June 2004 - GiNaC-devel

patch.
by Chris Dams 29 Jun '04

29 Jun '04

Dear GiNaCers, Could somebody change the line if (degsum>order) { that occurs in the function mul::series into if (degsum>=order) { for obvious reasons? Thanks. Best, Chris 3603 38th St. NW Suite 201 Washington, DC 20008

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Writing bindings for C++ (template) libraries in Mathemagix (fwd)
by Richard B. Kreckel 25 Jun '04

25 Jun '04

Hi, I just received an email from Joris van der Hoeven. In case somebody wishes to give it a try. Have fun -richy. -- Richard B. Kreckel <http://www.ginac.de/~kreckel/> ---------- Forwarded message ---------- Date: Fri, 25 Jun 2004 16:45:34 +0200 (CEST) From: Joris van der Hoeven <vdhoeven(a)texmacs.org> To: mathemagix-devel(a)mathemagix.org Cc: kreckel(a)thep.physik.uni-mainz.de, haible(a)ilog.fr Subject: Writing bindings for C++ (template) libraries in Mathemagix Hi All, I am happy to announce that the new version 0.1.41 of Mathemagix (available from mathemagix.org) should allow you to easily glue C++ libraries as well as C++ template libraries to the interpreter. The main mechanism is as follows: from an abstract description of your library in a file like 'myglue.mmh' (see the examples provided in src/glue), the mmx-extend script automatically generates a C++ file which is compiled as a shared library 'mmx-myglue.so'. This library can be loaded dynamically into Mathemagix via 'use "myglue"'. Your library may also contain templates and the mmx-extend script *automatically* creates an extension of your library which enables you to use these templates in a generic way. I.e., having a template class "Matrix", you will typically be able to use matrices over matrices over matrices over integers. Moreover, this generic extension should imply only a minimal overhead. In the above matrix example, and as long as the operations on the scalars are implemented in your library, no re-entrant calls to Mathemagix are needed and operations are done quickly using some void* magic. The code has been (incompletely) tested together with several libraries (STL, Gmp, Synaps and Mmxlib) and contributions in this direction would be *very much* appreciated. Apart from completing the existing binding files, support for the following mathematical libraries would be nice: mpfr mpfi CLN NTL GiNaC Linbox libfactory CGAL etc. Further suggestions for interesting scientific libraries are welcome, the aim being to focus on incorporating as much existing software as possible before starting to write programs in Mathemagix itself. It would also be interesting to have bindings for libraries like gtk, qt, opengl, unicode, cryptography, etc. etc. Some shortcomings of the current implementation are as follows: * The GC garbage collector from Boehm seems to be bugged; it does not allow the use of dynamic libraries ;^( You may either configure Mathemagix using ./configure --disable-gc or add an additional section for your library in the current configure.in file, add your bindings to the src/glue directory and use static compilation. * It is only possible to import generic routines from Mathemagix. Such routines correspond to the operations you wish to perform on types which occur as template arguments (like the scalar type for matrices). It is not possible yet to import ordinary routines or types from Mathemagix. As a consequence, if you want to write bindings for several libraries, then you usually have to produce the glue for all of them together. From an efficiency point of view, this is better anyway. * The names of exported C++ classes and functions should be of the form "identifier" or "identifier<id1,...,idn>". Special syntactic forms for operations like "x.f", "x->f", "x::f", etc. are not provided yet. You may always add the necessary macros or code to the preamble though. * There may still be some bugs. Feedback on this is appreciated. Don't hesitate to ask further questions on this list. Any feedback is appreciated. Best wishes, Joris

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cln::divisors()
by Ralf Stephan 22 Jun '04

22 Jun '04

The complete factor() patch was sent to Richy. Should the divisors be sorted? Do we leave that to the client? Can someone tell me why gcc barfs when I declare f const? vector<cl_I> divisors(const cl_I& n) { cl_FEV f = factor(n); vector<long> v(f.size()); vector<cl_I> res; res.push_back(1); while (true) { vector<long>::iterator vit = v.begin(); cl_FEV::iterator fit = f.begin(); while (*vit == (*fit)->exp) { *vit = 0; if (++vit == v.end()) return res; ++fit; } cl_I prod = expt_pos((*fit)->fact, ++(*vit)); ++vit; ++fit; while (vit != v.end()) { if (*vit > 0) prod = prod * expt_pos((*fit)->fact, *vit); ++vit; ++fit; } res.push_back(prod); } } ralf

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Lib not found
by Tapan 22 Jun '04

22 Jun '04

Dear sir/m'me With g++ test.cpp -lcln -lginac -lm (compile command) compiling the the attached programme the following errors occurs: In file included from /usr/include/c++/3.3.3/backward/iostream.h:31, from test.cpp:1: /usr/include/c++/3.3.3/backward/backward_warning.h:32:2: warning: #warning This file includes at least one deprecated or antiquated header. Please consider usin g one of the 32 headers found in section 17.4.1.2 of the C++ standard. Examples include substituting the <X> header for the <X.h> header for C++ includes, or <s stream> instead of the deprecated header <strstream.h>. To disable this warning use -Wno-deprecated. test.cpp:2:24: ginac/ginac.h: No such file or directory test.cpp:4: error: namespace `GiNaC' undeclared test.cpp: In function `int main()': test.cpp:8: error: `symbol' undeclared (first use this function) test.cpp:8: error: (Each undeclared identifier is reported only once for each function it appears in.) test.cpp:8: error: syntax error before `(' token test.cpp:9: error: `ex' undeclared (first use this function) test.cpp:12: error: `poly' undeclared (first use this function) test.cpp:12: error: `fractorial' undeclared (first use this function) test.cpp:12: error: `x' undeclared (first use this function) test.cpp:12: error: `y' undeclared (first use this function) [tapan@shaula tapan]$ g++ test.cpp -lcln -lginac -lm In file included from /usr/include/c++/3.3.3/backward/iostream.h:31, from test.cpp:1: /usr/include/c++/3.3.3/backward/backward_warning.h:32:2: warning: #warning This file includes at least one deprecated or antiquated header. Please consider usin g one of the 32 headers found in section 17.4.1.2 of the C++ standard. Examples include substituting the <X> header for the <X.h> header for C++ includes, or <s stream> instead of the deprecated header <strstream.h>. To disable this warning use -Wno-deprecated. test.cpp:2:24: ginac/ginac.h: No such file or directory test.cpp:4: error: namespace `GiNaC' undeclared test.cpp: In function `int main()': test.cpp:8: error: `symbol' undeclared (first use this function) test.cpp:8: error: (Each undeclared identifier is reported only once for each function it appears in.) test.cpp:8: error: syntax error before `(' token test.cpp:9: error: `ex' undeclared (first use this function) test.cpp:12: error: `poly' undeclared (first use this function) test.cpp:12: error: `fractorial' undeclared (first use this function) test.cpp:12: error: `x' undeclared (first use this function) test.cpp:12: error: `y' undeclared (first use this functio With command $ locate cln following occure: /usr/share/doc/cln-1.1.7 /usr/share/doc/cln-1.1.7/README /usr/share/doc/cln-1.1.7/TODO /usr/share/doc/cln-1.1.7/NEWS /usr/share/doc/cln-1.1.7/FILES /usr/share/doc/cln-1.1.7/ChangeLog /usr/share/doc/cln-1.1.7/TODO-verylong /usr/share/doc/cln-1.1.7/COPYING /usr/share/doc/cln-1.1.7/TODO-subclass /usr/share/doc/cln-1.1.7 /usr/share/doc/ruby-1.8.1/sample/clnt.rb /usr/share/man/man3/clnt_create.3.gz /usr/share/man/man3/clnt_geterr.3.gz /usr/share/man/man3/clntudp_create.3.gz /usr/share/man/man3/clnt_destroy.3.gz /usr/share/man/man3/clntudp_bufcreate.3.gz /usr/share/man/man3/clnt_freeres.3.gz /usr/share/man/man3/clntraw_create.3.gz /usr/share/man/man3/clnt_broadcast.3.gz /usr/share/man/man3/clnttcp_create.3.gz /usr/share/man/man3/clnt_pcreateerror.3.gz /usr/share/man/man3/clnt_perror.3.gz /usr/share/man/man3/clnt_sperror.3.gz /usr/share/man/man3/clnt_perrno.3.gz /usr/share/man/man3/clnt_sperrno.3.gz /usr/share/man/man3/clnt_call.3.gz /usr/share/man/man3/clnt_control.3.gz /usr/share/man/man3/clnt_spcreateerror.3.gz /usr/share/man/ja/man3/clnt_create.3.gz /usr/share/man/ja/man3/clnt_geterr.3.gz /usr/share/man/ja/man3/clntudp_create.3.gz /usr/share/man/ja/man3/clnt_destroy.3.gz /usr/share/man/ja/man3/clntudp_bufcreate.3.gz /usr/share/man/ja/man3/clnt_freeres.3.gz /usr/share/man/ja/man3/clntraw_create.3.gz /usr/share/man/ja/man3/clnt_broadcast.3.gz /usr/share/man/ja/man3/clnttcp_create.3.gz /usr/share/man/ja/man3/clnt_pcreateerror.3.gz /usr/share/man/ja/man3/clnt_perror.3.gz /usr/share/man/ja/man3/clnt_sperror.3.gz /usr/share/man/ja/man3/clnt_perrno.3.gz /usr/share/man/ja/man3/clnt_sperrno.3.gz /usr/share/man/ja/man3/clnt_call.3.gz /usr/share/man/ja/man3/clnt_control.3.gz /usr/share/man/ja/man3/clnt_spcreateerror.3.gz /usr/share/man/fr/man3/clnt_create.3.gz /usr/share/man/fr/man3/clnt_geterr.3.gz /usr/share/man/fr/man3/clntudp_create.3.gz /usr/share/man/fr/man3/clnt_destroy.3.gz /usr/share/man/fr/man3/clntudp_bufcreate.3.gz /usr/share/man/fr/man3/clnt_freeres.3.gz /usr/share/man/fr/man3/clntraw_create.3.gz /usr/share/man/fr/man3/clnt_broadcast.3.gz /usr/share/man/fr/man3/clnttcp_create.3.gz /usr/share/man/fr/man3/clnt_pcreateerror.3.gz /usr/share/man/fr/man3/clnt_perror.3.gz /usr/share/man/fr/man3/clnt_sperror.3.gz /usr/share/man/fr/man3/clnt_perrno.3.gz /usr/share/man/fr/man3/clnt_sperrno.3.gz /usr/share/man/fr/man3/clnt_call.3.gz /usr/share/man/fr/man3/clnt_control.3.gz /usr/share/man/fr/man3/clnt_spcreateerror.3.gz /usr/share/cvs/contrib/cln_hist /usr/src/linux-2.6.5-1.358/fs/xfs/xfs_clnt.h /usr/src/linux-2.6.5-1.358/fs/nfs/mount_clnt.c /usr/src/linux-2.6.5-1.358/fs/lockd/clntlock.c /usr/src/linux-2.6.5-1.358/fs/lockd/clntproc.c /usr/src/linux-2.6.5-1.358/net/sunrpc/clnt.c /usr/src/linux-2.6.5-1.358/net/sunrpc/pmap_clnt.c /usr/src/linux-2.6.5-1.358/include/linux/sunrpc/clnt.h /usr/lib/libkadm5clnt.so.5 /usr/lib/libkadm5clnt.so /usr/lib/dietlibc/include/rpc/clnt.h /usr/lib/dietlibc/include/rpc/pmap_clnt.h /usr/lib/libkadm5clnt.a /usr/lib/libcln.so.3 /usr/lib/libcln.so.3.0.1 /usr/lib/libkadm5clnt.so.5.1 /usr/include/rpcsvc/ypclnt.h /usr/include/linux/sunrpc/clnt.h /usr/include/rpc/clnt.h /usr/include/rpc/pmap_clnt.h /dos/Program Files/Common Files/Real/Plugins/clntxres.dll /dos/windows/system32/dllcache/davclnt.dll /dos/windows/system32/dllcache/fldrclnr.dll /dos/windows/system32/dllcache/fxsclnt.exe /dos/windows/system32/dllcache/fxsclntr.dll /dos/windows/system32/dllcache/webclnt.dll /dos/windows/system32/webclnt.dll /dos/windows/system32/davclnt.dll /dos/windows/system32/fldrclnr.dll /dos/windows/Help/fxsclnt.chm /dos/windows/Help/fxsclnt.hlp /dos/Documents and Settings/Tapan/My Documents/cln-1.1.7.tar.bz2 /lib/modules/2.6.5-1.358/build/include/linux/sunrpc/clnt.h with command $locate ginac following occurs : /usr/share/doc/HTML/en/kdelibs-apidocs/kdeprint/html/management_2pluginaction_8cpp-source.html /usr/share/doc/HTML/en/kdelibs-apidocs/kdeprint/html/kdeprint_2pluginaction_8cpp-source.html /usr/share/doc/HTML/en/kdelibs-apidocs/kdeprint/html/kdeprint_2pluginaction_8h-source.html /usr/share/doc/HTML/en/kdelibs-apidocs/kdeprint/html/management_2pluginaction_8h-source.html /usr/lib/libginac-1.2.so.0.0.1 /usr/lib/libginac-1.2.so.0 Now how to fixed the bug. I am using Fedora core 2. Thanks Tapan Naskar Ph: +91 022 25604222 (Off) IUCAA 25604525 (Res) Post Bag:04 Mob: 91 022 9890430978 Ganeshkhind Fax: 91 022 335760 Pune 411007 Telex: 0145 7658 GMRT IN

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Resultant patch
by Ralf Stephan 21 Jun '04

21 Jun '04

Please include. This works with any polynomial. Best, ralf diff -u --recursive GiNaC-1.2.1-orig/doc/tutorial/ginac.texi GiNaC-1.2.1/doc/tutorial/ginac.texi --- GiNaC-1.2.1-orig/doc/tutorial/ginac.texi Mon Mar 15 18:47:17 2004 +++ GiNaC-1.2.1/doc/tutorial/ginac.texi Sun Jun 20 15:45:19 2004 @@ -4371,7 +4399,7 @@ original polynomial. -@subsection GCD and LCM +@subsection GCD, LCM, resultant @cindex GCD @cindex LCM @cindex @code{gcd()} @@ -4408,7 +4436,37 @@ @} @end example +@cindex resultant +@cindex @code{resultant()} + +The resultant of two expressions only makes sense with polynomials. +It is always computed with respect to a specific symbol within the +expressions. The function has the interface + +@example +ex resultant(const ex & a, const ex & b, const symbol & s); +@end example +Resultants are commutative. The following example computes the resultant +of two expressions with respect to both @code{x} and @code{y}: + +@example +#include <ginac/ginac.h> +using namespace GiNaC; + +int main() +@{ + symbol x("x"), y("y"); + + ex e1 = x+pow(y,2), e2 = 2*pow(x,3)-1; // x+y^2, 2*x^3-1 + ex r; + + r = resultant (e1, e2, x); + // -> 1+2*y^6 + r = resultant (e1, e2, y); + // -> 1-4*x^3+4*x^6 +@} +@end example @subsection Square-free decomposition @cindex square-free decomposition @cindex factorization diff -u --recursive GiNaC-1.2.1-orig/ginac/normal.cpp GiNaC-1.2.1/ginac/normal.cpp --- GiNaC-1.2.1-orig/ginac/normal.cpp Thu Jan 8 16:06:50 2004 +++ GiNaC-1.2.1/ginac/normal.cpp Sun Jun 20 11:58:11 2004 @@ -2374,5 +2374,33 @@ return e; } +/** Resultant of two expressions e1,e2 with respect to symbol s. + * Method: Compute determinant of Sylvester matrix of e1,e2,s. */ +ex resultant (const ex &e1, const ex &e2, const symbol &s) +{ + const int h1 = e1.degree (s); + const int l1 = e1.ldegree (s); + const int h2 = e2.degree (s); + const int l2 = e2.ldegree (s); + + const int msize = h1 + h2; + matrix m (msize, msize); + + for (int l = h1; l >= l1; --l) + { + const ex e = e1.coeff (s, l); + for (int k = 0; k < h2; ++k) + m (k, k+h1-l) = e; + } + for (int l = h2; l >= l2; --l) + { + const ex e = e2.coeff (s, l); + for (int k = 0; k < h1; ++k) + m (k+h2, k+h2-l) = e; + } + + return m.determinant(); +} + } // namespace GiNaC diff -u --recursive GiNaC-1.2.1-orig/ginac/normal.h GiNaC-1.2.1/ginac/normal.h --- GiNaC-1.2.1-orig/ginac/normal.h Thu Jan 8 16:06:50 2004 +++ GiNaC-1.2.1/ginac/normal.h Sun Jun 20 11:57:22 2004 @@ -66,6 +66,9 @@ // Collect common factors in sums. extern ex collect_common_factors(const ex & e); +// Resultant of two polynomials e1,e2 with respect to symbol s +extern ex resultant (const ex& e1, const ex& e2, const symbol& s); + } // namespace GiNaC #endif // ndef __GINAC_NORMAL_H__

2 1

series and expansion.
by Chris Dams 20 Jun '04

20 Jun '04

Dear developers, Some time ago I sent a patch to prevent .series() to revert to .expand() internally. This was because in the case that one has polynomial^some_large_integer the expansion will be hopeless. However, I keep running into this kind of problems. To determine the real_ldegree in mul::pseries, still expansion is used with potentially the same problems. I think there are two possible solutions to this problem. (1) Tell your users (me included) that they should not be substituting polynomials into each others when they should have used power series from the start. (2) Create (or ask me to create) a patch that solves this particular case and hope that there will not be ten other instances where .series() is going to crash a program. (3) Forbid any occurance of .expand() in any method or function that may be called from .series(). Create a new method to determine the leading behaviour of any expression. Let .series() use this and let .series() work by calculating power series of subexpressions and combining these into the power series for the entire expression. I am in favour of (3). The only reason not to use (3) would be if someone in this mailing list could come up with an example where (3) clearly is horribly inefficient. What do other people think? Best, Chris Dams

2 3

CLN/ginac: factoring announce, questions
by Ralf Stephan 19 Jun '04

19 Jun '04

Hello, the following is concerned with the numtheory part of CLN. I have appended a patch to numtheory/cl_IF.h file and three new files for the same directory that would provide a factoring engine. The code is a much improved version of what I sent to Richy Kreckel a few days ago, and it explains itself. I have serious design questions on the interface, though. Shortly summed, you can factor any integer now within a minute whose second largest prime factor is less than ~10^11. I am not an expert, and I will not even think about implementing one of the more exotic algorithms (squfof, elliptic curves, all kind of sieves). I did this because I need ginac with a divisors() function. The people familiar with ginac/CLN design are asked to please answer QUESTION 1. The function cl_factor_rec() is the recursive main engine and will be called by factor() that is the interface to it. What should factor() return to the outside? We have - two lists (prime factors, exponents) - a list of pairs (p1,e1) (p2,e2) ... pari does return data like this - a simple list (p1, e1, p2, e2, p3, ...) QUESTION 2. How should the pairs/lists be implemented? We have - vectors provided by CLN (GV/SV where's the difference?) - STL containers An alternative would be to implement factor() outside CLN, ie, within ginac using lst, but I think there is interest having it in CLN. I just ask because I do not think the STL should be duplicated by GV/SV which, supposedly, was started when gcc did not have a working STL. I am no expert there, either, but I think CLN's memory scheme can be adapted to STL by simply(?) using a tailored allocator object. QUESTION 3. Should divisors() go into CLN or ginac? Many thanks for your time reading through to here. Please help---I am just starting C++ again after 8 years of hiatus, and design thinking is a bit unfamiliar at this time. Anyway, here is the beef: Sincerely, ralf --- cl_IF.h.orig Wed Jun 16 16:16:08 2004 +++ cl_IF.h Tue Jun 15 19:50:14 2004 @@ -3,6 +3,7 @@ #ifndef _CL_IF_H #define _CL_IF_H +#include <vector> #include "cln/number.h" #include "cln/integer.h" @@ -49,6 +50,15 @@ // Returns false if n is definitely composite, and then sets factor = some // nontrivial factor or 0. extern cl_boolean cl_miller_rabin_test (const cl_I& n, int count, cl_I* factor); + +// Pollard rho algorithm +extern cl_I cl_pollard_rho (const cl_I& n, long iters); + +// Pollard p-1 algorithm +extern cl_I cl_pollard_pmone (const cl_I& n); + +// Core recursive factoring routine, needs container +extern int cl_factor_rec (const cl_I& n, std::vector<cl_I>& v); } // namespace cln --- cl_IF_factor_rec.cc.orig Wed Jun 16 16:18:44 2004 +++ cl_IF_factor_rec.cc Tue Jun 15 19:10:12 2004 @@ -0,0 +1,109 @@ +// cl_factor_rec(). + +// General includes. +#include "cl_sysdep.h" + +// Specification. +#include "cl_IF.h" + + +// Implementation. + +#include "cln/integer.h" + +namespace cln { + +int cl_factor_rec(const cl_I& n, std::vector<cl_I>& v) +// recursive buildup of prime factors vector, part of code stolen from +// isprobprime.cc. +// prime factors of n are collected in v, 0 returned if factorization complete. +{ + // With a Miller-Rabin count = 50 the final error probability is + // 4^-50 < 10^-30. + int count = 50; + // Trial division (rules out 87% of all numbers quickly). + const uintL l = integer_length(n); + if (l <= 32) + { + uint32 nn = cl_I_to_UL(n); + if (nn <= cl_small_prime_table_limit) + { + // Table lookup. + uintL i = cl_small_prime_table_search(nn); + if (i < cl_small_prime_table_size + && ((unsigned int) cl_small_prime_table[i] == nn + || nn == 2)) + { v.push_back (n); return 0; } // end leaf of recursion + } + if ((nn % 2) == 0) + { v.push_back (2); return cl_factor_rec (n>>1, v); } + if ((nn = cl_trialdivision(nn,1,cl_small_prime_table_limit)) >0) + { v.push_back (nn); return cl_factor_rec (exquo (n,nn), v); } + + // For small n, only few Miller-Rabin tests are needed. + if (nn < 2000U) count = 1; // {2} + else if (nn < 1300000U) count = 2; // {2,3} + else if (nn < 25000000U) count = 3; // {2,3,5} + else if (nn < 3200000000U) count = 4; // {2,3,5,7} + } + else if (l <= 64) + { + uint32 nhi = cl_I_to_UL(ldb(n,cl_byte(32,32))); + uint32 nlo = cl_I_to_UL(ldb(n,cl_byte(32,0))); + if ((nlo % 2) == 0) + { v.push_back (2); return cl_factor_rec (n>>1, v); } + uint32 t; + if ((t = cl_trialdivision (nhi,nlo,1,cl_small_prime_table_limit)) >0) + { v.push_back (t); return cl_factor_rec (exquo (n,t), v); } + } + else + { + if (evenp (n)) + { v.push_back (2); return cl_factor_rec (n>>1, v); } + uint32 t; + if ((t = cl_trialdivision (n,1,cl_small_prime_table_limit)) >0) + { v.push_back (t); return cl_factor_rec (exquo (n,t), v); } + } + + // Handle perfect powers. + int m; + cl_I r; + if (rootp (n, m, &r)) + { + std::vector<cl_I> vv; + int ret = cl_factor_rec (r, vv); + for (int l=0; l<m; ++l) + copy (vv.begin(), vv.end(), v.begin()); + return ret; + } + + // After factoring out small factors: is remaining number prime? + if (cl_miller_rabin_test (n, count, NULL)) + { + v.push_back (n); + return 0; + } // end leaf of recursion + + // 30k iterations of Pollard rho finds most 8-digit factors. + // 150k iterations of Pollard rho finds most 10-digit factors. + cl_I f; + f = cl_pollard_rho (n, 150000L); + if (f != 1 && f != n) + { v.push_back (f); return cl_factor_rec (exquo (n,f), v); } + + // Pollard p-1 using cl_small_prime_table. Does not often find a factor + // but does not cost much, either. If it finds one, it may have + // up to 18-20 digits, occasionally. + f = cl_pollard_pmone (n); + if (f != 1 && f != n) + { v.push_back (f); return cl_factor_rec (exquo (n,f), v); } + + // Last step (for now): let Pollard rho run 'forever'. + // If you don't want this, return 1 without calling rho() again. + v.push_back (cl_pollard_rho (n, 0)); + return 0; // end leaf of recursion +} + + +} // namespace cln + --- cl_IF_pollard_rho.cc.orig Wed Jun 16 16:21:23 2004 +++ cl_IF_pollard_rho.cc Tue Jun 15 17:04:20 2004 @@ -0,0 +1,42 @@ +// cl_pollard_rho(). + +// General includes. +#include "cl_sysdep.h" + +// Specification. +#include "cl_IF.h" + + +// Implementation. + +#include "cln/integer.h" + +namespace cln { + +cl_I cl_pollard_rho (const cl_I& n, long iters) +// If N is composite, returns a factor of N, for iters>0 not necessarily <>N. +// Adaptation of an implementation by Richard Crandall (giantint). +// This gets slow when factors become larger than 10^10. iters=0 runs until +// factor is found. Using modinteger slows function down by 10 percent. +{ + cl_I g=1, t1=3, t2=3; + + for (long l=0; !iters || l<iters; ++l) + { + if (l%100 == 0) // removing this line seems to make no big difference + { + if ((g = gcd (g, n)) != 1) + break; + } + t1 = mod (square (t1) + 2, n); + t2 = mod (square (t2) + 2, n); + t2 = mod (square (t2) + 2, n); + g = mod (g * abs (t2-t1), n); + } + g = gcd (g, n); + return g; +} + +} // namespace cln + + --- cl_IF_pollard_pmone.cc.orig Wed Jun 16 16:22:45 2004 +++ cl_IF_pollard_pmone.cc Tue Jun 15 17:48:57 2004 @@ -0,0 +1,48 @@ +// cl_pollard_pmone(). + +// General includes. +#include "cl_sysdep.h" + +// Specification. +#include "cl_IF.h" + + +// Implementation. + +#include "cln/modinteger.h" + +namespace cln { + +cl_I cl_pollard_pmone (const cl_I& n) +// Pollard p-1 using cl_small_prime_table. Does not often find a factor +// but does not cost much, either. If it finds one, it may have +// up to 18-20 digits, occasionally. +// Returns a factor of N, not necessarily <>n. +// Adaptation of an implementation by Richard Crandall (giantint). +{ + cl_modint_ring R = find_modint_ring (n); + cl_MI g(R,cl_I(1)), t1(R,cl_I(3)); + cl_I t; + + for(long l=0; l<cl_small_prime_table_size; ++l) + { + long cnt = long((8.0*log(2.0))/log(1.0*cl_small_prime_table[l])); + if (cnt < 2) + cnt = 1; + for (long k=0; k<cnt; ++k) + t1 = expt_pos (t1, cl_small_prime_table[l]); + + g = g * (t1-1); + if (l%100==0) + { + if ((t = gcd (R->retract(g), n)) != 1) + break; + g = R->canonhom (t); + } + } + t = gcd (R->retract(g), n); + return t; +} + +} // namespace cln +

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cl_N log(const cl_N& a, const cl_N& b) returns zero when an exact negative integer is expected
by Niklas Knutsson 18 Jun '04

18 Jun '04

hi. the following bug required a workaround when writing source code for Qalculate!: cl_N log(const cl_N& a, const cl_N& b) returns zero when an exact negative integer is expected. example: log(recip(cl_RA(1000)), cl_N(10)); returns 0 log(cl_N(0.001), cl_N(10)); returns -3 using cln-1.1.6 gmp-4.1.2 gcc-3.3.3 glibc-2.3.3_pre20040207 linux-2.6.5-mm1 //niklas k.

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patch for pseries.
by Chris Dams 15 Jun '04

15 Jun '04

Dear GiNaCers, Some more changes for pseries. I think most of them do not need explaination. Best, Chrsi

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Bug? Failure running make check.
by Sala Lorenzo 09 Jun '04

09 Jun '04

I encountered this problem installing GiNaC on my Linux/Mandrake uname -a returns 2.4.22-10mdk #1 .. i686 unknown unknown GNU/Linux gcc --version return gcc (GCC) 3.3.1 (Mandrake Linux 9.2 3.3.1-2mdk) Version and release of GiNaC: GiNaC 1.2.1-1.src.rpm No option passed to configure. I've done ./configure, make install (all is OK), but running make check I can see this message examing series expansion ......../run_exams: line 3: 19967 Segmentation fault ./exams 2>exams.out ./exams.ref exams.out differ: byte 433 line 18 FAIL: run_exams I attach the file exams.out Thanks for your job, Sala Lorenzo

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