<s>
Macaulay2	B-General_Concept
is	O
a	O
free	B-Application
computer	B-General_Concept
algebra	I-General_Concept
system	I-General_Concept
created	O
by	O
Daniel	O
Grayson	O
(	O
from	O
the	O
University	O
of	O
Illinois	O
at	O
Urbana	O
–	O
Champaign	O
)	O
and	O
Michael	O
Stillman	O
(	O
from	O
Cornell	O
University	O
)	O
for	O
computation	O
in	O
commutative	O
algebra	O
and	O
algebraic	O
geometry	O
.	O
</s>
<s>
Macaulay2	B-General_Concept
is	O
built	O
around	O
fast	O
implementations	O
of	O
algorithms	O
useful	O
for	O
computation	O
in	O
commutative	O
algebra	O
and	O
algebraic	O
geometry	O
.	O
</s>
<s>
This	O
core	O
functionality	O
includes	O
arithmetic	O
on	O
rings	O
,	O
modules	O
,	O
and	O
matrices	O
,	O
as	O
well	O
as	O
algorithms	O
for	O
Gröbner	O
bases	O
,	O
free	B-Application
resolutions	O
,	O
Hilbert	O
series	O
,	O
determinants	O
and	O
Pfaffians	O
,	O
factoring	O
,	O
and	O
similar	O
.	O
</s>
<s>
Nearly	O
200	O
packages	O
are	O
included	O
in	O
the	O
distribution	O
of	O
Macaulay2	B-General_Concept
as	O
of	O
2019	O
,	O
and	O
notable	O
package	O
authors	O
include	O
Craig	O
Huneke	O
and	O
Frank-Olaf	O
Schreyer	O
.	O
</s>
<s>
The	O
Journal	O
of	O
Software	O
for	O
Algebra	O
and	O
Geometry	O
has	O
published	O
numerous	O
packages	O
and	O
programs	O
for	O
Macaulay2	B-General_Concept
.	O
</s>
<s>
Macaulay2	B-General_Concept
has	O
an	O
interactive	O
command-line	B-Application
interface	I-Application
used	O
from	O
the	O
terminal	O
(	O
see	O
)	O
.	O
</s>
<s>
It	O
can	O
also	O
use	O
emacs	B-Application
or	O
GNU	B-Application
TeXmacs	I-Application
as	O
a	O
user	O
interface	O
.	O
</s>
<s>
Macaulay2	B-General_Concept
uses	O
its	O
own	O
interpreted	B-Application
high-level	B-Language
programming	I-Language
language	I-Language
both	O
from	O
the	O
command	B-Application
line	I-Application
and	O
in	O
saved	O
programs	O
.	O
</s>
<s>
This	O
language	O
is	O
intended	O
to	O
be	O
easy	O
to	O
use	O
for	O
mathematicians	O
,	O
and	O
many	O
parts	O
of	O
the	O
system	O
are	O
indeed	O
written	O
in	O
the	O
Macaulay2	B-General_Concept
language	O
.	O
</s>
<s>
The	O
algebraic	O
algorithms	O
that	O
form	O
the	O
core	O
functionality	O
are	O
written	O
in	O
C++	B-Language
for	O
speed	O
.	O
</s>
<s>
The	O
interpreter	B-Application
itself	O
is	O
written	O
in	O
a	O
custom	O
type	O
safety	O
layer	O
over	O
C	B-Language
.	O
Both	O
the	O
system	O
and	O
the	O
programming	O
language	O
are	O
published	O
under	O
the	O
GNU	B-License
General	I-License
Public	I-License
License	I-License
version	O
2	O
or	O
3	O
.	O
</s>
<s>
Using	O
the	O
experience	O
with	O
Macaulay	O
,	O
Grayson	O
and	O
Stillman	O
began	O
work	O
on	O
Macaulay2	B-General_Concept
in	O
1993	O
.	O
</s>
<s>
The	O
Macaulay2	B-General_Concept
language	O
and	O
design	O
has	O
a	O
number	O
of	O
improvements	O
over	O
that	O
of	O
Macaulay	O
,	O
allowing	O
for	O
infinite	O
coefficient	O
rings	O
,	O
new	O
data	O
types	O
,	O
and	O
other	O
useful	O
features	O
.	O
</s>
<s>
Macaulay	O
continued	O
to	O
be	O
updated	O
and	O
used	O
for	O
some	O
time	O
after	O
the	O
1993	O
introduction	O
of	O
Macaulay2	B-General_Concept
.	O
</s>
<s>
The	O
Macaulay	O
webpage	O
currently	O
recommends	O
switching	O
to	O
Macaulay2	B-General_Concept
.	O
</s>
<s>
Macaulay2	B-General_Concept
has	O
been	O
updated	O
regularly	O
since	O
its	O
introduction	O
.	O
</s>
<s>
In	O
a	O
2006	O
interview	O
,	O
Andrei	O
Okounkov	O
cited	O
Macaulay2	B-General_Concept
along	O
with	O
TeX	B-Application
as	O
a	O
successful	O
open-source	B-Application
project	O
used	O
in	O
mathematics	O
and	O
suggested	O
that	O
funding	O
agencies	O
look	O
into	O
and	O
learn	O
from	O
these	O
examples	O
.	O
</s>
<s>
Macaulay2	B-General_Concept
has	O
been	O
cited	O
in	O
over	O
2,600	O
scholarly	O
publications	O
.	O
</s>
