- GiNaC-list - ginac.de

Intervals in GiNaC
by Simon Langley 01 Dec '03

01 Dec '03

Carl, I have an interval class which I use in GiNaC. It isn't as tidy as I'd like but it works in the following sense: * I'm only interested in polynomials so the interval class doesn't have other functions like sin/exp/etc just field operations and powers. * It assumes that either rational or s/w floating point arithmetic is used. There is a problem with h/w floating point in GiNaC because underflow/overflow errors may not get noted. That said because of the way GiNaC works you can mix floating point and rational arithmetic. * When used in Ginac expressions, interval expressions aren't simplified. I.e. you can write ex z = interval(-1,1) + x + interval(1, 3)*4 + interval(1.3, 3.1) but z.simplify() won't add the intervals and z.subs(x == 2.3) won't reduce the expression to an interval. I've written a procedure to evaluate a Ginac expression in intervals to an interval (again assuming you only need polynomial expressions). If you want it let me know. By the way are you working with Dan Richardson or has interest in intervals at Bath spread? Simon ~~~~~ Simon Langley c/o CEMS, UWE, BS16 1QY

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automatic differentiation and change expression ordering
by Andrius Kurtinaitis 20 Nov '03

20 Nov '03

Hello, I have two questions: 1. is it possible to prevent automatic differentiation of some expression? For example, when I do (with ginac 1.1.4): DECLARE_FUNCTION_1P( intensity ) static ex intensity_eval( const ex & r ) { return intensity(r).hold(); } // here i tried to hold it :-) REGISTER_FUNCTION( intensity, eval_func(intensity_eval) ) int main() { symbol r("r"); ex der1 = mul( diff( intensity(r), r ), r ).hold(); ex deriv = der1.diff(r); cout << deriv << endl; return 0; } I get the following output: D[0,0](intensity)(r)*r+D[0](intensity)(r) But I would like to get something like this: D[0]( D[0](intensity)(r)*r )(r) Is it possible with ginac? 2. What is the simplest way to change the order in multiplication so that the differential operators print after all other terms: r*D[0,0](intensity)(r) instead of D[0,0](intensity)(r)*r And the third one ;-) Is there maybe some work done to output fderivative in latex style? Thanks in advance Andrius

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CLN + GiNaC on MinGW
by Jonathan Brandmeyer 05 Nov '03

05 Nov '03

I am attempting to build CLN (and later, GiNaC) on my Windows XP machine with Mingw. I am using g++ 3.2.3 and the latest binary utilities. I have a build of GMP 4.2.1 for use as a backend for CLN (installed under c:\msys\1.0\local\). CLN was configured with CPPFLAGS=-I/usr/local/include LIBS=/usr/local/lib/libgmp-3.dll CXXFLAGS="-O2 -finline-functions -fomit-frame-pointer -march=i686 -finline-limit=1000" ./configure --with-gmp. The build progressed and after a couple hours the link failed for the shared library. It looks a lot like what was described on ginac-devel when a fellow had problems on Alpha (thread begins here: http://www.ginac.de/lists/ginac-devel/msg00091.html) except that I am using a relatively modern toolchain. The linker errors are of the form: cl_t_c2.lo(.text+0x4e):cl_t_c2.cc: undefined reference to `_GLOBAL__I_cl_module__cl_prin_globals__firstglobalfun' Any thoughts? -Jonathan Brandmeyer P.S. I am using msys to drive the build, but I do not want to use Cygwin.

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GiNaC 1.1.5 now available
by Christian Bauer 05 Nov '03

05 Nov '03

Hello! "Release Early, Release Often" The GiNaC Group is pleased to announce the immediate availability of GiNaC 1.1.5 which contains lots of improvements to the nestedsums functions: - Harmonic polylogarithms now numerically evaluate for arbitrary arguments (parameter must still be positive integers). - The zeta function now can also be given a lst as a parameter in which case it becomes a multiple zeta value. The use of mZeta is deprecated. - The order of parameters for the multiple polylogarithm has been corrected. - Documentation for the nested sums functions zeta, harmonic polylog, multiple polylog, etc. has been added. Run, don't walk, to everyone's favorite FTP server: ftp://ftpthep.physik.uni-mainz.de/pub/GiNaC/ Have a nice day, Christian -- / Physics is an algorithm \/ http://www.uni-mainz.de/~bauec002/

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CLN + GiNaC on Apple OSX
by Jonathan Brandmeyer 04 Nov '03

04 Nov '03

In addition to building on Windows/MinGW, I am also trying to get this going on Mac OSX. I have had problems with Apple's early releases of GCC, so I am using a local build of GCC-3.3.1. I believe that the binary utilities are mostly GNU with Apple's linker. (as reports 1.38 as its version). I am building CLN against GMP 4.1.2. ( I said 4.2.1 earlier, but I really installed 4.1.2). CLN was configured with CC=gcc-3.3 CXX=g++-3.3 CXXFLAGS="-O2 -finline-functions" CFFLAGS="-Dunix -D__unix" (-D__unix was needed for a random number constructor) ./configure --with-gmp The build fails with cascading syntax errors in modinteger/cl_MI.cc and several other files. Thank you for any insight you may have on this problem, -Jonathan Brandmeyer g++-3.3 -v: Reading specs from /usr/local/lib/gcc-lib/powerpc-apple-darwin6.8/3.3.1/specs Configured with: ../gcc-3.3.1/configure --enable-languages=c,c++ --enable-threads=posix --program-suffix=-3.3 Thread model: posix gcc version 3.3.1 The build fails in the modinteger directory with this error: make SUBDIR=modinteger /bin/sh ../libtool --mode=compile g++-3.3 -O2 -finline-functions -Dunix -D__unix -I../include -I../include -I./integer/hash -I./integer -I./base/hash -I./base/digitseq -I./base/digit -Ibase -I./base -c ./modinteger/cl_MI.cc rm -f .libs/cl_MI.lo g++-3.3 -O2 -finline-functions -Dunix -D__unix -I../include -I../include -I./integer/hash -I./integer -I./base/hash -I./base/digitseq -I./base/digit -Ibase -I./base -c ./modinteger/cl_MI.cc -fno-common -DPIC -o .libs/cl_MI.lo In file included from modinteger/cl_MI.cc:80: modinteger/cl_MI_pow2.h:16: error: parse error before numeric constant modinteger/cl_MI_pow2.h: In function `const cln::cl_I cln::pow2_reduce_modulo(...)': modinteger/cl_MI_pow2.h:19: error: `x' undeclared (first use this function) modinteger/cl_MI_pow2.h:19: error: (Each undeclared identifier is reported only once for each function it appears in.) modinteger/cl_MI_pow2.h: In function `const cln::_cl_MI cln::pow2_canonhom(cln::cl_heap_modint_ring*, const cln::cl_I&)': modinteger/cl_MI_pow2.h:24: warning: cannot pass objects of non-POD type `const class cln::cl_I' through `...'; call will abort at runtime modinteger/cl_MI_pow2.h: At global scope: modinteger/cl_MI_pow2.h:27: error: parse error before numeric constant modinteger/cl_MI_pow2.h: In function `const cln::_cl_MI cln::pow2_plus(...)': modinteger/cl_MI_pow2.h:30: error: `y' undeclared (first use this function) modinteger/cl_MI_pow2.h: At global scope: modinteger/cl_MI_pow2.h:34: error: parse error before numeric constant modinteger/cl_MI_pow2.h:41: error: parse error before numeric constant modinteger/cl_MI_pow2.h:48: error: parse error before numeric constant modinteger/cl_MI_pow2.h:54: error: parse error before numeric constant modinteger/cl_MI_pow2.h:61: error: parse error before numeric constant modinteger/cl_MI_pow2.h:80: error: parse error before numeric constant modinteger/cl_MI_pow2.h:105: error: parse error before numeric constant modinteger/cl_MI_pow2.h:126: error: invalid conversion from `const cln::_cl_MI (*)(...)' to `const cln::_cl_MI (*)(cln::cl_heap_modint_ring*, const cln::_cl_MI&, const cln::_cl_MI&)' modinteger/cl_MI_pow2.h:126: error: invalid conversion from `const cln::_cl_MI (*)(...)' to `const cln::_cl_MI (*)(cln::cl_heap_modint_ring*, const cln::_cl_MI&, const cln::_cl_MI&)' modinteger/cl_MI_pow2.h:126: error: invalid conversion from `const cln::_cl_MI (*)(...)' to `const cln::_cl_MI (*)(cln::cl_heap_modint_ring*, const cln::_cl_MI&)' modinteger/cl_MI_pow2.h:138: error: invalid conversion from `const cln::_cl_MI (*)(...)' to `const cln::_cl_MI (*)(cln::cl_heap_modint_ring*)' modinteger/cl_MI_pow2.h:138: error: invalid conversion from `const cln::_cl_MI (*)(...)' to `const cln::_cl_MI (*)(cln::cl_heap_modint_ring*, const cln::_cl_MI&, const cln::_cl_MI&)' modinteger/cl_MI_pow2.h:138: error: invalid conversion from `const cln::_cl_MI (*)(...)' to `const cln::_cl_MI (*)(cln::cl_heap_modint_ring*, const cln::_cl_MI&)' modinteger/cl_MI_pow2.h:138: error: invalid conversion from `const cln::cl_MI_x (*)(...)' to `const cln::cl_MI_x (*)(cln::cl_heap_modint_ring*, const cln::_cl_MI&)' modinteger/cl_MI_pow2.h:138: error: invalid conversion from `const cln::cl_MI_x (*)(...)' to `const cln::cl_MI_x (*)(cln::cl_heap_modint_ring*, const cln::_cl_MI&, const cln::_cl_MI&)' modinteger/cl_MI_pow2.h:138: error: invalid conversion from `const cln::cl_I (*)(...)' to `const cln::cl_I (*)(cln::cl_heap_modint_ring*, const cln::cl_I&)' In file included from modinteger/cl_MI.cc:81: modinteger/cl_MI_pow2m1.h:16: error: parse error before numeric constant modinteger/cl_MI_pow2m1.h: In function `const cln::_cl_MI cln::pow2m1_canonhom(cln::cl_heap_modint_ring*, const cln::cl_I&)': modinteger/cl_MI_pow2m1.h:46: warning: cannot pass objects of non-POD type ` const class cln::cl_I' through `...'; call will abort at runtime modinteger/cl_MI_pow2m1.h: At global scope: modinteger/cl_MI_pow2m1.h:49: error: parse error before numeric constant modinteger/cl_MI_pow2m1.h:58: error: parse error before numeric constant modinteger/cl_MI_pow2m1.h:79: error: invalid conversion from `const cln::_cl_MI (*)(...)' to `const cln::_cl_MI (*)(cln::cl_heap_modint_ring*, const cln::_cl_MI&, const cln::_cl_MI&)' modinteger/cl_MI_pow2m1.h:79: error: invalid conversion from `const cln::_cl_MI (*)(...)' to `const cln::_cl_MI (*)(cln::cl_heap_modint_ring*, const cln::_cl_MI&)' modinteger/cl_MI_pow2m1.h:79: error: invalid conversion from `const cln::cl_I (*)(...)' to `const cln::cl_I (*)(cln::cl_heap_modint_ring*, const cln::cl_I&)' In file included from modinteger/cl_MI.cc:82: modinteger/cl_MI_pow2p1.h:16: error: parse error before numeric constant modinteger/cl_MI_pow2p1.h: In function `const cln::_cl_MI cln::pow2p1_canonhom(cln::cl_heap_modint_ring*, const cln::cl_I&)': modinteger/cl_MI_pow2p1.h:53: warning: cannot pass objects of non-POD type ` const class cln::cl_I' through `...'; call will abort at runtime modinteger/cl_MI_pow2p1.h: At global scope: modinteger/cl_MI_pow2p1.h:56: error: parse error before numeric constant modinteger/cl_MI_pow2p1.h:67: error: parse error before numeric constant modinteger/cl_MI_pow2p1.h:90: error: invalid conversion from `const cln::_cl_MI (*)(...)' to `const cln::_cl_MI (*)(cln::cl_heap_modint_ring*, const cln::_cl_MI&, const cln::_cl_MI&)' modinteger/cl_MI_pow2p1.h:90: error: invalid conversion from `const cln::_cl_MI (*)(...)' to `const cln::_cl_MI (*)(cln::cl_heap_modint_ring*, const cln::_cl_MI&)' modinteger/cl_MI_pow2p1.h:90: error: invalid conversion from `const cln::cl_I (*)(...)' to `const cln::cl_I (*)(cln::cl_heap_modint_ring*, const cln::cl_I&)' In file included from modinteger/cl_MI.cc:83: modinteger/cl_MI_montgom.h:87: error: parse error before numeric constant modinteger/cl_MI_montgom.h:93: error: parse error before numeric constant modinteger/cl_MI_montgom.h:99: error: parse error before numeric constant modinteger/cl_MI_montgom.h:106: error: parse error before numeric constant modinteger/cl_MI_montgom.h:112: error: parse error before numeric constant modinteger/cl_MI_montgom.h:118: error: parse error before numeric constant modinteger/cl_MI_montgom.h:132: error: parse error before numeric constant modinteger/cl_MI_montgom.h:158: error: invalid conversion from `const cln::_cl_MI (*)(...)' to `const cln::_cl_MI (*)(cln::cl_heap_modint_ring*)' modinteger/cl_MI_montgom.h:158: error: invalid conversion from `const cln::_cl_MI (*)(...)' to `const cln::_cl_MI (*)(cln::cl_heap_modint_ring*, const cln::cl_I&)' modinteger/cl_MI_montgom.h:158: error: invalid conversion from `const cln::_cl_MI (*)(...)' to `const cln::_cl_MI (*)(cln::cl_heap_modint_ring*, const cln::_cl_MI&, const cln::_cl_MI&)' modinteger/cl_MI_montgom.h:158: error: invalid conversion from `const cln::_cl_MI (*)(...)' to `const cln::_cl_MI (*)(cln::cl_heap_modint_ring*, const cln::_cl_MI&)' modinteger/cl_MI_montgom.h:158: error: invalid conversion from `const cln::cl_MI_x (*)(...)' to `const cln::cl_MI_x (*)(cln::cl_heap_modint_ring*, const cln::_cl_MI&)' modinteger/cl_MI_montgom.h:158: error: invalid conversion from `const cln::cl_MI_x (*)(...)' to `const cln::cl_MI_x (*)(cln::cl_heap_modint_ring*, const cln::_cl_MI&, const cln::_cl_MI&)' modinteger/cl_MI_montgom.h:158: error: invalid conversion from `const cln::cl_I (*)(...)' to `const cln::cl_I (*)(cln::cl_heap_modint_ring*, const cln::_cl_MI&)' make[2]: *** [cl_MI.lo] Error 1

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Interval Arithmetic in GiNaC
by C T L O'Dwyer 20 Oct '03

20 Oct '03

I was wondering if GiNaC has support for interval arithmetic, and if not, then how to add it (would it just be a new numeric type with it's own rules?) or are there any other packages out there that can be combined with GiNaC? I need symbolic manipulation for my project, but I also need to be able to check very quickly if a given value exists in an interval. THx, Carl O'Dwyer cs1ctlo(a)bath.ac.uk

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Announcing GiNaC 1.1.4
by Richard B. Kreckel 17 Oct '03

17 Oct '03

* It has defied the world's greatest mathematicians. * It lies in wait wherever problems gather. * It is a timeless force with the power to change the course of history. Dear software aficionado, It is our pleasure to introduce GiNaC release 1.1.4. For the true software collecting enthusiast, this is a release like no other -- explaining, illuminating, and illustrating in depth how the bits, bytes and exabytes of the computing machinery more often than not solve problems of undreamed complexity. GiNaC 1.1.4 -- an opus like no other available today -- will bring you to the crossroads of mathematics and computing. Quite simply, GiNaC-1.1.4 is an unparalleled resource no serious software connoisseur can afford to overlook. Take advantage of this singular opportunity and download your very own copy today from URL <ftp://ftpthep.physik.uni-mainz.de/pub/GiNaC>. Best regards -rbk. -- Richard B. Kreckel <Richard.Kreckel(a)GiNaC.DE> <http://www.ginac.de/~kreckel/>

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ex to double
by Volker Vogel 15 Oct '03

15 Oct '03

Hi, I am a new user to ginac, and i am trying to find out how to convert an ex to a double. This of course only makes sense when ex contains something that is a double. I have been searching the tutorial and tried "expresion output". There it explains in section 5.12.1 how to manipulate the outputstream with "csrc" but I can not get the examples working. I also dont know if this is the right way get my double. #include <iostream> #include <stdio.h> #include <ginac/ginac.h> using namespace std; using namespace GiNaC; int main(){ ex poly=2.7; double val; std::ostream & csrc(std::ostream & os); cout << csrc <<poly <<"\n"; return 0; } When I run the example above I get the error below, and I don not know how to handle it. /tmp/cczNv1jd.o: In function `main': /tmp/cczNv1jd.o(.text+0x36): undefined reference to `csrc(ostream &)' collect2: ld returned 1 exit status I am working wih ginac version : 1.1.1 g++: 2.95.3 I am not that much intro programming to understand how stream manipulation really works and to understand the ginac source code. Can anyone help me to get my double ?? Saludos de España, Volker ______________________________________________________________________________ Horoskop, Comics, VIPs, Wetter, Sport und Lotto im WEB.DE Screensaver1.2 Kostenlos downloaden: http://screensaver.web.de/?mc=021110

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<no subject>
by Volker Vogel 15 Oct '03

15 Oct '03

ginac-list bananabird(a)web.de ______________________________________________________________________________ Horoskop, Comics, VIPs, Wetter, Sport und Lotto im WEB.DE Screensaver1.2 Kostenlos downloaden: http://screensaver.web.de/?mc=021110

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Benchmarks don't lie (TM)
by Richard B. Kreckel 28 Sep '03

28 Sep '03

Hi, AMD released the Opteron processor family today leaving people with the budget to buy new hardware wondering what exactly to purchase next. Here are some data to underpin your decision-making and convincing (whomever: head of department, parents, wife). I've let the suite of benchmarks from GiNaC-1.1.3 run on various machines, all clocked at 1.4 GHz, with one exception: the Itanium1 in the list was clocked at a mere 930MHz. Its timings were adjusted to accomodate for this difference in clock rates as far as possible. You'll notice anyway how that early silicon isn't worth being listed, it's just way slower than all the other machines. This has changed with the Itanium2. But apart from the two monsters M2 and N (with unconclusive results) it seems like the AMD chips generally perform faster than the Intel silicon. Naturally, all functions (except, perhaps, A, B and C) exercise some fairly jerky code with many branches. This is generally the case with CAS. Note that with the machines tested, the P-IV's handicap (its ridiculously large pipeline) was compensated by it having a comparatively fast DDR333, as opposed to the P-III which had less memory bandwith. Well, for such reasons the numbers below should be taken with a grain of salt. But still, my next personal machine won't be from Intel, and it won't be 32Bit either. So, without further ado, here are the numbers: Opteron Itanium2 Itanium1 P-III P-IV Athlon ------------------------------------------------------------------------------------------------------------ commutative expansion and substitution, size 200. 0.45s 0.55s 1.04s 0.63s 0.56s 0.53s commutative expansion and substitution, size 500. 3.43s 4.17s 7.78s 4.46s 4.25s 4.22s Laurent series expansion of Gamma function, order 20. 0.34s 0.43s 0.84s 0.57s 0.5s 0.36s Laurent series expansion of Gamma function, order 25. 1.37s 1.65s 3.27s 2.29s 2.01s 1.59s determinant of symbolic 10x10 Vandermonde matrix. 0.32s 0.37s 0.65s 0.45s 0.38s 0.27s determinant of symbolic 12x12 Vandermonde matrix. 2.99s 3.56s 6.07s 4.14s 3.48s 2.62s determinant of symbolic 8x8 Toeplitz matrix. 0.31s 0.37s 0.66s 0.43s 0.45s 0.27s determinant of symbolic 9x9 Toeplitz matrix. 1.25s 0.89s 2.59s 1.64s 1.88s 1.29s hash map size 500000 insert. 1.02s 1.16s 1.8s 1.01s 1.35s 1.15s hash map size 500000 find. 0.56s 0.69s 1.15s 0.63s 0.93s 0.62s hash map size 500000 erase. 0.43s 0.5s 0.85s 0.44s 0.66s 0.5s Lewis-Wester test A (divide factorials). 0.34s 0.357s 0.61s 0.38s 0.4s 0.43s Lewis-Wester test B (sum of rational numbers). 0.005s 0.008s 0.01s 0.006s 0.005s 0.004s Lewis-Wester test C (gcd of big integers). 0.059s 0.129s 0.16s 0.093s 0.116s 0.059s Lewis-Wester test D (normalized sum of rational fcns). 0.095s 0.136s 0.21s 0.135s 0.13s 0.083s Lewis-Wester test E (normalized sum of rational fcns). 0.07s 0.093s 0.16s 0.10s 0.098s 0.062s Lewis-Wester test F (gcd of 2-var polys). 0.009s 0.011s 0.021s 0.015s 0.011s 0.008s Lewis-Wester test G (gcd of 3-var polys). 0.27s 0.42s 0.65s 0.38s 0.43s 0.27s Lewis-Wester test H (det of 80x80 Hilbert). 1.37s 1.63s 2.45s 2.32s 2.08s 1.18s Lewis-Wester test I (invert rank 40 Hilbert). 0.38s 0.47s 0.73s 0.64s 0.56s 0.33s Lewis-Wester test J (check rank 40 Hilbert). 0.21s 0.28s 0.43s 0.34s 0.33s 0.18s Lewis-Wester test K (invert rank 70 Hilbert). 2.62s 3.24s 4.93s 4.28s 3.92s 2.31s Lewis-Wester test L (check rank 70 Hilbert). 1.28s 1.7s 2.69s 1.96s 1.9s 1.14s Lewis-Wester test M1 (26x26 sparse, det). 0.055s 0.064s 0.105s 0.093s 0.07s 0.049s Lewis-Wester test M2 (101x101 sparse, det). 264.99s 247.25s ---- 219.45s 304.25s 325.45s Lewis-Wester test N (poly at rational fcns). 205.08s 219.29s ---- 186.6s 242.13s 236.26s Lewis-Wester test O1 (three 15x15 dets)... (average) 7.95s 9.32s 16.14s 9.23s 10.0s 9.54s Lewis-Wester test P (det of sparse rank 101). 0.289s 0.24s 0.35s 0.38s 0.38s 0.3s Lewis-Wester test P' (det of less sparse rank 101). 0.78s 0.96s 1.46s 1.35s 1.16s 0.68s Lewis-Wester test Q (charpoly(P)). 16.54s 19.18s 31.04s 25.22s 24.01s 14.29s Lewis-Wester test Q' (charpoly(P')). 33.75s 41.05s 64.28s 49.95s 51.62s 27.46s computation of antipodes in Yukawa theory...... (total) 8.27s 10.4s 18.52s 12.54s 11.51s 7.15s Fateman's polynomial expand benchmark. 28.84s 28.29s 38.86s 31.72s 41.8s 41.17s Cheers -richy. -- Richard B. Kreckel <Richard.Kreckel(a)GiNaC.DE> <http://www.ginac.de/~kreckel/>

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