<s>
Normaliz	B-Operating_System
is	O
a	O
free	B-Application
computer	B-General_Concept
algebra	I-General_Concept
system	I-General_Concept
developed	O
by	O
Winfried	O
Bruns	O
,	O
Robert	O
Koch	O
(	O
1998	O
–	O
2002	O
)	O
,	O
Bogdam	O
Ichim	O
(	O
2007/08	O
)	O
and	O
Christof	O
Soeger	O
(	O
2009	O
–	O
2016	O
)	O
.	O
</s>
<s>
It	O
is	O
published	O
under	O
the	O
GNU	B-License
General	I-License
Public	I-License
License	I-License
version	O
2	O
.	O
</s>
<s>
Normaliz	B-Operating_System
computes	O
lattice	O
points	O
in	O
rational	O
polyhedra	O
,	O
or	O
,	O
in	O
other	O
terms	O
,	O
solves	O
linear	O
diophantine	O
systems	O
of	O
equations	O
,	O
inequalities	O
,	O
and	O
congruences	O
.	O
</s>
<s>
Normaliz	B-Operating_System
also	O
computes	O
enumerative	O
data	O
,	O
such	O
as	O
multiplicities	O
(	O
volumes	O
)	O
and	O
Hilbert	O
series	O
.	O
</s>
<s>
The	O
kernel	O
of	O
Normaliz	B-Operating_System
is	O
a	O
templated	O
C++	B-Language
class	O
library	O
.	O
</s>
<s>
For	O
multivariate	O
polynomial	O
arithmetic	O
it	O
uses	O
CoCoALib	B-Language
.	O
</s>
<s>
Normaliz	B-Operating_System
has	O
interfaces	O
to	O
several	O
general	O
computer	B-General_Concept
algebra	I-General_Concept
systems	I-General_Concept
:	O
CoCoA	B-Language
,	O
GAP	B-General_Concept
,	O
Macaulay2	B-General_Concept
and	O
Singular	B-General_Concept
.	O
</s>
<s>
It	O
can	O
be	O
used	O
interactively	O
via	O
its	O
Python	B-Language
interface	O
PyNormaliz	O
.	O
</s>
<s>
Jesús	O
A	O
.	O
De_Loera	O
cites	O
Normaliz	B-Operating_System
among	O
his	O
favorite	O
programs	O
for	O
computing	O
Hilbert	O
basis	O
.	O
</s>
