</b> <td>
class <tt>zz_pX</tt>: polynomials over <tt>zz_p</tt>;
provides the same functionality as class <tt>ZZ_pX</tt>,
but for single-precision <tt>p</tt>


<!-- ----------- lzz_pXFactoring.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="lzz_pXFactoring.txt"><tt>lzz_pXFactoring</tt></a>

</b> <td>
routines for factoring polynomials over <tt>zz_p</tt>;
provides the same functionality as class <tt>ZZ_pX</tt>,
but for single-precision <tt>p</tt>


<!-- ----------- matrix.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="matrix.txt"><tt>matrix</tt></a>

</b> <td>
template-like macros for 
dynamic-size 2-dimensional arrays

<!-- ----------- mat_GF2.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="mat_GF2.txt"><tt>mat_GF2</tt></a>

</b> <td>
class <tt>mat_GF2</tt>: matrices over <tt>GF(2)</tt>;
includes basic matrix arithmetic operations,
including determinant calculation, matrix inversion,
solving nonsingular systems of linear equations,
and Gaussian elimination


<!-- ----------- mat_GF2E.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="mat_GF2E.txt"><tt>mat_GF2E</tt></a>

</b> <td>
class <tt>mat_GF2E</tt>: matrices over <tt>GF2E</tt>;
includes basic matrix arithmetic operations,
including determinant calculation, matrix inversion,
solving nonsingular systems of linear equations,
and Gaussian elimination



<!-- ----------- mat_RR.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="mat_RR.txt"><tt>mat_RR</tt></a>

</b> <td>
class <tt>mat_RR</tt>: matrices over <tt>RR</tt>;
includes basic matrix arithmetic operations,
including determinant calculation, matrix inversion,
and solving nonsingular systems of linear equations.



<!-- ----------- mat_ZZ.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="mat_ZZ.txt"><tt>mat_ZZ</tt></a>

</b> <td>
class <tt>mat_ZZ</tt>: matrices over <tt>ZZ</tt>;
includes basic matrix arithmetic operations,
including determinant calculation, matrix inversion,
and solving nonsingular systems of linear equations.
See also the LLL module for additional routines.



<!-- ----------- mat_ZZ_p.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="mat_ZZ_p.txt"><tt>mat_ZZ_p</tt></a>

</b> <td>
class <tt>mat_ZZ_p</tt>: matrices over <tt>ZZ_p</tt>;
includes basic matrix arithmetic operations,
including determinant calculation, matrix inversion,
solving nonsingular systems of linear equations,
and Gaussian elimination


<!-- ----------- mat_ZZ_pE.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="mat_ZZ_pE.txt"><tt>mat_ZZ_pE</tt></a>

</b> <td>
class <tt>mat_ZZ_pE</tt>: matrices over <tt>ZZ_pE</tt>;
includes basic matrix arithmetic operations,
including determinant calculation, matrix inversion,
solving nonsingular systems of linear equations,
and Gaussian elimination




<!-- ----------- mat_lzz_p.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="mat_lzz_p.txt"><tt>mat_lzz_p</tt></a>

</b> <td>
class <tt>mat_zz_p</tt>: matrices over <tt>zz_p</tt>;
includes basic matrix arithmetic operations,
including determinant calculation, matrix inversion,
solving nonsingular systems of linear equations,
and Gaussian elimination

<!-- ----------- mat_lzz_pE.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="mat_lzz_pE.txt"><tt>mat_lzz_pE</tt></a>

</b> <td>
class <tt>mat_zz_pE</tt>: matrices over <tt>zz_pE</tt>;
includes basic matrix arithmetic operations,
including determinant calculation, matrix inversion,
solving nonsingular systems of linear equations,
and Gaussian elimination



<!-- ----------- mat_poly_ZZ.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="mat_poly_ZZ.txt"><tt>mat_poly_ZZ</tt></a>

</b> <td>
routine for computing the characteristic
polynomial of a <tt>mat_ZZ</tt>



<!-- ----------- mat_poly_ZZ_p.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="mat_poly_ZZ_p.txt"><tt>mat_poly_ZZ_p</tt></a>

</b> <td>
routine for computing the characteristic
polynomial of a <tt>mat_ZZ_p</tt>



<!-- ----------- mat_poly_lzz_p.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="mat_poly_lzz_p.txt"><tt>mat_poly_lzz_p</tt></a>

</b> <td>
routine for computing the characteristic
polynomial of a <tt>mat_zz_p</tt>





<!-- ----------- pair.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="pair.txt"><tt>pair</tt></a>

</b> <td>
template-like macros for 
pairs



<!-- ----------- quad_float.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="quad_float.txt"><tt>quad_float</tt></a>

</b> <td>
class <tt>quad_float</tt>: quadruple-precision floating point numbers.



<!-- ----------- tools.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="tools.txt"><tt>tools</tt></a>

</b> <td>
some basic types and utility routines, including the
timing function <tt>GetTime()</tt>, and several overloaded
versions of <tt>min()</tt> and <tt>max()</tt>


<!-- ----------- vector.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="vector.txt"><tt>vector</tt></a>

</b> <td>
template-like macros for 
dynamic-size vectors

<!-- ----------- vec_GF2.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="vec_GF2.txt"><tt>vec_GF2</tt></a>

</b> <td>
class <tt>vec_GF2</tt>: vectors over <tt>GF(2)</tt>, with arithmetic

<!-- ----------- vec_GF2E.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="vec_GF2E.txt"><tt>vec_GF2E</tt></a>

</b> <td>
class <tt>vec_GF2E</tt>: vectors over <tt>GF2E</tt>, with arithmetic


<!-- ----------- vec_RR.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="vec_RR.txt"><tt>vec_RR</tt></a>

</b> <td>
class <tt>vec_RR</tt>: vectors over <tt>RR</tt>, with arithmetic



<!-- ----------- vec_ZZ.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="vec_ZZ.txt"><tt>vec_ZZ</tt></a>

</b> <td>
class <tt>vec_ZZ</tt>: vectors over <tt>ZZ</tt>, with arithmetic



<!-- ----------- vec_ZZ_p.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="vec_ZZ_p.txt"><tt>vec_ZZ_p</tt></a>

</b> <td>
class <tt>vec_ZZ_p</tt>: vectors over <tt>ZZ_p</tt>, with arithmetic

<!-- ----------- vec_ZZ_pE.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="vec_ZZ_pE.txt"><tt>vec_ZZ_pE</tt></a>

</b> <td>
class <tt>vec_ZZ_pE</tt>: vectors over <tt>ZZ_pE</tt>, with arithmetic



<!-- ----------- vec_lzz_p.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="vec_lzz_p.txt"><tt>vec_lzz_p</tt></a>

</b> <td>
class <tt>vec_zz_p</tt>: vectors over <tt>zz_p</tt>, with arithmetic


<!-- ----------- vec_lzz_pE.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="vec_lzz_pE.txt"><tt>vec_lzz_pE</tt></a>

</b> <td>
class <tt>vec_zz_pE</tt>: vectors over <tt>zz_pE</tt>, with arithmetic


<!-- ----------- version.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="version.txt"><tt>version</tt></a>

</b> <td>
macros defining the NTL version number



<!-- ----------- xdouble.txt ----------- -->
<p><tr valign=top> <td> <b>
<a href="xdouble.txt"><tt>xdouble</tt></a>

</b> <td>
class <tt>xdouble</tt>: double-precision floating point numbers with
extended exponent range.

</table>

<p>

<h3>
Some other types
</h3>


<p>
In addition to the above, other generic vectors are declared,
not explicitly documented elsewhere:
<p>

<ul>
<li> <tt>vec_GF2XVec</tt>
<li> <tt>vec_ZZVec</tt>
<li> <tt>vec_double</tt>
<li> <tt>vec_long</tt>
<li> <tt>vec_quad_float</tt>
<li> <tt>vec_ulong</tt>
<li> <tt>vec_vec_GF2</tt>
<li> <tt>vec_vec_GF2E</tt>
<li> <tt>vec_vec_RR</tt>
<li> <tt>vec_vec_ZZ</tt>
<li> <tt>vec_vec_ZZ_p</tt>
<li> <tt>vec_vec_ZZ_pE</tt>
<li> <tt>vec_vec_long</tt>
<li> <tt>vec_vec_lzz_p</tt>
<li> <tt>vec_vec_lzz_pE</tt>
<li> <tt>vec_vec_ulong</tt>
<li> <tt>vec_xdouble</tt>
</ul>

<p>

These decalarations are found in "<tt>.h</tt>" files with
corresponding names.
No additional functionality is provided.

<p>
All of the header files for polynomial classes <tt>ZZ_pX</tt>,
<tt>ZZX</tt>, etc., declare generic vectors <tt>vec_ZZ_pX</tt>,
<tt>vec_ZZX</tt>, etc.

<p>
There are also a number of generic pair classes defined,
not explicitly documented elsewhere:

<p>

<ul>
<li> <tt>pair_GF2EX_long</tt>
<li> <tt>pair_GF2X_long</tt>
<li> <tt>pair_ZZX_long</tt>
<li> <tt>pair_ZZ_pEX_long</tt>
<li> <tt>pair_ZZ_pX_long</tt>
<li> <tt>pair_lzz_pEX_long</tt>
<li> <tt>pair_lzz_pX_long</tt>
</ul>

<p>

These decalarations are found in "<tt>.h</tt>" files with
corresponding names.
These files also declare corresponding generic vector types
<tt>vec_pair_GF2EX_long</tt>, etc.
No additional functionality is provided.


<p>

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