1 | <html> |
---|
2 | <head> |
---|
3 | <title> |
---|
4 | A Tour of NTL: Summary of NTL's Main Modules </title> |
---|
5 | </head> |
---|
6 | |
---|
7 | <body bgcolor="#fff9e6"> |
---|
8 | <center> |
---|
9 | <a href="tour-struct.html"><img src="arrow1.gif" alt="[Previous]" align=bottom></a> |
---|
10 | <a href="tour.html"><img src="arrow2.gif" alt="[Up]" align=bottom></a> |
---|
11 | <a href="tour-stdcxx.html"> <img src="arrow3.gif" alt="[Next]" align=bottom></a> |
---|
12 | </center> |
---|
13 | |
---|
14 | <h1> |
---|
15 | <p align=center> |
---|
16 | A Tour of NTL: Summary of NTL's Main Modules |
---|
17 | </p> |
---|
18 | </h1> |
---|
19 | |
---|
20 | <p> <hr> <p> |
---|
21 | |
---|
22 | <p> |
---|
23 | |
---|
24 | NTL consists of a number of software modules. |
---|
25 | Generally speaking, for each module <tt>foo</tt>, there is |
---|
26 | <ul> |
---|
27 | <li> |
---|
28 | a header |
---|
29 | file <tt><NTL/foo.h></tt>, found in subdirectory <tt>include</tt>, |
---|
30 | <li> |
---|
31 | a documentation file <tt>foo.txt</tt>, |
---|
32 | found in subdirectory <tt>doc</tt>, |
---|
33 | and |
---|
34 | <li> |
---|
35 | a source file <tt>foo.c</tt>, found in subdirectory <tt>src</tt>. |
---|
36 | </ul> |
---|
37 | |
---|
38 | <p> |
---|
39 | Note that all of the header files for NTL modules include the header file |
---|
40 | <tt><NTL/tools.h></tt>, and by default, this header file includes |
---|
41 | the standard headers |
---|
42 | <ul> |
---|
43 | <li> |
---|
44 | <tt><cstdlib></tt>, |
---|
45 | <li> |
---|
46 | <tt><cmath></tt>, and |
---|
47 | <li> |
---|
48 | <tt><iostream></tt>. |
---|
49 | </ul> |
---|
50 | Moreover, |
---|
51 | the standard library is wrapped in namespace <tt>std</tt> |
---|
52 | and NTL is wrapped in namespace <tt>NTL</tt>. |
---|
53 | |
---|
54 | |
---|
55 | <p> |
---|
56 | |
---|
57 | However, if you compiled NTL in |
---|
58 | <a href="tour-stdcxx.html">traditional (non-ISO mode)</a>, |
---|
59 | then <tt><NTL/tools.h></tt> |
---|
60 | includes the traditional (pre-ISO) headers |
---|
61 | <ul> |
---|
62 | <li> |
---|
63 | <tt><stdlib.h></tt>, |
---|
64 | <li> |
---|
65 | <tt><math.h></tt>, and |
---|
66 | <li> |
---|
67 | <tt><iostream.h></tt>. |
---|
68 | </ul> |
---|
69 | Moreover, |
---|
70 | all of names of the standard library and NTL are defined |
---|
71 | in the global namespace. |
---|
72 | |
---|
73 | |
---|
74 | <p> |
---|
75 | |
---|
76 | The documentation file takes the form of a header file, |
---|
77 | but stripped of implementation |
---|
78 | details and declarations of some of the more esoteric |
---|
79 | routines and data structures, and it contains more complete |
---|
80 | and usually clearer documentation than in the header file. |
---|
81 | Also, note that the documentation files do not explicitly |
---|
82 | mention anything about namespaces <tt>std</tt> and <tt>NTL</tt>. |
---|
83 | |
---|
84 | |
---|
85 | <p> |
---|
86 | |
---|
87 | There is a plethora of conversion routines. |
---|
88 | These are not documented in any of the individual |
---|
89 | documentation files, but rather, |
---|
90 | they are all briefly summarized in |
---|
91 | <a href="conversions.txt"><tt>conversions.txt</tt></a>. |
---|
92 | |
---|
93 | <p> |
---|
94 | |
---|
95 | The following is a summary of the main NTL modules. |
---|
96 | The corresponding documentation file can be obtained by clicking on |
---|
97 | the module name. |
---|
98 | |
---|
99 | <p> |
---|
100 | |
---|
101 | <table > |
---|
102 | |
---|
103 | |
---|
104 | |
---|
105 | <!-- ----------- GF2.txt ----------- --> |
---|
106 | <p><tr valign=top> <td> <b> |
---|
107 | <a href="GF2.txt"><tt>GF2</tt></a> |
---|
108 | |
---|
109 | </b> <td> |
---|
110 | |
---|
111 | class <tt>GF2</tt>: integers mod 2 |
---|
112 | |
---|
113 | |
---|
114 | <!-- ----------- GF2X.txt ----------- --> |
---|
115 | <p><tr valign=top> <td> <b> |
---|
116 | <a href="GF2X.txt"><tt>GF2X</tt></a> |
---|
117 | |
---|
118 | </b> <td> |
---|
119 | |
---|
120 | class <tt>GF2X</tt>: polynomials over <tt>GF(2)</tt> (much more efficient |
---|
121 | than using <tt>zz_pX</tt> with <tt>p=2</tt>); |
---|
122 | includes routines for GCDs and minimal polynomials |
---|
123 | |
---|
124 | |
---|
125 | <!-- ----------- GF2XFactoring.txt ----------- --> |
---|
126 | <p><tr valign=top> <td> <b> |
---|
127 | <a href="GF2XFactoring.txt"><tt>GF2XFactoring</tt></a> |
---|
128 | |
---|
129 | </b> <td> |
---|
130 | routines for factoring polynomials over <tt>GF(2)</tt>; |
---|
131 | also includes routines for testing for and constructing |
---|
132 | irreducible polynomials |
---|
133 | |
---|
134 | |
---|
135 | <!-- ----------- GF2XVec.txt ----------- --> |
---|
136 | <p><tr valign=top> <td> <b> |
---|
137 | <a href="GF2XVec.txt"><tt>GF2XVec</tt></a> |
---|
138 | |
---|
139 | </b> <td> |
---|
140 | class <tt>GF2XVec</tt>: fixed-length vectors of fixed-length <tt>GF2X</tt>s; |
---|
141 | less flexible, but more efficient than <tt>vec_GF2X</tt> |
---|
142 | |
---|
143 | |
---|
144 | |
---|
145 | |
---|
146 | <!-- ----------- GF2E.txt ----------- --> |
---|
147 | <p><tr valign=top> <td> <b> |
---|
148 | <a href="GF2E.txt"><tt>GF2E</tt></a> |
---|
149 | |
---|
150 | </b> <td> |
---|
151 | class <tt>GF2E</tt>: polynomial extension field/ring over <tt>GF(2)</tt>, |
---|
152 | implemented as GF(2)[X]/(P). |
---|
153 | |
---|
154 | |
---|
155 | <!-- ----------- GF2EX.txt ----------- --> |
---|
156 | <p><tr valign=top> <td> <b> |
---|
157 | <a href="GF2EX.txt"><tt>GF2EX</tt></a> |
---|
158 | |
---|
159 | </b> <td> |
---|
160 | class <tt>GF2EX</tt> |
---|
161 | class <tt>GF2EX</tt>: polynomials over <tt>GF2E</tt>; |
---|
162 | includes routines for modular polynomials arithmetic, |
---|
163 | modular composition, minimal and characteristic |
---|
164 | polynomials, and interpolation. |
---|
165 | |
---|
166 | |
---|
167 | |
---|
168 | <!-- ----------- GF2EXFactoring.txt ----------- --> |
---|
169 | <p><tr valign=top> <td> <b> |
---|
170 | <a href="GF2EXFactoring.txt"><tt>GF2EXFactoring</tt></a> |
---|
171 | |
---|
172 | </b> <td> |
---|
173 | routines for factoring polynomials over <tt>GF2E</tt>; |
---|
174 | also includes routines for testing for and constructing |
---|
175 | irreducible polynomials |
---|
176 | |
---|
177 | |
---|
178 | <!-- ----------- HNF.txt ----------- --> |
---|
179 | <p><tr valign=top> <td> <b> |
---|
180 | <a href="HNF.txt"><tt>HNF</tt></a> |
---|
181 | |
---|
182 | </b> <td> |
---|
183 | routines for computing the Hermite Normal Form |
---|
184 | of a lattice |
---|
185 | |
---|
186 | |
---|
187 | |
---|
188 | <!-- ----------- LLL.txt ----------- --> |
---|
189 | <p><tr valign=top> <td> <b> |
---|
190 | <a href="LLL.txt"><tt>LLL</tt></a> |
---|
191 | |
---|
192 | </b> <td> |
---|
193 | routines for performing lattice basis reduction, |
---|
194 | including very fast and robust implementations of the Schnorr-Euchner LLL |
---|
195 | and Block Korkin Zolotarev reduction algorithm, |
---|
196 | as well as an integer-only reduction algorithm. |
---|
197 | Also, there are routines here for computing the kernel |
---|
198 | and image of an integer matrix, as well as finding integer |
---|
199 | solutions to linear systems of equations over the integers. |
---|
200 | |
---|
201 | |
---|
202 | |
---|
203 | <!-- ----------- RR.txt ----------- --> |
---|
204 | <p><tr valign=top> <td> <b> |
---|
205 | <a href="RR.txt"><tt>RR</tt></a> |
---|
206 | |
---|
207 | </b> <td> |
---|
208 | class <tt>RR</tt>: arbitrary-precision floating point numbers. |
---|
209 | |
---|
210 | |
---|
211 | |
---|
212 | <!-- ----------- ZZ.txt ----------- --> |
---|
213 | <p><tr valign=top> <td> <b> |
---|
214 | <a href="ZZ.txt"><tt>ZZ</tt></a> |
---|
215 | |
---|
216 | </b> <td> |
---|
217 | class <tt>ZZ</tt>: arbitrary length integers; |
---|
218 | includes routines for GCDs, Jacobi symbols, |
---|
219 | modular arithmetic, and primality testing; |
---|
220 | also includes small prime generation routines |
---|
221 | and in-line routines for single-precision |
---|
222 | modular arithmetic |
---|
223 | |
---|
224 | |
---|
225 | |
---|
226 | <!-- ----------- ZZVec.txt ----------- --> |
---|
227 | <p><tr valign=top> <td> <b> |
---|
228 | <a href="ZZVec.txt"><tt>ZZVec</tt></a> |
---|
229 | |
---|
230 | </b> <td> |
---|
231 | class <tt>ZZVec</tt>: fixed-length vectors of fixed-length <tt>ZZ</tt>s; |
---|
232 | less flexible, but more efficient than <tt>vec_ZZ</tt> |
---|
233 | |
---|
234 | |
---|
235 | |
---|
236 | <!-- ----------- ZZX.txt ----------- --> |
---|
237 | <p><tr valign=top> <td> <b> |
---|
238 | <a href="ZZX.txt"><tt>ZZX</tt></a> |
---|
239 | |
---|
240 | </b> <td> |
---|
241 | class <tt>ZZX</tt>: polynomials over <tt>ZZ</tt>; |
---|
242 | includes routines for GCDs, minimal and characteristic |
---|
243 | polynomials, norms and traces |
---|
244 | |
---|
245 | |
---|
246 | |
---|
247 | <!-- ----------- ZZXFactoring.txt ----------- --> |
---|
248 | <p><tr valign=top> <td> <b> |
---|
249 | <a href="ZZXFactoring.txt"><tt>ZZXFactoring</tt></a> |
---|
250 | |
---|
251 | </b> <td> |
---|
252 | routines for factoring univariate polynomials over <tt>ZZ</tt> |
---|
253 | |
---|
254 | |
---|
255 | |
---|
256 | <!-- ----------- ZZ_p.txt ----------- --> |
---|
257 | <p><tr valign=top> <td> <b> |
---|
258 | <a href="ZZ_p.txt"><tt>ZZ_p</tt></a> |
---|
259 | |
---|
260 | </b> <td> |
---|
261 | class <tt>ZZ_p</tt>: integers mod <tt>p</tt> |
---|
262 | |
---|
263 | <!-- ----------- ZZ_pE.txt ----------- --> |
---|
264 | <p><tr valign=top> <td> <b> |
---|
265 | <a href="ZZ_pE.txt"><tt>ZZ_pE</tt></a> |
---|
266 | |
---|
267 | </b> <td> |
---|
268 | class <tt>ZZ_pE</tt>: ring/field extension of <tt>ZZ_p</tt> |
---|
269 | |
---|
270 | |
---|
271 | |
---|
272 | <!-- ----------- ZZ_pEX.txt ----------- --> |
---|
273 | <p><tr valign=top> <td> <b> |
---|
274 | <a href="ZZ_pEX.txt"><tt>ZZ_pEX</tt></a> |
---|
275 | |
---|
276 | </b> <td> |
---|
277 | class <tt>ZZ_pEX</tt>: polynomials over <tt>ZZ_pE</tt>; |
---|
278 | includes routines for modular polynomials arithmetic, |
---|
279 | modular composition, minimal and characteristic |
---|
280 | polynomials, and interpolation. |
---|
281 | |
---|
282 | <!-- ----------- ZZ_pEXFactoring.txt ----------- --> |
---|
283 | <p><tr valign=top> <td> <b> |
---|
284 | <a href="ZZ_pEXFactoring.txt"><tt>ZZ_pEXFactoring</tt></a> |
---|
285 | |
---|
286 | </b> <td> |
---|
287 | routines for factoring polynomials over <tt>ZZ_pE</tt>; |
---|
288 | also includes routines for testing for and constructing |
---|
289 | irreducible polynomials |
---|
290 | |
---|
291 | |
---|
292 | |
---|
293 | <!-- ----------- ZZ_pX.txt ----------- --> |
---|
294 | <p><tr valign=top> <td> <b> |
---|
295 | <a href="ZZ_pX.txt"><tt>ZZ_pX</tt></a> |
---|
296 | |
---|
297 | </b> <td> |
---|
298 | class <tt>ZZ_pX</tt>: polynomials over <tt>ZZ_p</tt>; |
---|
299 | includes routines for modular polynomials arithmetic, |
---|
300 | modular composition, minimal and characteristic |
---|
301 | polynomials, and interpolation. |
---|
302 | |
---|
303 | |
---|
304 | |
---|
305 | <!-- ----------- ZZ_pXFactoring.txt ----------- --> |
---|
306 | <p><tr valign=top> <td> <b> |
---|
307 | <a href="ZZ_pXFactoring.txt"><tt>ZZ_pXFactoring</tt></a> |
---|
308 | |
---|
309 | </b> <td> |
---|
310 | routines for factoring polynomials over <tt>ZZ_p</tt>; |
---|
311 | also includes routines for testing for and constructing |
---|
312 | irreducible polynomials |
---|
313 | |
---|
314 | |
---|
315 | |
---|
316 | <!-- ----------- lzz_p.txt ----------- --> |
---|
317 | <p><tr valign=top> <td> <b> |
---|
318 | <a href="lzz_p.txt"><tt>lzz_p</tt></a> |
---|
319 | |
---|
320 | </b> <td> |
---|
321 | class <tt>zz_p</tt>: |
---|
322 | integers mod <tt>p</tt>, where <tt>p</tt> is single-precision |
---|
323 | |
---|
324 | |
---|
325 | <!-- ----------- lzz_pE.txt ----------- --> |
---|
326 | <p><tr valign=top> <td> <b> |
---|
327 | <a href="lzz_pE.txt"><tt>lzz_pE</tt></a> |
---|
328 | |
---|
329 | </b> <td> |
---|
330 | class <tt>zz_pE</tt>: |
---|
331 | ring/field extension of zz_p |
---|
332 | |
---|
333 | |
---|
334 | <!-- ----------- lzz_pEX.txt ----------- --> |
---|
335 | <p><tr valign=top> <td> <b> |
---|
336 | <a href="lzz_pEX.txt"><tt>lzz_pEX</tt></a> |
---|
337 | |
---|
338 | </b> <td> |
---|
339 | class <tt>zz_pEX</tt>: polynomials over <tt>zz_pE</tt>; |
---|
340 | provides the same functionality as class <tt>ZZ_pEX</tt>, |
---|
341 | but for single-precision <tt>p</tt> |
---|
342 | |
---|
343 | <!-- ----------- lzz_pEXFactoring.txt ----------- --> |
---|
344 | <p><tr valign=top> <td> <b> |
---|
345 | <a href="lzz_pEXFactoring.txt"><tt>lzz_pEXFactoring</tt></a> |
---|
346 | |
---|
347 | </b> <td> |
---|
348 | routines for factoring polynomials over <tt>zz_pE</tt>; |
---|
349 | provides the same functionality as class <tt>ZZ_pEX</tt>, |
---|
350 | but for single-precision <tt>p</tt> |
---|
351 | |
---|
352 | |
---|
353 | <!-- ----------- lzz_pX.txt ----------- --> |
---|
354 | <p><tr valign=top> <td> <b> |
---|
355 | <a href="lzz_pX.txt"><tt>lzz_pX</tt></a> |
---|
356 | |
---|
357 | </b> <td> |
---|
358 | class <tt>zz_pX</tt>: polynomials over <tt>zz_p</tt>; |
---|
359 | provides the same functionality as class <tt>ZZ_pX</tt>, |
---|
360 | but for single-precision <tt>p</tt> |
---|
361 | |
---|
362 | |
---|
363 | <!-- ----------- lzz_pXFactoring.txt ----------- --> |
---|
364 | <p><tr valign=top> <td> <b> |
---|
365 | <a href="lzz_pXFactoring.txt"><tt>lzz_pXFactoring</tt></a> |
---|
366 | |
---|
367 | </b> <td> |
---|
368 | routines for factoring polynomials over <tt>zz_p</tt>; |
---|
369 | provides the same functionality as class <tt>ZZ_pX</tt>, |
---|
370 | but for single-precision <tt>p</tt> |
---|
371 | |
---|
372 | |
---|
373 | <!-- ----------- matrix.txt ----------- --> |
---|
374 | <p><tr valign=top> <td> <b> |
---|
375 | <a href="matrix.txt"><tt>matrix</tt></a> |
---|
376 | |
---|
377 | </b> <td> |
---|
378 | template-like macros for |
---|
379 | dynamic-size 2-dimensional arrays |
---|
380 | |
---|
381 | <!-- ----------- mat_GF2.txt ----------- --> |
---|
382 | <p><tr valign=top> <td> <b> |
---|
383 | <a href="mat_GF2.txt"><tt>mat_GF2</tt></a> |
---|
384 | |
---|
385 | </b> <td> |
---|
386 | class <tt>mat_GF2</tt>: matrices over <tt>GF(2)</tt>; |
---|
387 | includes basic matrix arithmetic operations, |
---|
388 | including determinant calculation, matrix inversion, |
---|
389 | solving nonsingular systems of linear equations, |
---|
390 | and Gaussian elimination |
---|
391 | |
---|
392 | |
---|
393 | <!-- ----------- mat_GF2E.txt ----------- --> |
---|
394 | <p><tr valign=top> <td> <b> |
---|
395 | <a href="mat_GF2E.txt"><tt>mat_GF2E</tt></a> |
---|
396 | |
---|
397 | </b> <td> |
---|
398 | class <tt>mat_GF2E</tt>: matrices over <tt>GF2E</tt>; |
---|
399 | includes basic matrix arithmetic operations, |
---|
400 | including determinant calculation, matrix inversion, |
---|
401 | solving nonsingular systems of linear equations, |
---|
402 | and Gaussian elimination |
---|
403 | |
---|
404 | |
---|
405 | |
---|
406 | <!-- ----------- mat_RR.txt ----------- --> |
---|
407 | <p><tr valign=top> <td> <b> |
---|
408 | <a href="mat_RR.txt"><tt>mat_RR</tt></a> |
---|
409 | |
---|
410 | </b> <td> |
---|
411 | class <tt>mat_RR</tt>: matrices over <tt>RR</tt>; |
---|
412 | includes basic matrix arithmetic operations, |
---|
413 | including determinant calculation, matrix inversion, |
---|
414 | and solving nonsingular systems of linear equations. |
---|
415 | |
---|
416 | |
---|
417 | |
---|
418 | <!-- ----------- mat_ZZ.txt ----------- --> |
---|
419 | <p><tr valign=top> <td> <b> |
---|
420 | <a href="mat_ZZ.txt"><tt>mat_ZZ</tt></a> |
---|
421 | |
---|
422 | </b> <td> |
---|
423 | class <tt>mat_ZZ</tt>: matrices over <tt>ZZ</tt>; |
---|
424 | includes basic matrix arithmetic operations, |
---|
425 | including determinant calculation, matrix inversion, |
---|
426 | and solving nonsingular systems of linear equations. |
---|
427 | See also the LLL module for additional routines. |
---|
428 | |
---|
429 | |
---|
430 | |
---|
431 | <!-- ----------- mat_ZZ_p.txt ----------- --> |
---|
432 | <p><tr valign=top> <td> <b> |
---|
433 | <a href="mat_ZZ_p.txt"><tt>mat_ZZ_p</tt></a> |
---|
434 | |
---|
435 | </b> <td> |
---|
436 | class <tt>mat_ZZ_p</tt>: matrices over <tt>ZZ_p</tt>; |
---|
437 | includes basic matrix arithmetic operations, |
---|
438 | including determinant calculation, matrix inversion, |
---|
439 | solving nonsingular systems of linear equations, |
---|
440 | and Gaussian elimination |
---|
441 | |
---|
442 | |
---|
443 | <!-- ----------- mat_ZZ_pE.txt ----------- --> |
---|
444 | <p><tr valign=top> <td> <b> |
---|
445 | <a href="mat_ZZ_pE.txt"><tt>mat_ZZ_pE</tt></a> |
---|
446 | |
---|
447 | </b> <td> |
---|
448 | class <tt>mat_ZZ_pE</tt>: matrices over <tt>ZZ_pE</tt>; |
---|
449 | includes basic matrix arithmetic operations, |
---|
450 | including determinant calculation, matrix inversion, |
---|
451 | solving nonsingular systems of linear equations, |
---|
452 | and Gaussian elimination |
---|
453 | |
---|
454 | |
---|
455 | |
---|
456 | |
---|
457 | <!-- ----------- mat_lzz_p.txt ----------- --> |
---|
458 | <p><tr valign=top> <td> <b> |
---|
459 | <a href="mat_lzz_p.txt"><tt>mat_lzz_p</tt></a> |
---|
460 | |
---|
461 | </b> <td> |
---|
462 | class <tt>mat_zz_p</tt>: matrices over <tt>zz_p</tt>; |
---|
463 | includes basic matrix arithmetic operations, |
---|
464 | including determinant calculation, matrix inversion, |
---|
465 | solving nonsingular systems of linear equations, |
---|
466 | and Gaussian elimination |
---|
467 | |
---|
468 | <!-- ----------- mat_lzz_pE.txt ----------- --> |
---|
469 | <p><tr valign=top> <td> <b> |
---|
470 | <a href="mat_lzz_pE.txt"><tt>mat_lzz_pE</tt></a> |
---|
471 | |
---|
472 | </b> <td> |
---|
473 | class <tt>mat_zz_pE</tt>: matrices over <tt>zz_pE</tt>; |
---|
474 | includes basic matrix arithmetic operations, |
---|
475 | including determinant calculation, matrix inversion, |
---|
476 | solving nonsingular systems of linear equations, |
---|
477 | and Gaussian elimination |
---|
478 | |
---|
479 | |
---|
480 | |
---|
481 | <!-- ----------- mat_poly_ZZ.txt ----------- --> |
---|
482 | <p><tr valign=top> <td> <b> |
---|
483 | <a href="mat_poly_ZZ.txt"><tt>mat_poly_ZZ</tt></a> |
---|
484 | |
---|
485 | </b> <td> |
---|
486 | routine for computing the characteristic |
---|
487 | polynomial of a <tt>mat_ZZ</tt> |
---|
488 | |
---|
489 | |
---|
490 | |
---|
491 | <!-- ----------- mat_poly_ZZ_p.txt ----------- --> |
---|
492 | <p><tr valign=top> <td> <b> |
---|
493 | <a href="mat_poly_ZZ_p.txt"><tt>mat_poly_ZZ_p</tt></a> |
---|
494 | |
---|
495 | </b> <td> |
---|
496 | routine for computing the characteristic |
---|
497 | polynomial of a <tt>mat_ZZ_p</tt> |
---|
498 | |
---|
499 | |
---|
500 | |
---|
501 | <!-- ----------- mat_poly_lzz_p.txt ----------- --> |
---|
502 | <p><tr valign=top> <td> <b> |
---|
503 | <a href="mat_poly_lzz_p.txt"><tt>mat_poly_lzz_p</tt></a> |
---|
504 | |
---|
505 | </b> <td> |
---|
506 | routine for computing the characteristic |
---|
507 | polynomial of a <tt>mat_zz_p</tt> |
---|
508 | |
---|
509 | |
---|
510 | |
---|
511 | |
---|
512 | |
---|
513 | <!-- ----------- pair.txt ----------- --> |
---|
514 | <p><tr valign=top> <td> <b> |
---|
515 | <a href="pair.txt"><tt>pair</tt></a> |
---|
516 | |
---|
517 | </b> <td> |
---|
518 | template-like macros for |
---|
519 | pairs |
---|
520 | |
---|
521 | |
---|
522 | |
---|
523 | <!-- ----------- quad_float.txt ----------- --> |
---|
524 | <p><tr valign=top> <td> <b> |
---|
525 | <a href="quad_float.txt"><tt>quad_float</tt></a> |
---|
526 | |
---|
527 | </b> <td> |
---|
528 | class <tt>quad_float</tt>: quadruple-precision floating point numbers. |
---|
529 | |
---|
530 | |
---|
531 | |
---|
532 | <!-- ----------- tools.txt ----------- --> |
---|
533 | <p><tr valign=top> <td> <b> |
---|
534 | <a href="tools.txt"><tt>tools</tt></a> |
---|
535 | |
---|
536 | </b> <td> |
---|
537 | some basic types and utility routines, including the |
---|
538 | timing function <tt>GetTime()</tt>, and several overloaded |
---|
539 | versions of <tt>min()</tt> and <tt>max()</tt> |
---|
540 | |
---|
541 | |
---|
542 | <!-- ----------- vector.txt ----------- --> |
---|
543 | <p><tr valign=top> <td> <b> |
---|
544 | <a href="vector.txt"><tt>vector</tt></a> |
---|
545 | |
---|
546 | </b> <td> |
---|
547 | template-like macros for |
---|
548 | dynamic-size vectors |
---|
549 | |
---|
550 | <!-- ----------- vec_GF2.txt ----------- --> |
---|
551 | <p><tr valign=top> <td> <b> |
---|
552 | <a href="vec_GF2.txt"><tt>vec_GF2</tt></a> |
---|
553 | |
---|
554 | </b> <td> |
---|
555 | class <tt>vec_GF2</tt>: vectors over <tt>GF(2)</tt>, with arithmetic |
---|
556 | |
---|
557 | <!-- ----------- vec_GF2E.txt ----------- --> |
---|
558 | <p><tr valign=top> <td> <b> |
---|
559 | <a href="vec_GF2E.txt"><tt>vec_GF2E</tt></a> |
---|
560 | |
---|
561 | </b> <td> |
---|
562 | class <tt>vec_GF2E</tt>: vectors over <tt>GF2E</tt>, with arithmetic |
---|
563 | |
---|
564 | |
---|
565 | <!-- ----------- vec_RR.txt ----------- --> |
---|
566 | <p><tr valign=top> <td> <b> |
---|
567 | <a href="vec_RR.txt"><tt>vec_RR</tt></a> |
---|
568 | |
---|
569 | </b> <td> |
---|
570 | class <tt>vec_RR</tt>: vectors over <tt>RR</tt>, with arithmetic |
---|
571 | |
---|
572 | |
---|
573 | |
---|
574 | <!-- ----------- vec_ZZ.txt ----------- --> |
---|
575 | <p><tr valign=top> <td> <b> |
---|
576 | <a href="vec_ZZ.txt"><tt>vec_ZZ</tt></a> |
---|
577 | |
---|
578 | </b> <td> |
---|
579 | class <tt>vec_ZZ</tt>: vectors over <tt>ZZ</tt>, with arithmetic |
---|
580 | |
---|
581 | |
---|
582 | |
---|
583 | <!-- ----------- vec_ZZ_p.txt ----------- --> |
---|
584 | <p><tr valign=top> <td> <b> |
---|
585 | <a href="vec_ZZ_p.txt"><tt>vec_ZZ_p</tt></a> |
---|
586 | |
---|
587 | </b> <td> |
---|
588 | class <tt>vec_ZZ_p</tt>: vectors over <tt>ZZ_p</tt>, with arithmetic |
---|
589 | |
---|
590 | <!-- ----------- vec_ZZ_pE.txt ----------- --> |
---|
591 | <p><tr valign=top> <td> <b> |
---|
592 | <a href="vec_ZZ_pE.txt"><tt>vec_ZZ_pE</tt></a> |
---|
593 | |
---|
594 | </b> <td> |
---|
595 | class <tt>vec_ZZ_pE</tt>: vectors over <tt>ZZ_pE</tt>, with arithmetic |
---|
596 | |
---|
597 | |
---|
598 | |
---|
599 | <!-- ----------- vec_lzz_p.txt ----------- --> |
---|
600 | <p><tr valign=top> <td> <b> |
---|
601 | <a href="vec_lzz_p.txt"><tt>vec_lzz_p</tt></a> |
---|
602 | |
---|
603 | </b> <td> |
---|
604 | class <tt>vec_zz_p</tt>: vectors over <tt>zz_p</tt>, with arithmetic |
---|
605 | |
---|
606 | |
---|
607 | <!-- ----------- vec_lzz_pE.txt ----------- --> |
---|
608 | <p><tr valign=top> <td> <b> |
---|
609 | <a href="vec_lzz_pE.txt"><tt>vec_lzz_pE</tt></a> |
---|
610 | |
---|
611 | </b> <td> |
---|
612 | class <tt>vec_zz_pE</tt>: vectors over <tt>zz_pE</tt>, with arithmetic |
---|
613 | |
---|
614 | |
---|
615 | <!-- ----------- version.txt ----------- --> |
---|
616 | <p><tr valign=top> <td> <b> |
---|
617 | <a href="version.txt"><tt>version</tt></a> |
---|
618 | |
---|
619 | </b> <td> |
---|
620 | macros defining the NTL version number |
---|
621 | |
---|
622 | |
---|
623 | |
---|
624 | <!-- ----------- xdouble.txt ----------- --> |
---|
625 | <p><tr valign=top> <td> <b> |
---|
626 | <a href="xdouble.txt"><tt>xdouble</tt></a> |
---|
627 | |
---|
628 | </b> <td> |
---|
629 | class <tt>xdouble</tt>: double-precision floating point numbers with |
---|
630 | extended exponent range. |
---|
631 | |
---|
632 | </table> |
---|
633 | |
---|
634 | <p> |
---|
635 | |
---|
636 | <h3> |
---|
637 | Some other types |
---|
638 | </h3> |
---|
639 | |
---|
640 | |
---|
641 | <p> |
---|
642 | In addition to the above, other generic vectors are declared, |
---|
643 | not explicitly documented elsewhere: |
---|
644 | <p> |
---|
645 | |
---|
646 | <ul> |
---|
647 | <li> <tt>vec_GF2XVec</tt> |
---|
648 | <li> <tt>vec_ZZVec</tt> |
---|
649 | <li> <tt>vec_double</tt> |
---|
650 | <li> <tt>vec_long</tt> |
---|
651 | <li> <tt>vec_quad_float</tt> |
---|
652 | <li> <tt>vec_ulong</tt> |
---|
653 | <li> <tt>vec_vec_GF2</tt> |
---|
654 | <li> <tt>vec_vec_GF2E</tt> |
---|
655 | <li> <tt>vec_vec_RR</tt> |
---|
656 | <li> <tt>vec_vec_ZZ</tt> |
---|
657 | <li> <tt>vec_vec_ZZ_p</tt> |
---|
658 | <li> <tt>vec_vec_ZZ_pE</tt> |
---|
659 | <li> <tt>vec_vec_long</tt> |
---|
660 | <li> <tt>vec_vec_lzz_p</tt> |
---|
661 | <li> <tt>vec_vec_lzz_pE</tt> |
---|
662 | <li> <tt>vec_vec_ulong</tt> |
---|
663 | <li> <tt>vec_xdouble</tt> |
---|
664 | </ul> |
---|
665 | |
---|
666 | <p> |
---|
667 | |
---|
668 | These decalarations are found in "<tt>.h</tt>" files with |
---|
669 | corresponding names. |
---|
670 | No additional functionality is provided. |
---|
671 | |
---|
672 | <p> |
---|
673 | All of the header files for polynomial classes <tt>ZZ_pX</tt>, |
---|
674 | <tt>ZZX</tt>, etc., declare generic vectors <tt>vec_ZZ_pX</tt>, |
---|
675 | <tt>vec_ZZX</tt>, etc. |
---|
676 | |
---|
677 | <p> |
---|
678 | There are also a number of generic pair classes defined, |
---|
679 | not explicitly documented elsewhere: |
---|
680 | |
---|
681 | <p> |
---|
682 | |
---|
683 | <ul> |
---|
684 | <li> <tt>pair_GF2EX_long</tt> |
---|
685 | <li> <tt>pair_GF2X_long</tt> |
---|
686 | <li> <tt>pair_ZZX_long</tt> |
---|
687 | <li> <tt>pair_ZZ_pEX_long</tt> |
---|
688 | <li> <tt>pair_ZZ_pX_long</tt> |
---|
689 | <li> <tt>pair_lzz_pEX_long</tt> |
---|
690 | <li> <tt>pair_lzz_pX_long</tt> |
---|
691 | </ul> |
---|
692 | |
---|
693 | <p> |
---|
694 | |
---|
695 | These decalarations are found in "<tt>.h</tt>" files with |
---|
696 | corresponding names. |
---|
697 | These files also declare corresponding generic vector types |
---|
698 | <tt>vec_pair_GF2EX_long</tt>, etc. |
---|
699 | No additional functionality is provided. |
---|
700 | |
---|
701 | |
---|
702 | <p> |
---|
703 | |
---|
704 | <center> |
---|
705 | <a href="tour-struct.html"><img src="arrow1.gif" alt="[Previous]" align=bottom></a> |
---|
706 | <a href="tour.html"><img src="arrow2.gif" alt="[Up]" align=bottom></a> |
---|
707 | <a href="tour-stdcxx.html"> <img src="arrow3.gif" alt="[Next]" align=bottom></a> |
---|
708 | </center> |
---|
709 | </body> |
---|
710 | </html> |
---|