	O
GP-language	O
scripting	O
;	O
the	O
gp2c	O
compiler	O
compiles	O
GP	O
scripts	O
into	O
C	B-Language
;	O
and	O
the	O
PARI	B-Language
C	B-Language
library	O
allows	O
C	B-Language
programs	I-Language
to	O
use	O
PARI/GP	B-Language
functions	O
.	O
</s>
<s>
Sympy	B-Application
is	O
a	O
computer	B-General_Concept
algebra	I-General_Concept
system	I-General_Concept
written	O
in	O
Python	B-Language
.	O
</s>
<s>
Xcas/Giac	O
is	O
an	O
open-source	B-Application
project	O
developed	O
at	O
the	O
Joseph	O
Fourier	O
University	O
of	O
Grenoble	O
since	O
2000	O
.	O
</s>
<s>
Written	O
in	O
C++	B-Language
,	O
maintained	O
by	O
Bernard	O
Parisse	O
's	O
et	O
al	O
.	O
</s>
<s>
and	O
available	O
for	O
Windows	B-Application
,	O
Mac	B-Application
,	O
Linux	B-Application
and	O
many	O
others	O
platforms	O
.	O
</s>
<s>
It	O
has	O
a	O
compatibility	O
mode	O
with	O
Maple	B-Language
,	O
Derive	B-Language
and	O
MuPAD	B-Language
software	O
and	O
TI-89	B-Device
,	O
TI-92	B-Device
and	O
Voyage	O
200	O
calculators	B-Application
.	O
</s>
<s>
The	O
system	O
was	O
chosen	O
by	O
Hewlett-Packard	O
as	O
the	O
CAS	O
for	O
their	O
HP	B-Device
Prime	I-Device
calculator	B-Application
,	O
which	O
utilizes	O
the	O
Giac/Xcas	O
1.1.2	O
engine	O
under	O
a	O
dual-license	O
scheme	O
.	O
</s>
<s>
Geogebra	B-Language
(	O
Geometry	O
and	O
Algebra	O
)	O
-	O
combines	O
geometric	O
objects	O
like	O
circles	O
and	O
graphs	O
of	O
functions	O
with	O
its	O
algebraic	O
representation	O
e.g.	O
</s>
<s>
Numerical	B-General_Concept
analysis	I-General_Concept
is	O
an	O
area	O
of	O
mathematics	O
that	O
creates	O
and	O
analyzes	O
algorithms	O
for	O
obtaining	O
numerical	B-General_Concept
approximations	I-General_Concept
to	O
problems	O
involving	O
continuous	O
variables	O
.	O
</s>
<s>
FreeMat	B-Language
is	O
an	O
alternative	O
to	O
MATLAB	B-Language
.	O
</s>
<s>
The	O
GNU	B-Application
Scientific	I-Application
Library	I-Application
(	O
or	O
GSL	O
)	O
is	O
a	O
software	O
library	O
for	O
numerical	B-General_Concept
computations	I-General_Concept
in	O
applied	O
mathematics	O
and	O
science	O
.	O
</s>
<s>
The	O
GSL	O
is	O
written	O
in	O
C	B-Language
and	O
wrappers	O
are	O
available	O
for	O
other	O
programming	O
languages	O
.	O
</s>
<s>
The	O
GSL	O
is	O
part	O
of	O
the	B-Application
GNU	I-Application
Project	I-Application
and	O
is	O
distributed	O
under	O
the	O
GNU	B-License
General	I-License
Public	I-License
License	I-License
.	O
</s>
<s>
Octave	B-Language
(	O
aka	O
GNU	B-Language
Octave	I-Language
)	O
is	O
an	O
alternative	O
to	O
MATLAB	B-Language
.	O
</s>
<s>
Octave	B-Language
is	O
a	O
high	O
level	O
language	O
with	O
the	O
primary	O
intention	O
in	O
numerical	B-General_Concept
computation	I-General_Concept
.	O
</s>
<s>
Modelica	B-Application
is	O
an	O
object-oriented	O
,	O
declarative	O
,	O
multi-domain	O
modeling	O
language	O
for	O
component-oriented	O
modeling	O
of	O
complex	O
systems	O
including	O
algebraic	O
and	O
differential	O
equations	O
.	O
</s>
<s>
Inspired	O
by	O
MATLAB	B-Language
,	O
Scilab	B-Application
was	O
initiated	O
in	O
the	O
mid-1980s	O
at	O
the	O
INRIA	O
(	O
French	O
national	O
Institute	O
for	O
computer	O
science	O
and	O
control	O
)	O
.	O
</s>
<s>
François	O
Delebecque	O
and	O
Serge	O
Steer	O
developed	O
it	O
and	O
it	O
was	O
released	O
by	O
INRIA	O
in	O
1994	O
as	O
an	O
open-source	B-Application
software	I-Application
.	O
</s>
<s>
Since	O
2008	O
,	O
Scilab	B-Application
has	O
been	O
distributed	O
under	O
the	O
CeCILL	B-License
license	I-License
,	O
which	O
is	O
GPL	B-License
compatible	O
.	O
</s>
<s>
In	O
2010	O
,	O
Scilab	B-Application
Enterprise	O
was	O
founded	O
to	O
provide	O
even	O
more	O
support	O
to	O
the	O
software	O
.	O
</s>
<s>
SciPy	B-Application
is	O
a	O
python	B-Language
programming	I-Language
language	I-Language
library	O
to	O
take	O
advantage	O
of	O
Python	B-Language
's	O
ability	O
to	O
handle	O
large	O
data	O
sets	O
.	O
</s>
<s>
Descriptive	B-General_Concept
statistics	I-General_Concept
involves	O
methods	O
of	O
organizing	O
,	O
picturing	O
and	O
summarizing	O
information	O
from	O
data	O
.	O
</s>
<s>
R	B-Language
Statistics	I-Language
Software	I-Language
,	O
SOFA	B-Language
Statistics	I-Language
,	O
PSPP	B-Language
and	O
JASP	B-Application
are	O
open	B-Application
source	I-Application
software	I-Application
competitors	O
to	O
SPSS	B-Algorithm
,	O
widely	O
used	O
for	O
statistical	O
analysis	O
of	O
sampled	O
data	O
.	O
</s>
<s>
PSPP	B-Language
is	O
maintained	O
by	O
the	B-Application
GNU	I-Application
project	I-Application
.	O
</s>
<s>
SOFA	B-Language
Statistics	I-Language
is	O
addressing	O
beginners	O
with	O
basic	O
features	O
,	O
while	O
GNU-R	B-Language
Statistics	I-Language
Software	I-Language
has	O
a	O
large	O
community	O
that	O
maintains	O
R	B-Language
packages	I-Language
also	O
beyond	O
statistical	O
analysis	O
.	O
</s>
<s>
R	B-Language
is	O
both	O
a	O
language	O
and	O
software	O
used	O
for	O
statistical	B-Algorithm
computing	I-Algorithm
and	O
graphing	O
.	O
</s>
<s>
R	B-Language
was	O
originally	O
developed	O
by	O
Bell	O
Laboratories	O
(	O
Currently	O
known	O
as	O
Lucent	O
Technologies	O
)	O
by	O
John	O
Chambers	O
.	O
</s>
<s>
Since	O
R	B-Language
is	O
largely	O
written	O
in	O
C	B-Language
language	I-Language
,	O
users	O
can	O
use	O
C	B-Language
or	O
C++	B-Language
commands	O
to	O
manipulate	O
R-objects	O
directly	O
.	O
</s>
<s>
Also	O
,	O
R	B-Language
runs	O
on	O
most	O
UNIX	B-Application
platforms	O
.	O
</s>
<s>
R	B-Language
is	O
currently	O
part	O
of	O
the	B-Operating_System
Free	I-Operating_System
Software	I-Operating_System
Foundation	I-Operating_System
GNU	B-Application
project	I-Application
.	O
</s>
<s>
Such	O
software	O
were	O
created	O
with	O
the	O
original	O
intent	O
of	O
providing	O
a	O
math	O
platform	O
that	O
can	O
be	O
compared	O
to	O
proprietary	B-Application
software	I-Application
such	O
as	O
MATLAB	B-Language
and	O
Mathematica	B-Language
.	O
</s>
<s>
They	O
contain	O
multiple	O
other	O
free	B-Application
software	I-Application
and	O
hence	O
have	O
more	O
features	O
than	O
the	O
rest	O
of	O
the	O
software	O
mentioned	O
.	O
</s>
<s>
SageMath	B-Application
is	O
designed	O
partially	O
as	O
a	O
free	O
alternative	O
to	O
the	O
general-purpose	O
mathematics	O
products	O
Maple	B-Language
and	O
MATLAB	B-Language
.	O
</s>
<s>
SageMath	B-Application
comprises	O
a	O
variety	O
of	O
other	O
free	O
packages	O
,	O
with	O
a	O
common	O
interface	B-Application
and	O
language	O
.	O
</s>
<s>
SageMath	B-Application
is	O
developed	O
in	O
Python	B-Language
.	O
</s>
<s>
SageMath	B-Application
was	O
initiated	O
by	O
William	O
Stein	O
,	O
of	O
Harvard	O
University	O
in	O
2005	O
for	O
his	O
personal	O
project	O
in	O
number	O
theory	O
.	O
</s>
<s>
It	O
already	O
consisted	O
of	O
Pari	B-Language
,	O
GAP	B-General_Concept
,	O
Singular	B-General_Concept
and	O
Maxima	B-Language
with	O
an	O
interface	B-Application
that	O
rivals	O
that	O
of	O
Mathematica	B-Language
.	O
</s>
