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 characteristicpolynomial 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 characteristicpolynomial 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 characteristicpolynomial 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 thetiming function <tt>GetTime()</tt>, and several overloadedversions 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 withextended 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 withcorresponding 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 withcorresponding names.These files also declare corresponding generic vector types<tt>vec_pair_GF2EX_long</tt>, etc.No 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