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Austin Schuh405fa6c2015-09-06 18:13:55 -07001libcdd, cdd & cdd+ HISTORY file (as of April 30, 2015)
2
3*** libcdd version (date) / changes ***
4
5Version 094h (April 30, 2015) /
6 - Thanks to Mathieu Dutour, one minor bug has been fixed.
7
8Version 094g (March 23, 2012) /
9 - Thanks to both Anders Jensen and Mathieu Dutour
10 a few memory leaks in cddlib.c and cddlp.c have been
11 fixed. Also, some patches sent by Jerry James have
12 been applied. These were for making the library
13 shared and more compatible for C++ compilers.
14
15Version 094f (February 7, 2008) /
16 - Thanks to Sven Verdoolaege's fixes,
17 the "configure" script now uses "gcc" as the default
18 compiler, rather than "g++" in earlier releases,
19 and the libraries can be linked properly with
20 both C and C++ programs.
21
22Version 094e (January 27, 2008) /
23 - A bug of reporting a wrong (sign) certificate of
24 an infeasible LP is fixed. This bug reported by
25 Charles Geyer, occurs if the exact GMP version of
26 the dd_LPSolve is used with minimization. A bug of
27 reporting infeasibility of a feasible LP with
28 column non-full rank LP is fixed. This bug was reported
29 by Sven Verdoolaege.
30
31Version 094d (February 12, 2007) /
32 - A bug of reporting a wrong unbounded direction vector of
33 a dual inconsistent LP is fixed. This bug occurs only
34 if the exact GMP version of the dd_LPSolve is used.
35 For example, this error may occur in scdd_gmp. This
36 error was reported by Lars Schewe.
37
38Version 094c (April 23, 2006) /
39 - A bug for reading a rational number of length longer
40 than 255 characters have been fixed. This was reported
41 by Ruriko Yoshida. Now the longest
42 number is controlled by dd_wordlenmax defined in
43 cddtypes.h . The longest line is also controlled by
44 dd_linelenmax . These are currently fixed to
45 1024 and 4096. Larger numbers and lines can be
46 handled by modifying these numbers and recompilation.
47
48Version 094b (August 25, 2005) /
49 - A bug for the representation conversion, reported by
50 Michal Kvasnica, was fixed. The earlier 094* versions
51 prematurely terminate the conversion when the number
52 of rows is equal to the number of columns in the input.
53 This means the earlier 094* do not compute correctly
54 for simplices, for example.
55
56Version 094a (August 24, 2005) /
57 - A bug of dd_LPSolve is fixed. This bug, reported by
58 Dima Pasechnik, due to a mishandling of cycling of LP
59 algorithms, is fixed.
60
61Version 094 (August 4, 2005) /
62 - dd_MatrixCanonicalize has been added. This reduces
63 matrix M to a minimal representation by computing
64 all implicit linearity rows and all redundant rows.
65 It applies lexicographic sorting of rows to remove
66 duplicates before applying redundancy removal.
67 This function combines the two computations together
68 in more efficient manner than before.
69 See the new redcheck.c for its use. Several basic
70 operations for matrices have been added, such as
71 dd_MatrixRowsRemove and dd_MatrixRowsRemove2.
72
73 The representation conversion dd_DDMatrix2Poly now
74 handles the empty H-polyhedra properly, by calling
75 an LP-based emptiness checker before running the double
76 description algorithm.
77
78 New functions finding specific points in H-polyhedra
79 are added. dd_ExistsRestrictedFace is a general inequality
80 system solver with specified equations, inequalities and
81 strict inequalities. dd_FindRelativeInterior finds
82 a point in the relative interior of a polyhedron.
83
84
85Version 093d (February 27, 2005) /
86 - The problem of outputting the running log has been corrected.
87 This problem and a solution was communicated by Charles Geyer.
88 Now, a new global dd_boolean variable dd_log (= dd_FALSE by default)
89 controls log output. An scdd/lcdd bug of terminating with segmentation
90 fault when an input polyhedron is numerically delicate has been
91 corrected. This bug was reported by Stefan Volkwein.
92
93Version 093c (December 26, 2003) /
94 - A bug of Phase I of the dual simplex method in floating-point
95 arithmetics is fixed. The problem (bus error) occurred when input data
96 is not appropriate for floating-point arithmetics. The problem
97 occurrs even for the GMP executables as the exact LP solver first
98 tries to detect the terminal basis with float-point arithmetics.
99
100Version 093b (November 10, 2003) /
101 - The nonterminating problem of the LP solver has been fixed.
102 This was due to a cycling of the criss-cross method in
103 floating-point arithmetics, that is extremely rare.
104 Also, the phase I of the dual simplex method has been
105 modified. The auxiliary LP is perhaps less likely to
106 be degenerate.
107
108Version 093a (Augst 11, 2003) /
109 - The LP basis finding procedure dd_FindLPBasis2 has been
110 updated. The functions dd_Matrix2WeakAdjacency, dd_SRedundant and
111 dd_SRedundantRows are added. The manual has been updated.
112
113Version 093 (July 18, 2003) /
114 - dd_LPSolve with GMP now runs fisrt with floating point arithmetics
115 and checks with GMP the correctness of the result. New functions dd_Matrix2Adjacency,
116 dd_FourierElimination, dd_BlockElimination, dd_DDMatrix2Poly2 are added.
117 Some minor memory leak problems are fixed. (Thanks to the excellent
118 memory debugger valgrind on linux.)
119
120Version 092b (October 19, 2002) /
121 - An illegal memory access for EqualityIndex reported by
122 Thao Dang is fixed. Another bug of lcdd_gmp which takes
123 "real" data and return a false result is fixed. It now warns
124 that input is not correct for the exact arithmetic lcdd_gmp.
125 This error was reported by Andras Salamon.
126
127Version 092a (December 19, 2001) /
128 - Joerg Rambau kindly created an autoconf distribution of
129 cddlib-092. This version 092a is made from Rambau's
130 version with a slight modification. For the momoment,
131 the Mathematica cdd interface, cddmathlink (in src-mathlink),
132 still needs to be handled in the conventional manner by
133 editing Makefile.
134
135Version 092 (December 12, 2001) /
136 - the default value of dd_almostzero is now set to 1.0E-7
137 instead of 1.0E-6. New functions are added for checking
138 redundancy of H- and V- representations such as
139 dd_Redundant, dd_RedundantRows, dd_ImplicitLinearity,
140 dd_ImplicitLinearityRows, and dd_RayShooting.
141 Also some basic operations on dd_MatrixPtr have been added such as
142 dd_MatrixAppendTo, dd_MatrixRowRemove, dd_MatrixSubmatrix.
143
144 The names of enumeration type variables have been modified.
145 Now all names have prefix "dd_", e.g. Rational, Integer are
146 now dd_Rational and dd_Integer. This applies to TRUE and FALSE,
147 which are now dd_TRUE and dd_FALSE.
148
149Version 091d (March 9, 2001) /
150 - Memory leak in dd_FreeLPData and dd_FreeLPSolution are
151 fixed.
152
153Version 091c (February 27, 2001) /
154 - Bug to terminate before the completion of computation
155 (to produce a segmentation fault) is fixed. This
156 bug was reported by Hugh Anderson.
157
158Version 091b (February 26, 2001) /
159 - Numerous memory leak bugs with GMP exact arithmetic,
160 reported by Marc Pfetsch, are fixed. Also, a minor
161 bug of cddlib to terminate with core dump, reported by
162 Hugh Anderson, is fixed. The messages printed to
163 the standard output "stdout" are now sent to "stderr".
164 This was suggested by Ingo Schurr.
165
166Version 091a (February 16, 2001) /
167 - Memory leak problems when GMP is used are fixed for
168 dd_InitializeAmatrix, dd_CreateMatrix and
169 dd_Larger. These bugs, reported by Marc Pfetsch,
170 can be fatal if GMP is used and the functions are
171 called many times. It has no effect for floating-point
172 arithmetic computation.
173
174Version 091 (Sept. 25, 2000) /
175 - Memory leak in FreeDDMemory (cddcore.c)
176 is fixed. This bug, which might cause a serious problem,
177 was reported by Shawn Rusaw. Also, a bug reported by
178 Istvan Csabai on dynamic row ordering is fixed. This
179 problem is most likely not affecting anyone, since the
180 dynamic row ordering option is not available via the
181 publicly released documentations. David Avis contributed
182 a sample cddlib code, lcdd.c, which runs like his convex
183 hull code, lrs. In particular, it is useful to generate
184 standard output stream for piping in unix.
185
186Version 090e (July 12, 2000) /
187 - A bug of reading very large integer values incorrectly
188 is fixed. The previous versions were truncating very large
189 integer values to a number representable by long integer.
190
191Version 090d (June 25, 2000) /
192 - Serious bugs of dd_CopyOutput, dd_CopyInequalities are fixed.
193 This bug is found by Istvan Csabai. Earlier versions 090*
194 output wrong H-representations whenever the RHS constants
195 are not nonnegative, even though the computation runs
196 correctly internally.
197
198Version 090c (June 12, 2000) /
199 - set_intialize is modified so that it allocates a smallest space even when
200 a nonpositive length is requested.
201 The bug of not outputting the origin is fixed
202 when input is homogeneous inequality system and the cone contains
203 no extreme rays. Note that cddlib does not output this vertex
204 when the homogeneous cone has extreme rays, since cddlib outputs
205 a minimal representation.
206
207 - A new function dd_DDInputAppend is added.
208
209 - dd_DDMatrix2Poly replaces (and combines) the two old functions
210 dd_Matrix2Poly and dd_DoubleDescription.
211
212 - dd_LPSolutionLoad is renamed as dd_CopyLPSolution.
213
214Version 090b (June 2, 2000) /
215 - Thanks to Shawn Rusaw's great help, I could detect and fix many
216 memory related problems (memory leak, out-of-bounds, etc).
217 Also, when input is not regular (nonfull or containing line),
218 cddlib did not generate adjacency/incidence properly and
219 this version should work more correctly.
220
221Version 090a (May 30, 2000) /
222 - a small bug fix in cddarith.c. The bug is reported by Shawn Rusaw.
223
224Version 090 (May 28, 2000) /
225 - Major revision over the previous versions. It can be now compiled
226 with GMP rational (-DGMPRATIONAL) as well as the standard C double.
227 cdd and lp codes are merged and easily called together. Many functions
228 and data types are modified and renamed. It comes with a simple
229 cdd/cdd+-type standalne program scdd which does the standard
230 representation conversion (*.ine <-> *.ext) and outputs all four
231 types of auxiliary files (*.icd, *.iad, *.ecd, *ead). Although it
232 lacks some functions such as preprojection of cdd+, scdd is potentially
233 the most powerful cdd ever since it runs in the two arithmetics and
234 it can handle any input.
235
236 Because of the better readability and the overhead of employing
237 function calls to do GMP arithmetic, the speed is little slower than
238 cdd+-076 on both arithmetics C double and GMP rational.
239
240Version 086 (Jan 22, 2000) /
241 - A bug fixed in dd_LexSmaller that affercted the lexicographic
242 ordering of input data. This fix is essential for efficiency.
243 Also several memory leaks have been fixed. Many of these bugs
244 were found by Mr. Masanori Sato of Tokyo Institute of Technology.
245 Never released.
246
247Version 085 (October 4, 1999) /
248 - It can read rational data. Several minor bugs have been fixed.
249 The new makefile creates cdd and dplex library archives
250 libcdd.a and libdplex.a for unix systems.
251
252Version 080 (March 24, 1999) /
253 - The first C-library version of cdd. It is stilll very primitive
254 and has no documentation. See README.libcdd. Unlike the existing
255 versions of cdd/cdd+, cddlib can deal with essentially any input,
256 namely, non-full-dimensional convex hull problems and
257 vertex-free extreme point (i.e. generator) listing problems. Also
258 it comes with MathLink program cddmathlink that can be called from
259 Mathematica to perform cdd operations.
260
261
262*** cdd version (date) / changes ***
263
264Version 0.61a (December, 1997) /
265 Few minor corrections over 0.61.
266
267Version 0.61 (December 1, 1997) /
268 It accepts "H-representation" and "V-representation" statements
269 which are added to a Polyhedra format (1997).
270 dp_FindInteriorPoint is added to dplex. Some small bugs are
271 fixed in dplex.
272
273Version 0.60 (August 27, 1996) /
274 The following changes are equivalent to ones that had been made
275 for cdd+-074.
276 The default output file names have been changed to be consistent
277 with the transformation. To avoid confusion, *.ine file should
278 be used only for a system of linear inequalities, and *.ext file
279 only for a set of extreme points and rays. Accordingly,
280 the files *.ead (previously *.adj) and *.ecd (previously *.icd)
281 are reserved for the adjacency and incidence files for the extremal
282 vertices/rays.
283 Similarly, *.iad (previously *.iad) and *.icd (previously none)
284 are reserved for the adjacency and incidence files for the inequality
285 data.
286
287 The LP code is now independent of cdd, and rewritten as a C library.
288 This library is called dplex, and contains two algorithms,
289 the dual simplex and the criss-cross method.
290
291Version C0.56 (August 7, 1995) /
292 Some compilation problem associated with incompatible set_type
293 variables in setoper.c is fixed. Various minor bugs are fixed.
294 The output format of incidence file is slightly modified. (See
295 the Reference Manual cddman.tex).
296
297Version C0.55a (December 18, 1994) /
298 The broken "preprojection" option in Version 0.55 is fixed.
299
300Version C0.55 (December 5, 1994) /
301 Set operation library setoper has been modified to use
302 the optimized set_card function by David Bremner. It is expected
303 that cdd runs much faster for problems with large row sizes.
304 The package organization has been changed. Now the package
305 consists of four C-programs, cdd.c, cddio.c, cddarith.c and setoper.c.
306 New options verify_input, equality and strict_inequality are added.
307 Also new options, lineshelling and row_decomposition are added but
308 these options are still not in very reliable form and not
309 recommended to use. Some newly found (minor) bugs are fixed.
310
311Version C0.54 (October 30, 1994) /
312 The partial_enumeration option is renamed as "equality" option.
313 A new option of "strict_inequality" is added to enumerate those
314 vertices/rays satisfying some specified inequalities with strict
315 inequality. Some bugs in reporting progress of iteration is fixed.
316
317Version C0.53 (July 29, 1994) /
318 - Some imcompatibility of cdd and domcheck has been fixed. Namely, one can
319 write any comments after each inequality data as long as it is written in
320 the same line as the last number (i.e., a_{id}, for each i) of each ith
321 inequality data. Anything written after the last number will be ignored.
322 Also, random ordering option is added for specifying the ordering of
323 rows (inequalities).
324
325Version C0.52b (March 28, 1994) /
326 - The slowness problem of Version C0.52(a) is fixed.
327
328Version C0.51d (March 28, 1994) /
329 - Because of the slowness of Version 0.52* due to unknown reasons, this version
330 has been produced for a temporary replacement. This version fixes the bug
331 mentioned in Version C0.52 release.
332
333Version C0.52a (March 28, 1994) /
334 - A bug of Version C0.52 generating unnecessary information when
335 maximize, minimize and find_interior are chosen is fixed.
336
337Version C0.52 (March 21, 1994) /
338 - A bug of Version C0.51c generating segmentation fault when the option
339 preprojection is used is fixed. This bug was reported by Alexander Bockmayr of
340 Max-Planck Institute.
341 - Some structural changes in the programs, cdd.c and cddarith.c, have been made
342 mainly for a future planning of adding an option to decompose a problem into
343 smaller subproblems.
344
345Version C0.51c (March 15, 1994) /
346 - A bug of Version C0.51b (mishandling of homogeneous inputs, i.e. zero RHS)
347 is fixed. This bug was reported by Alexander Bockmayr of
348 Max-Planck Institute.
349
350Version C0.51b (March 9, 1994) /
351 - A bug of Version C0.51a (mishandling of non full-dimensional
352 polyhedron) is fixed. The bug was reported by Alexander Bockmayr of
353 Max-Planck Institute.
354
355Version C0.51a (Feb. 16, 1994) /
356 - A bug of Version C0.51 (mishandling of empty polyhedron) is fixed.
357
358Version C0.51 (Feb. 12, 1994) /
359 - Some bugs of Version C0.50 has been fixed.
360 - The option "algebraic" for selecting the algebraic adjacency computation
361 is deleted. The reason is the combinatorial adjacency computation
362 is almost always faster.
363 - The option "minimize" is implemented to minimize a linear function over
364 the polytope. Previously, only "maximize" was supported.
365 - The option "find_interior" has been added to compute an interior point of
366 the input polyhedron.
367
368Version C0.50 (Feb. 7, 1994) /
369 - Major upgrade to implement a new data structure to store adjacencies of rays.
370 The adjacency record lists, Edges(iteration), are used to store only necessary
371 adjacencies for each iteration. This version runs much faster unless
372 a dynamic ordering of rows (i.e. maxcutoff or mincutoff) is chosen.
373 The users are strongly discouraged to use these dynamic ordering options.
374
375Version C0.38(Jan. 31, 1994) /
376 - Bmatrix struct has been modified to store only the row pointers. Thus the program
377 does not use any 2-dim arrays, and uses mainly dynamic allocation memory as much
378 as necessary irrespective of the declared maximum size MMAX times NMAX.
379 Thus, even in Macintosh computers large problems can be solved.
380 - CrissCrossSolve LP solver has been updated to output dual solutions as well.
381
382Version C0.37(Jan. 25, 1994) /
383 - Amatrix struct has been modified to store only the row pointers.
384
385Version C0.36(Jan. 23, 1994) /
386 - RayRecord struct has been modified to store only a pointer for a ZeroSet so that
387 the necessary space for the set is allocated each time. This saves a space for
388 storing each RayRecord ZeroSet. For this modification, the setoper library
389 must have been changed so that set_initialize allocates the minimum space.
390 Note that this new version (Jan. 23, 1994) does not work with the older cdd
391 programs.
392
393Version C0.35(Jan. 23, 1994) /
394 - RayRecord struct has been modified to store only a pointer for a Ray vector so that
395 the necessary space for the vector is allocated each time. This saves a space for
396 storing each RayRecord.
397
398Version C0.34(Jan. 22, 1994) /
399 - adjacency option has been added to output the adjacency list of output.
400
401Version C0.33(Jan. 16, 1994) /
402 - partial_enumeration option has been added. By this option, one can enumerate all vertices
403 and rays which are lying on a selected set of inequalities. The input
404 -------------
405 begin
406 m n Type
407 b -A1 -A2
408 end
409 partial_enumeration
410 4 1 4 6 7
411 -------------
412 restricts the enumeration for those lying on the 1st, 4th, 6th & 7th hyperplanes.
413
414Version C0.32(Jan. 11, 1994) /
415 - "preprojection" option has been added. This option can be considered as a preprocessing
416 of orthogonal projection of the polyhedon to a subset of variables. That is, if the inequality
417 inequality system is of form A1 x1 + A2 x2 <= b, and the variable indices for x2, say 1, 4, 6, 7,
418 are listed in the input file as
419 -------------
420 begin
421 m n Type
422 b -A1 -A2
423 end
424 preprojection
425 4 1 4 6 7
426 -------------
427 Then, cdd will output the inequality system, A1 x1 <= b, together with the list R of extremal
428 rays of the homogeneous cone {z: z >=0 and z A2 = 0 }. Consequently, the inequality system
429 {r A1 x1 <= r b for each r in R} represents the projection of the original polyhedron onto
430 x1-space with possible redundancy. The supplementary C program (written by F. Margot)
431 will be used to obtain a minimal system from these two outputs.
432
433Version C0.31(December 20, 1993) /
434 - The main program cdd.c has been divided into two parts, cdd.c and cddarith.c, the latter
435 contains all the procedures dealing with floating point numbers and operations.
436 - LP solver CrissCrossSolve has been added. Now the option "maximize" can be used to
437 optimize any linear function over the polyhedron.
438 - The setoper library has been updated to accomodate set_card(set) function.
439
440Version C0.27(December 8, 1993) /
441 - It uses a new versions of setoper.h and setoper.c (Dec 8, 1993 version) which have
442 set complemen procedure set_compl.
443
444Version C0.26b(December 8, 1993) /
445 - FindBasis and ComputeRank have been replaced with new programs which do not copy
446 Amatrix (for save storage and time). Accordingly, the procedure CopyAmarix has been
447 removed.
448
449Version C0.26 (November 29, 1993) /
450 - FindBasis has been modified to be faster when the number of inequalities is large.
451 - addition of #incidence option for outputting the cardinality of active
452 hyperplanes instead of the set of all active hyperplanes at each vertex.
453 - InitBasisAtBottom option has been added to select the last set of rows
454 as the initial basis (determining a simplex cone/polytope).
455 This option is {\em not\/} default. See User's manual.
456
457
458Version C0.25 (November 28, 1993)
459 - The bug for mishandling the empty polyhedra input is fixed.
460 Accordingly, the new variable CompStatus (Completion Status)
461 has been added.
462
463 - The procedure AddNewHyperplane and EvaluateARay have been completely
464 changed. EvaluateARay computes A(hnew) * Ray for each Rays, and sort
465 the linked list of rays so that the hnew-infeasible rays will be
466 put consecutively from FirstRay.
467
468
469Version C0.24 (November 27, 1993) /
470 - Modified to be able to deal with column size (nn) larger than 32.
471 - Bugs of LexMin, LexMax ordering options are fixed.
472
473Version C0.23a, b (November 23, 1993) /
474 - Few small bugs of C0.23 have been fixed.
475 - Up to this version, the program can deal with column size at most 32.
476
477Version C0.23 (November 22, 1993) /
478 - First release of cdd.
479
480Version C0.22 (November 21, 1993) /
481 - File open procedures have been updated.
482
483Version C0.21 (November 10, 1993) /
484 - The first version of cdd created by translating pdd.p (0.21) with
485 Dave Gillespie's p2c translator and by modifying the c-code. The set operation
486 libraries setoper.c, setoper.h (Nov.14, 1993) were created to make the code run
487 without any p2c libraries.
488
489*** cdd+ version (date) / changes ***
490
491cdd+ Version 0.77beta (April 20, 2003) /
492 This version is made so that it can be compiled with
493 newer gcc. such as gcc 3.1.*.
494
495cdd+ Version 0.76 (March 17, 1999) /
496 This is functionally the same as Ver. 075. This version can
497 be compiled to run with GNU's GMP rational arithmetic library using
498 Polymake's GMP-wrappers. cddr+ with GMP runs much faster than
499 the previous versions of cddr+ (with g++ Rational library).
500
501cdd+ Version 0.75 (November 30, 1997) /
502 This is a maintenance update of the previous version to employ the
503 new 1997 Polyhedra format (introducing H-representation and
504 V-representation statements). Three options for accuracy control
505 is added: "zero_tolerance", "round_output_off" and "output_digits".
506
507cdd+ Version 0.74 (June 17, 1996) /
508 Few minor bug fixes were made.
509
510cdd+ Version 0.74beta2 (June 5, 1996) /
511 Also "vertex_listing_external" and "facet_listing_external"
512 are added. These options do "vertex_listing" and "facet_listing"
513 against the external file which can be huge. These options are
514 useful when one has a small candidate set of vertices (or inequalities)
515 and a large set of perhaps-redundant points (or inequalities).
516 The external file must be named as "test.ext.external" (test.ine.external)
517 if the candidate input file is test.ext (test.ine).
518
519cdd+ Version 0.74beta (June 4, 1996) /
520 The option "vertex_listing" is added.
521 The dual simplex method uses the standard Phase I instead of
522 the criss-cross method. Consequently the LP code is faster.
523
524cdd+ Version 0.74alpha (March 30, 1996) /
525 The default output file names have been changed to be consistent
526 with the transformation. To avoid confusion, *.ine file should
527 be used only for a system of linear inequalities, and *.ext file
528 only for a set of extreme points and rays. Accordingly,
529 the files *.ead (previously *.adj) and *.ecd (previously *.icd)
530 are reserved for the adjacency and incidence files for the extremal
531 vertices/rays.
532 Similarly, *.iad (previously *.iad) and *.icd (previously none)
533 are reserved for the adjacency and incidence files for the inequality
534 data.
535
536 Also, when a file with default file name exists in the current
537 directory, the default extension name will be doubled. For instance,
538 if test.ine is input and test.ext exists, then the extreme points
539 and rays will be written in the file test.ext.ext. The program
540 does not check "test.ext.ext" exists, and thus such a file
541 will be overwritten if exists.
542
543cdd+ Version 0.73 (Septembe 6, 1995) /
544 A new option "input_adjacency" has been added.
545 The output format of incidence file is slightly modified. (See
546 the Reference Manual cddman.tex). This incidence file format is compatible
547 with cdd-056 and we will try not to change the format any more.
548
549cdd+ Version 0.72a (April 16, 1995) /
550 Cycling bug of Version 072 of LP maximize and minimize has been
551 fixed.
552cdd+ Version 0.72 (April 16, 1995) /
553 The option "postanalysis" is added. This option is to be used
554 after *.ext file is obtained. When this option is set
555 with adjacency and/or incidence options, one can get
556 adjacency and incidence files from both *.ine and *.ext
557 files. Thus it is not necessary to generate *.adj and *.icd
558 files together with *.ext file.
559
560cdd+ Version 0.71 (April 15, 1995) /
561 Two new functions (through options) are added. The option
562 "facet_listing" checks whether each input inequality determines
563 a facet or not. The second option "tope_listing" generates
564 all full-dimensional regions (topes) of the associated
565 arrangement of hyperplanes by reverse search algorithm.
566 Also, the option "show_tableau" is added to illustrate
567 how the criss-cross method works in the tableau (dictornary)
568 form. Criss-cross LP solver is now sensitive to ordering
569 options, lexmin, minindex, radom, etc.
570
571 cdd+ Version 0.70 (April 3, 1995) /
572 The first C++ version of cdd which can run on both floating-point
573 and rational (exact) arithmetics. The basic functions are
574 identical to cdd-055. This version requires GNU gcc compilers
575 (2.6.0 or higher) and a compatible g++lib.
576
577
578--- end of file: cddHISTORY ---
579