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A Tour of NTL: Summary of NTL's Main Modules


NTL consists of a number of software modules. Generally speaking, for each module foo, there is

Note that all of the header files for NTL modules include the header file <NTL/tools.h>, and by default, this header file includes the standard headers

Moreover, the standard library is wrapped in namespace std and NTL is wrapped in namespace NTL.

However, if you compiled NTL in traditional (non-ISO mode), then <NTL/tools.h> includes the traditional (pre-ISO) headers

Moreover, all of names of the standard library and NTL are defined in the global namespace.

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. Also, note that the documentation files do not explicitly mention anything about namespaces std and NTL.

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 conversions.txt.

The following is a summary of the main NTL modules. The corresponding documentation file can be obtained by clicking on the module name.

GF2 class GF2: integers mod 2

GF2X class GF2X: polynomials over GF(2) (much more efficient than using zz_pX with p=2); includes routines for GCDs and minimal polynomials

GF2XFactoring routines for factoring polynomials over GF(2); also includes routines for testing for and constructing irreducible polynomials

GF2XVec class GF2XVec: fixed-length vectors of fixed-length GF2Xs; less flexible, but more efficient than vec_GF2X

GF2E class GF2E: polynomial extension field/ring over GF(2), implemented as GF(2)[X]/(P).

GF2EX class GF2EX class GF2EX: polynomials over GF2E; includes routines for modular polynomials arithmetic, modular composition, minimal and characteristic polynomials, and interpolation.

GF2EXFactoring routines for factoring polynomials over GF2E; also includes routines for testing for and constructing irreducible polynomials

HNF routines for computing the Hermite Normal Form of a lattice

LLL 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 class RR: arbitrary-precision floating point numbers.

ZZ class ZZ: 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 class ZZVec: fixed-length vectors of fixed-length ZZs; less flexible, but more efficient than vec_ZZ

ZZX class ZZX: polynomials over ZZ; includes routines for GCDs, minimal and characteristic polynomials, norms and traces

ZZXFactoring routines for factoring univariate polynomials over ZZ

ZZ_p class ZZ_p: integers mod p

ZZ_pE class ZZ_pE: ring/field extension of ZZ_p

ZZ_pEX class ZZ_pEX: polynomials over ZZ_pE; includes routines for modular polynomials arithmetic, modular composition, minimal and characteristic polynomials, and interpolation.

ZZ_pEXFactoring routines for factoring polynomials over ZZ_pE; also includes routines for testing for and constructing irreducible polynomials

ZZ_pX class ZZ_pX: polynomials over ZZ_p; includes routines for modular polynomials arithmetic, modular composition, minimal and characteristic polynomials, and interpolation.

ZZ_pXFactoring routines for factoring polynomials over ZZ_p; also includes routines for testing for and constructing irreducible polynomials

lzz_p class zz_p: integers mod p, where p is single-precision

lzz_pE class zz_pE: ring/field extension of zz_p

lzz_pEX class zz_pEX: polynomials over zz_pE; provides the same functionality as class ZZ_pEX, but for single-precision p

lzz_pEXFactoring routines for factoring polynomials over zz_pE; provides the same functionality as class ZZ_pEX, but for single-precision p

lzz_pX class zz_pX: polynomials over zz_p; provides the same functionality as class ZZ_pX, but for single-precision p

lzz_pXFactoring routines for factoring polynomials over zz_p; provides the same functionality as class ZZ_pX, but for single-precision p

matrix template-like macros for dynamic-size 2-dimensional arrays

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

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

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

mat_ZZ class mat_ZZ: matrices over ZZ; 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 class mat_ZZ_p: matrices over ZZ_p; includes basic matrix arithmetic operations, including determinant calculation, matrix inversion, solving nonsingular systems of linear equations, and Gaussian elimination

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

mat_lzz_p class mat_zz_p: matrices over zz_p; includes basic matrix arithmetic operations, including determinant calculation, matrix inversion, solving nonsingular systems of linear equations, and Gaussian elimination

mat_lzz_pE class mat_zz_pE: matrices over zz_pE; includes basic matrix arithmetic operations, including determinant calculation, matrix inversion, solving nonsingular systems of linear equations, and Gaussian elimination

mat_poly_ZZ routine for computing the characteristic polynomial of a mat_ZZ

mat_poly_ZZ_p routine for computing the characteristic polynomial of a mat_ZZ_p

mat_poly_lzz_p routine for computing the characteristic polynomial of a mat_zz_p

pair template-like macros for pairs

quad_float class quad_float: quadruple-precision floating point numbers.

tools some basic types and utility routines, including the timing function GetTime(), and several overloaded versions of min() and max()

vector template-like macros for dynamic-size vectors

vec_GF2 class vec_GF2: vectors over GF(2), with arithmetic

vec_GF2E class vec_GF2E: vectors over GF2E, with arithmetic

vec_RR class vec_RR: vectors over RR, with arithmetic

vec_ZZ class vec_ZZ: vectors over ZZ, with arithmetic

vec_ZZ_p class vec_ZZ_p: vectors over ZZ_p, with arithmetic

vec_ZZ_pE class vec_ZZ_pE: vectors over ZZ_pE, with arithmetic

vec_lzz_p class vec_zz_p: vectors over zz_p, with arithmetic

vec_lzz_pE class vec_zz_pE: vectors over zz_pE, with arithmetic

version macros defining the NTL version number

xdouble class xdouble: double-precision floating point numbers with extended exponent range.

Some other types

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

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

All of the header files for polynomial classes ZZ_pX, ZZX, etc., declare generic vectors vec_ZZ_pX, vec_ZZX, etc.

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

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

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