<s>
Axiom	B-Language
is	O
a	O
free	B-Application
,	O
general-purpose	O
computer	B-General_Concept
algebra	I-General_Concept
system	I-General_Concept
.	O
</s>
<s>
Two	O
computer	B-General_Concept
algebra	I-General_Concept
systems	I-General_Concept
named	O
Scratchpad	B-Language
were	O
developed	O
by	O
IBM	O
.	O
</s>
<s>
The	O
first	O
one	O
was	O
started	O
in	O
1965	O
by	O
James	O
Griesmer	O
at	O
the	O
request	O
of	O
Ralph	O
Gomory	O
,	O
and	O
written	O
in	O
Fortran	B-Application
.	O
</s>
<s>
The	O
second	O
Scratchpad	B-Language
,	O
originally	O
named	O
Scratchpad	B-Language
II	O
,	O
was	O
developed	O
from	O
1977	O
on	O
,	O
at	O
Thomas	O
J	O
.	O
Watson	O
Research	O
Center	O
,	O
under	O
the	O
direction	O
of	O
Richard	O
Dimick	O
Jenks	O
.	O
</s>
<s>
Scratchpad	B-Language
II	O
was	O
renamed	O
Axiom	B-Language
when	O
IBM	O
decided	O
,	O
circa	O
1990	O
,	O
to	O
make	O
it	O
a	O
commercial	O
product	O
.	O
</s>
<s>
In	O
2001	O
,	O
it	O
was	O
withdrawn	O
from	O
the	O
market	O
and	O
re-released	O
under	O
the	O
Modified	B-Operating_System
BSD	I-Operating_System
License	I-Operating_System
.	O
</s>
<s>
In	O
2007	O
,	O
Axiom	B-Language
was	O
forked	B-Application
twice	O
,	O
originating	O
two	O
different	O
open-source	B-Application
projects	O
:	O
OpenAxiom	B-Language
and	O
FriCAS	B-Language
,	O
following	O
"	O
serious	O
disagreement	O
about	O
project	O
goals	O
"	O
.	O
</s>
<s>
The	O
Axiom	B-Language
project	O
continued	O
to	O
be	O
developed	O
by	O
Tim	O
Daly	O
.	O
</s>
<s>
Axiom	B-Language
is	O
a	O
literate	B-Application
program	I-Application
.	O
</s>
<s>
The	O
source	O
code	O
is	O
becoming	O
available	O
in	O
a	O
set	O
of	O
volumes	O
which	O
are	O
available	O
on	O
the	O
axiom-developer.org	O
website	O
.	O
</s>
<s>
The	O
Axiom	B-Language
project	O
has	O
a	O
major	O
focus	O
on	O
providing	O
documentation	O
.	O
</s>
<s>
Recently	O
the	O
project	O
announced	O
the	O
first	O
in	O
a	O
series	O
of	O
instructional	O
videos	O
,	O
which	O
are	O
also	O
available	O
on	O
the	O
axiom-developer.org	O
website	O
.	O
</s>
<s>
The	O
first	O
video	O
provides	O
details	O
on	O
the	O
Axiom	B-Language
information	O
sources	O
.	O
</s>
<s>
The	O
Axiom	B-Language
project	O
focuses	O
on	O
the	O
“	O
30	O
Year	O
Horizon	O
”	O
.	O
</s>
<s>
The	O
primary	O
philosophy	O
is	O
that	O
Axiom	B-Language
needs	O
to	O
develop	O
several	O
fundamental	O
features	O
in	O
order	O
to	O
be	O
useful	O
to	O
the	O
next	O
generation	O
of	O
computational	O
mathematicians	O
.	O
</s>
<s>
Knuth	O
's	O
literate	B-Application
programming	I-Application
technique	O
is	O
used	O
throughout	O
the	O
source	O
code	O
.	O
</s>
<s>
Axiom	B-Language
plans	O
to	O
use	O
proof	O
technology	O
to	O
prove	O
the	O
correctness	O
of	O
the	O
algorithms	O
(	O
such	O
as	O
Coq	B-Application
and	O
ACL2	B-Application
)	O
.	O
</s>
<s>
Axiom	B-Language
uses	O
Docker	B-Language
Containers	O
as	O
part	O
of	O
a	O
continuous	O
release	O
process	O
.	O
</s>
<s>
The	O
latest	O
image	O
is	O
available	O
on	O
any	O
platform	O
using	O
docker	B-Language
and	O
the	O
commands	O
:	O
</s>
<s>
In	O
Axiom	B-Language
,	O
each	O
object	O
has	O
a	O
type	O
.	O
</s>
<s>
Examples	O
of	O
types	O
are	O
mathematical	O
structures	O
(	O
such	O
as	O
rings	O
,	O
fields	O
,	O
polynomials	O
)	O
as	O
well	O
as	O
data	O
structures	O
from	O
computer	O
science	O
(	O
e.g.	O
,	O
lists	O
,	O
trees	O
,	O
hash	B-Algorithm
tables	I-Algorithm
)	O
.	O
</s>
<s>
function	B-Language
overloading	I-Language
)	O
.	O
</s>
<s>
Axiom	B-Language
comes	O
with	O
an	O
extension	O
language	O
called	O
SPAD	O
.	O
</s>
<s>
All	O
the	O
mathematical	O
knowledge	O
of	O
Axiom	B-Language
is	O
written	O
in	O
this	O
language	O
.	O
</s>
<s>
Within	O
the	O
interpreter	O
environment	O
,	O
Axiom	B-Language
uses	O
type	O
inference	O
and	O
a	O
heuristic	O
algorithm	O
to	O
make	O
explicit	O
type	O
annotations	O
mostly	O
unnecessary	O
.	O
</s>
<s>
It	O
also	O
has	O
a	O
specialized	O
interaction	O
mode	O
for	O
Emacs	B-Application
,	O
as	O
well	O
as	O
a	O
plugin	O
for	O
the	O
TeXmacs	B-Application
editor	O
.	O
</s>
<s>
Axiom	B-Language
has	O
an	O
implementation	O
of	O
the	O
Risch	O
algorithm	O
for	O
elementary	O
integration	O
,	O
which	O
was	O
done	O
by	O
Manuel	O
Bronstein	O
and	O
Barry	O
Trager	O
.	O
</s>
