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<html><head><title>A Tour of NTL: Summary of NTL's Main Modules </title></head><body bgcolor="#fff9e6"><center><a href="tour-struct.html"><img src="arrow1.gif" alt="[Previous]" align=bottom></a> <a href="tour.html"><img src="arrow2.gif" alt="[Up]" align=bottom></a> <a href="tour-stdcxx.html"> <img src="arrow3.gif" alt="[Next]" align=bottom></a></center><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 headerfile <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 includesthe 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 implementationdetails and declarations of some of the more esoteric routines and data structures, and it contains more completeand usually clearer documentation than in the header file.<p>There is a plethora of conversion routines.These are not documented in any of the individualdocumentation 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 onthe 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 efficientthan 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 constructingirreducible 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 characteristicpolynomials, 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 constructingirreducible 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 Formof 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 LLLand Block Korkin Zolotarev reduction algorithm,as well as an integer-only reduction algorithm.Also, there are routines here for computing the kerneland image of an integer matrix, as well as finding integersolutions 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 routinesand in-line routines for single-precisionmodular 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 characteristicpolynomials, 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 characteristicpolynomials, 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 constructingirreducible 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 characteristicpolynomials, 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 constructingirreducible 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>,?? 快捷鍵說明
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