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A Tour of NTL: Summary of NTL's Main Modules </title>
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<h1>
<p align=center>
A Tour of NTL: Summary of NTL's Main Modules
</p>
</h1>
<p> <hr> <p>
<p>
NTL consists of a number of software modules.
Generally speaking, for each module <tt>foo</tt>, there is
<ul>
<li>
a header
file <tt><NTL/foo.h></tt>, found in subdirectory <tt>include</tt>,
<li>
a documentation file <tt>foo.txt</tt>,
found in subdirectory <tt>doc</tt>,
and
<li>
a source file <tt>foo.c</tt>, found in subdirectory <tt>src</tt>.
</ul>
<p>
Note that all of the header files for NTL modules include the header file
<tt><NTL/tools.h></tt>, and this header file includes
the standard headers
<ul>
<li>
<tt><stdlib.h></tt>,
<li>
<tt><math.h></tt>, and
<li>
<tt><iostream.h></tt>;
</ul>
Moreover,
these are the only standard header files included by NTL header files.
<p>
Also
note that in <a href="tour-stdcxx.html">ISO mode</a>,
<tt><NTL/tools.h></tt> instead includes the standard header files
<ul>
<li>
<tt><cstdlib></tt>,
<li>
<tt><cmath></tt>, and
<li>
<tt><iostream></tt>;
</ul>
moreover, in <a href="tour-stdcxx.html">ISO mode</a>,
the standard library is wrapped in namespace <tt>std</tt>
and NTL is wrapped in namespace <tt>NTL</tt>.
<p>
The documentation file takes the form of a header file,
but stripped of implementation
details and declarations of some of the more esoteric
routines and data structures, and it contains more complete
and usually clearer documentation than in the header file.
<p>
There is a plethora of conversion routines.
These are not documented in any of the individual
documentation files, but rather,
they are all briefly summarized in
<a href="conversions.txt"><tt>conversions.txt</tt></a>.
<p>
The following is a summary of the main NTL modules.
The corresponding documentation file can be obtained by clicking on
the module name.
<p>
<table >
<!-- ----------- GF2.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="GF2.txt"><tt>GF2</tt></a>
</b> <td>
class <tt>GF2</tt>: integers mod 2
<!-- ----------- GF2X.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="GF2X.txt"><tt>GF2X</tt></a>
</b> <td>
class <tt>GF2X</tt>: polynomials over <tt>GF(2)</tt> (much more efficient
than using <tt>zz_pX</tt> with <tt>p=2</tt>);
includes routines for GCDs and minimal polynomials
<!-- ----------- GF2XFactoring.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="GF2XFactoring.txt"><tt>GF2XFactoring</tt></a>
</b> <td>
routines for factoring polynomials over <tt>GF(2)</tt>;
also includes routines for testing for and constructing
irreducible polynomials
<!-- ----------- GF2XVec.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="GF2XVec.txt"><tt>GF2XVec</tt></a>
</b> <td>
class <tt>GF2XVec</tt>: fixed-length vectors of fixed-length <tt>GF2X</tt>s;
less flexible, but more efficient than <tt>vec_GF2X</tt>
<!-- ----------- GF2E.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="GF2E.txt"><tt>GF2E</tt></a>
</b> <td>
class <tt>GF2E</tt>: polynomial extension field/ring over <tt>GF(2)</tt>,
implemented as GF(2)[X]/(P).
<!-- ----------- GF2EX.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="GF2EX.txt"><tt>GF2EX</tt></a>
</b> <td>
class <tt>GF2EX</tt>
class <tt>GF2EX</tt>: polynomials over <tt>GF2E</tt>;
includes routines for modular polynomials arithmetic,
modular composition, minimal and characteristic
polynomials, and interpolation.
<!-- ----------- GF2EXFactoring.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="GF2EXFactoring.txt"><tt>GF2EXFactoring</tt></a>
</b> <td>
routines for factoring polynomials over <tt>GF2E</tt>;
also includes routines for testing for and constructing
irreducible polynomials
<!-- ----------- HNF.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="HNF.txt"><tt>HNF</tt></a>
</b> <td>
routines for computing the Hermite Normal Form
of a lattice
<!-- ----------- LLL.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="LLL.txt"><tt>LLL</tt></a>
</b> <td>
routines for performing lattice basis reduction,
including very fast and robust implementations of the Schnorr-Euchner LLL
and Block Korkin Zolotarev reduction algorithm,
as well as an integer-only reduction algorithm.
Also, there are routines here for computing the kernel
and image of an integer matrix, as well as finding integer
solutions to linear systems of equations over the integers.
<!-- ----------- RR.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="RR.txt"><tt>RR</tt></a>
</b> <td>
class <tt>RR</tt>: arbitrary-precision floating point numbers.
<!-- ----------- ZZ.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="ZZ.txt"><tt>ZZ</tt></a>
</b> <td>
class <tt>ZZ</tt>: arbitrary length integers;
includes routines for GCDs, Jacobi symbols,
modular arithmetic, and primality testing;
also includes small prime generation routines
and in-line routines for single-precision
modular arithmetic
<!-- ----------- ZZVec.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="ZZVec.txt"><tt>ZZVec</tt></a>
</b> <td>
class <tt>ZZVec</tt>: fixed-length vectors of fixed-length <tt>ZZ</tt>s;
less flexible, but more efficient than <tt>vec_ZZ</tt>
<!-- ----------- ZZX.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="ZZX.txt"><tt>ZZX</tt></a>
</b> <td>
class <tt>ZZX</tt>: polynomials over <tt>ZZ</tt>;
includes routines for GCDs, minimal and characteristic
polynomials, norms and traces
<!-- ----------- ZZXFactoring.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="ZZXFactoring.txt"><tt>ZZXFactoring</tt></a>
</b> <td>
routines for factoring univariate polynomials over <tt>ZZ</tt>
<!-- ----------- ZZ_p.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="ZZ_p.txt"><tt>ZZ_p</tt></a>
</b> <td>
class <tt>ZZ_p</tt>: integers mod <tt>p</tt>
<!-- ----------- ZZ_pE.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="ZZ_pE.txt"><tt>ZZ_pE</tt></a>
</b> <td>
class <tt>ZZ_pE</tt>: ring/field extension of <tt>ZZ_p</tt>
<!-- ----------- ZZ_pEX.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="ZZ_pEX.txt"><tt>ZZ_pEX</tt></a>
</b> <td>
class <tt>ZZ_pEX</tt>: polynomials over <tt>ZZ_pE</tt>;
includes routines for modular polynomials arithmetic,
modular composition, minimal and characteristic
polynomials, and interpolation.
<!-- ----------- ZZ_pEXFactoring.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="ZZ_pEXFactoring.txt"><tt>ZZ_pEXFactoring</tt></a>
</b> <td>
routines for factoring polynomials over <tt>ZZ_pE</tt>;
also includes routines for testing for and constructing
irreducible polynomials
<!-- ----------- ZZ_pX.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="ZZ_pX.txt"><tt>ZZ_pX</tt></a>
</b> <td>
class <tt>ZZ_pX</tt>: polynomials over <tt>ZZ_p</tt>;
includes routines for modular polynomials arithmetic,
modular composition, minimal and characteristic
polynomials, and interpolation.
<!-- ----------- ZZ_pXFactoring.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="ZZ_pXFactoring.txt"><tt>ZZ_pXFactoring</tt></a>
</b> <td>
routines for factoring polynomials over <tt>ZZ_p</tt>;
also includes routines for testing for and constructing
irreducible polynomials
<!-- ----------- lzz_p.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="lzz_p.txt"><tt>lzz_p</tt></a>
</b> <td>
class <tt>zz_p</tt>:
integers mod <tt>p</tt>, where <tt>p</tt> is single-precision
<!-- ----------- lzz_pE.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="lzz_pE.txt"><tt>lzz_pE</tt></a>
</b> <td>
class <tt>zz_pE</tt>:
ring/field extension of zz_p
<!-- ----------- lzz_pEX.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="lzz_pEX.txt"><tt>lzz_pEX</tt></a>
</b> <td>
class <tt>zz_pEX</tt>: polynomials over <tt>zz_pE</tt>;
provides the same functionality as class <tt>ZZ_pEX</tt>,
but for single-precision <tt>p</tt>
<!-- ----------- lzz_pEXFactoring.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="lzz_pEXFactoring.txt"><tt>lzz_pEXFactoring</tt></a>
</b> <td>
routines for factoring polynomials over <tt>zz_pE</tt>;
provides the same functionality as class <tt>ZZ_pEX</tt>,
but for single-precision <tt>p</tt>
<!-- ----------- lzz_pX.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="lzz_pX.txt"><tt>lzz_pX</tt></a>
</b> <td>
class <tt>zz_pX</tt>: polynomials over <tt>zz_p</tt>;
provides the same functionality as class <tt>ZZ_pX</tt>,
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