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 this header file includes the standard headers
Also note that in ISO mode, <NTL/tools.h> instead includes the standard header files
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.
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. |
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.