- GiNaC-list - ginac.de

lsolve
by mdias＠ift.unesp.br 28 Jun '05

28 Jun '05

Hi guys, I am tring to solve a system (in my tests) like that: 16*Fv==16*k*p-32*m^2+16*k^2+32*p*p1 -16*Ga==0 -24*Fm*m^2-24*Fm*p*p1==0 2*m^2*Fs+2*p*Fs*p1==32*m*k*p+32*m^3+64*m*p*p1 8*m^2*Gp+8*p*Gp*p1==0 8*m^2*Ge-8*Ge*p*p1==0 {Fv==Fv,Ga==Ga,Fm==Fm,Fs==Fs,Gp==Gp,Ge==Ge} I think Ga==0, Fv== (...)/16 , etc. How to instruct lsolve only to solve nonzero elements? Thanks in advance, Marco A. F. Dias

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Vector algebra from Clifford units
by Vladimir Kisil 24 Jun '05

24 Jun '05

Hi, In response to the previous request on vector algebra in different bases I include a simple illustration how to achieve principal vector operations from the Clifford algebra functionality in GiNaC. This is working with current CVS but will not work yet with the current release 1.3.1. Hope this can be useful, Vladimir -- Vladimir V. Kisil email: kisilv(a)maths.leeds.ac.uk -- www: http://maths.leeds.ac.uk/~kisilv/ #include <ginac/ginac.h> using namespace std; using namespace GiNaC; ex vector3D(const ex & list, const ex & basis, const ex & mu) { varidx nu((new symbol)->setflag(status_flags::dynallocated), 3); return indexed(matrix(1, 3, ex_to<lst>(list)), nu.toggle_variance())*basis.subs(mu == nu); } ex scalar_product(const ex & v1, const ex & v2) { return remove_dirac_ONE(canonicalize_clifford(expand_dummy_sum((v1*v2 + v2*v1)/2))); } ex vector_product(const ex & v1, const ex & v2, const ex & e_prod) { return canonicalize_clifford(expand_dummy_sum((v1*v2 - v2*v1)*e_prod/2)); } int main(){ realsymbol a1("a1"), b1("b1"), c1("c1"), a2("a2"), b2("b2"), c2("c2"), a3("a3"), b3("b3"), c3("c3"), t("t"); varidx nu(symbol("nu", "\\nu"), 3), mu(symbol("mu", "\\mu"), 3); ex M = diag_matrix(lst(1, 1, 1)), // Metrics of point spaces T = matrix (3, 3, lst(0, 0, 1, 0, 1, 0, -1, 0, 0)),// Transformation matrix basis1 = clifford_unit(mu, M, 0), // Main basis defined by Clifford units basis2 = basis1 * indexed(T, nu, mu.toggle_variance()), // Transformed basis e1_prod = basis1.subs(mu == 0)*basis1.subs(mu == 1)*basis1.subs(mu == 2), // Maps bivecors to vectors vect1 = vector3D(lst(a1, b1, c1), basis1, mu), // vector in the main basis vect2 = vector3D(lst(a2, b2, c2), basis2, nu), // vector in the transformed basis vect3 = vector3D(lst(a3, b3, c3), basis1, mu); // second vector in the main basis cout << canonicalize_clifford(expand_dummy_sum(2*vect1+t*vect2)) << endl; //-> -e~0*c2*t+a2*t*e~2+2*a1*e~0+2*c1*e~2+e~1*b2*t+2*b1*e~1 cout << clifford_to_lst(2*vect1+t*vect2, basis1) << endl; //-> {-c2*t+2*a1,b2*t+2*b1,2*c1+a2*t} cout << scalar_product(vect1, vect3) << endl; //-> b3*b1+c1*c3+a3*a1 cout << scalar_product(vect1, vect2) << endl; //-> a2*c1+b1*b2-a1*c2 cout << vector_product(vect1, vect3, e1_prod) << endl; //-> a3*b1*e~2-c1*a3*e~1+c1*b3*e~0-b1*e~0*c3+a1*e~1*c3-b3*a1*e~2 cout << clifford_to_lst(vector_product(vect1, vect3, e1_prod), basis1) << endl; //-> {-b1*c3+c1*b3,a1*c3-c1*a3,-b3*a1+a3*b1} cout << vector_product(vect1, vect2, e1_prod) << endl; //-> c1*e~1*c2+a2*a1*e~1-a1*b2*e~2-a2*b1*e~0+c1*e~0*b2-b1*c2*e~2 cout << clifford_to_lst(vector_product(vect1, vect2, e1_prod), basis1) << endl; //-> {c1*b2-a2*b1,c1*c2+a2*a1,-b1*c2-a1*b2} }

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ginsh as a subroutine?
by John Fletcher 23 Jun '05

23 Jun '05

I would like to be able to call a subroutine with a string e.g. "x+y" and receive back an ex object containing the expression and also a map mapping "x" and "y" strings to symbol objects. The example program ginsh does this internally. I think it could be added within the class for ex objects. Has anyone done this? Thanks John -- Dr John P. Fletcher Tel: (44) 121 204 3389 (direct line) Chemical Engineering and Applied Chemistry (CEAC), School of Engineering and Applied Science (SEAS), Aston University, Aston Triangle, BIRMINGHAM B4 7ET U.K. CEAC Web site http://www.ceac.aston.ac.uk/ FAX: (44) 121 204 3679

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Covariant derivative(its long..)
by mdias＠ift.unesp.br 18 Jun '05

18 Jun '05

Hi, I tried this very confuse code, and I am happy if somebody could help-me. I tried to make covariant derivative derivated from a indexed. Use it like: D(indexed(A,mu),nu) But the fatal errors in this code (among millions..): i) simplify_indexed() crashs or doesnt work !! II) get_free_indexes not work, so D^\alpha(A_beta)A^\beta A_\alpha -D^\beta(A_alpha)A^\beta A_\alpha is not zero In the last post , Christian Bauer suggests "override is eval_indexed() (for automatic evaluation) and contract_with()/add_indexed()/scalar_mul_indexed() (for manual evaluation, AKA simplify_indexed())" and showed the way: look color.cpp source. Any suggestions are welcome Marco #include <iostream> #include <ginac/ginac.h> #define N 4 #define N1 8 using namespace std; using namespace GiNaC; const unsigned TINFO_covdiff = 0x42420001U; class covdiff : public indexed { GINAC_DECLARE_REGISTERED_CLASS(covdiff, indexed) public: covdiff(const ex & b,const ex & i1); covdiff(const ex & b, const ex & i1, const ex & i2); covdiff(const ex & b, const ex & i1, const ex & i2,const ex & i3); covdiff(const ex & b, const ex & i1, const ex & i2,const ex & i3, const ex & i4); covdiff(const ex & b, const lst & iv); size_t nops() const; ex op(size_t i) const; ex & let_op(size_t i); ex subs(const exmap & m, unsigned options) const; protected: void do_print(const print_context & c, unsigned level) const; ex symtree, arg,index; lst seq; }; GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(covdiff, indexed, print_func<print_context>(&covdiff::do_print)) covdiff::covdiff(const ex & b, const ex & i1) : inherited(b, i1),arg(b),index(i1), symtree(not_symmetric()) { tinfo_key = TINFO_covdiff; } covdiff::covdiff(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2),arg(b), symtree(not_symmetric()) { seq =i1,i2; tinfo_key = TINFO_covdiff; } covdiff::covdiff(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3),arg(b), symtree(not_symmetric()) { seq=i1,i2,i3; tinfo_key = TINFO_covdiff; } covdiff::covdiff(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4),arg(b), symtree(not_symmetric()) {seq = i1,i2,i3,i4; tinfo_key = TINFO_covdiff; } covdiff::covdiff(const ex & b, const lst & iv) : inherited(b),arg(b), symtree(not_symmetric()) { seq=iv; tinfo_key = TINFO_covdiff; } //archiving covdiff::covdiff(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst) { if (!n.find_ex("symmetry", symtree, sym_lst)) { // GiNaC versions <= 0.9.0 had an unsigned "symmetry" property unsigned symm = 0; n.find_unsigned("symmetry", symm); switch (symm) { case 1: symtree = sy_symm(); break; case 2: symtree = sy_anti(); break; default: symtree = not_symmetric(); break; } const_cast<symmetry &>(ex_to<symmetry>(symtree)).validate(seq.nops() - 1); } } void covdiff::archive(archive_node &n) const { inherited::archive(n); n.add_ex("symmetry", symtree); } ex covdiff::unarchive(const archive_node &n, lst &sym_lst) { return (new covdiff(n, sym_lst))->setflag(status_flags::dynallocated); } //comparation method void covdiff::do_print(const print_context & c, unsigned level) const { if (is_a<print_tree>(c)) covdiff::print(c,level); if (seq.nops() > 1) { for( lst::const_iterator it=seq.begin();it != seq.end();++it) c.s<<"D"<<*it; c.s<<"("<<arg<<")"; } else c.s << "D"<<index <<" ("<<arg<<")"; } int covdiff::compare_same_type(const basic & other) const { GINAC_ASSERT(is_a<covdiff>(other)); return inherited::compare_same_type(other); } ex covdiff::op(size_t i) const{ if(i==0) return arg; if(seq.nops() > 0 && i != 0) return seq[i-1]; if(seq.nops()==0 && i==1) return index; else throw std::range_error("covdiff::let_op(): no such operand"); } size_t covdiff::nops() const { if(seq.nops()>0) return seq.nops()+1; else return 2; } ex & covdiff:: let_op(size_t i) { ensure_if_modifiable(); if(i==0) return arg; if(seq.nops() > 0 && i != 0) return seq[i-1]; if(seq.nops()==0 && i==1) return index; else throw std::range_error("covdiff::let_op(): no such operand"); } ex covdiff::subs(const exmap & m, unsigned options) const { size_t num = nops(); if (num) { // Substitute in subexpressions for (size_t i=0; i<num; i++) { const ex & orig_op = op(i); const ex & subsed_op = orig_op.subs(m, options); if (!are_ex_trivially_equal(orig_op, subsed_op)) { // Something changed, clone the object basic *copy = duplicate(); copy->setflag(status_flags::dynallocated); copy->clearflag(status_flags::hash_calculated | status_flags::expanded); // Substitute the changed operand copy->let_op(i++) = subsed_op; // Substitute the other operands for (; i<num; i++) copy->let_op(i) = op(i).subs(m, options); // Perform substitutions on the new object as a whole return copy->subs_one_level(m, options); } } } // Nothing changed or no subexpressions return subs_one_level(m, options); } ex Derivative_helper(ex e, ex var) { lst iv; if(is_a<covdiff>(e)){ for(size_t i=1; i<e.nops();i++) iv.append(e.op(i)); iv.append(var); return covdiff(e.op(0),iv); }else if(is_a<indexed>(e)){ if(is_a<su3f>(e.op(0)) && e.nops()==4) return 0; else return covdiff(e,var); } else return 0; } struct make_diff : public map_function{ ex var; make_diff(ex var_): var(var_){} ex operator()(const ex & e) { if(is_a<add>(e)) return e.map(*this); else if(is_a<mul>(e)) { ex result =0; for(size_t i=0;i<e.nops();++i) { result +=e.subs(e.op(i)==Derivative_helper(e.op(i),var)); }; return result; }else return Derivative_helper(e,var); } }; ex D(ex e, ex index){ ex result; make_diff D(index); return D(e); } ------------------------------------------------- This mail sent through IMP: http://horde.org/imp/

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Question
by Javier Ros Ganuza 17 Jun '05

17 Jun '05

Hello!. I'm evaluating Ginac in order to replace my own symbolic manipulator for a program, 3D_Mec, for dynamical simulation of multibody systems. I've been for some days reading at C++ books and Ginac own documentation in order to see it it fit my needs (Experience in C an OO Pascal but no C+ +). I think that the answer is yes, but I need to do some simple tests in order to evaluate it more properly. I see that using the plain functionality that Ginac provides is pretty easy but when dealing with own types of symbolic data the problem surpasses my knowledge, so I'm asking for help on how to start or in how to focus my problem. Well, in fact I have some problems, but I'll will start for the most important one to me. Nevertheless I will somehow simplify the problem in order to make it more understandable and easy to ask/answer. The problem: I want to do algebra with cartesian (3x1) "vectors". Cartesian "vector"s are to be represented by a 3x1 Ginac vector (3-tuple) and a reference to a basis that tell us in which base the components have physical sense. for example (in my particular jargon): vector1.expresion=matrix(3,1,lst(a1,b1,c1)); vector1.basis=basis_k; vector2.expresion=matrix(3,1,lst(a2,b2,c2)); vector1.basis=basis_l; result=2*vector1+vector2; The last sentence will not have sense unless, when the summation is performed, the vectors are transformed to be expressed in the same basis. The result will get expressed in that same basis. Obviously I need more operators but I hope the above example will suffice. There is a base structure -with elements basis_k and l and others- that has a tree structure form. That structure allow us to decide to which base reduce the operation of the binary operator -base_m for example-, and to obtain the pertinent change of base matrices, so that the symbolic result keeps as simple as possible (transform every vector to a single basis gives usually symbolic complexity). To which base to transform an the transformation, should be made by the binary operator. For example if there is a third "vector" in base_j and left to right evaluation is assumed result=2*vector1+vector2+vector3 The summation vector1+vector2, will render as above a result in base_m and the second summation (vector1+vector2)+vector3, will render the result in a different base_n, that will be chosen at the time this last summation is performed (by inquiring base structure). Thus the question is, can be such a "cartesian vector" type be defined within Ginac philosophy?, or should I define a new kind of expression type of my own. (is it very complex?, assumed that the base structure and associated functions is implemented). I've read at the tutorial, through section 6.4 and 6.5. Is any of that philosophies the way to go?. I'm not sure, and I'm facing a big gap from what I want to do and what there is explained (or what I do understand). Can you give me some advice?. Thanks a lot Javier Ros

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When I compiled ginac with mingw....
by 曾仁宏 11 Jun '05

11 Jun '05

I get a error at make progress The error message: $ make make all-recursive make[1]: Entering directory `/f/dev-cpp/work/ginac' Making all in ginac make[2]: Entering directory `/f/dev-cpp/work/ginac/ginac' make[2]: Nothing to be done for `all'. make[2]: Leaving directory `/f/dev-cpp/work/ginac/ginac' Making all in check make[2]: Entering directory `/f/dev-cpp/work/ginac/check' make[2]: Nothing to be done for `all'. make[2]: Leaving directory `/f/dev-cpp/work/ginac/check' Making all in ginsh make[2]: Entering directory `/f/dev-cpp/work/ginac/ginsh' if g++ -DHAVE_CONFIG_H -I. -I. -I.. -I./../ginac -I../ginac -DIN_GINAC -I/usr/local/include -g -O2 -MT ginsh_parser.o -MD -MP -MF ".deps/ginsh_parser.Tpo" -c -o ginsh_parser.o ginsh_parser.cc; \ then mv -f ".deps/ginsh_parser.Tpo" ".deps/ginsh_parser.Po"; else rm -f ".deps/ginsh_parser.Tpo"; exit 1; fi ../../GiNaC/ginsh/ginsh_parser.yy:32:26: sys/resource.h: No such file or directory ../../GiNaC/ginsh/ginsh_parser.yy:64: error: aggregate `rusage start_time' has incomplete type and cannot be defined ../../GiNaC/ginsh/ginsh_parser.yy:64: error: aggregate `rusage end_time' has incomplete type and cannot be defined ../../GiNaC/ginsh/ginsh_parser.yy: In function `int yyparse()': ../../GiNaC/ginsh/ginsh_parser.yy:213: error: `RUSAGE_SELF' undeclared (first use this function) ../../GiNaC/ginsh/ginsh_parser.yy:213: error: (Each undeclared identifier is reported only once for each function it appears in.) ../../GiNaC/ginsh/ginsh_parser.yy:213: error: `getrusage' undeclared (first use this function) make[2]: *** [ginsh_parser.o] Error 1 make[2]: Leaving directory `/f/dev-cpp/work/ginac/ginsh' make[1]: *** [all-recursive] Error 1 make[1]: Leaving directory `/f/dev-cpp/work/ginac' make: *** [all] Error 2 have any solution? _________________________________________________________________ 信箱不夠大？MSN Hotmail Plus：讓你的 Hotmail 信箱容量增加 1000 倍 http://join.msn.com/?pgmarket=zh-tw

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differentiating with respect to a variable in a list
by Karen Yeats 23 May '05

23 May '05

Hi everyone, I have a small question. I'd like to make a function with a list as one argument and be able to take derivatives with respect to the variables encased in the list. The only such example among the built-in functions seems to be Li for lists in the second variable, but in this case all but the first element of that list seem to be ignored. Is there an example I've missed that I could look at, or some place that documents how this works? Thanks for your time. Karen

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GiNaC 1.3.1
by Jens Vollinga 09 May '05

09 May '05

Hi, GiNaC 1.3.1 is out and available. The changes are: - integral() and eval_integ() can be used from ginsh. - Integrals can be series-expanded. - Fixed a library initialization problem. - GiNaC compiles from tarball even if lex/flex is missing. - Fixed bugs in canonicalize_clifford(), clifford_prime() and clifford_to_lst(). - clifford_moebius_map(), remove_dirac_ONE() and LaTeX output of Clifford objects now care about representation labels. - Fixed bug in gcd. - Better output for slashed expressions. As always, this release can be downloaded from ftp://ftpthep.physik.uni-mainz.de/pub/GiNaC/ Enjoy, Jens

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[marius@physics.aamu.edu: GiNaC 1.3.1 under Mac OS X 10.4]
by Jens Vollinga 09 May '05

09 May '05

----- Forwarded message from Marius Schamschula <marius(a)physics.aamu.edu> ----- Envelope-to: ginac-bugs(a)ginac.de Delivery-date: Mon, 09 May 2005 03:26:17 +0200 To: ginac-bugs(a)ginac.de From: Marius Schamschula <marius(a)physics.aamu.edu> Subject: GiNaC 1.3.1 under Mac OS X 10.4 Date: Sun, 8 May 2005 20:25:37 -0500 Hi there, I have build cln 1.1.9 and GiNaC 1.3.1 under Mac OS X 10.3 w/o any problems. However, under Mac OS X 10.4 I have two problems. 1) /usr/bin/locale This issue exisit both in cln 1.1.9 and GiNaC 1.3.1 (example from cln compile): In file included from /usr/include/gcc/darwin/4.0/c++/fstream:47, from ./base/cl_debugout.cc:15: /usr/bin/locale:1: error: stray '\254' in program /usr/bin/locale:1: error: stray '\237' in program /usr/bin/locale:1: error: stray '\250' in program /usr/bin/locale:1: error: stray '\206' in program /usr/bin/locale:1: error: stray '\18' in program /usr/bin/locale:1: error: stray '\2' in program /usr/bin/locale:2: error: stray '\8' in program /usr/bin/locale:2: error: stray '\184' in program /usr/bin/locale:2: error: stray '\133' in program /usr/bin/locale:2: error: stray '\1' in program ... etc, many pages. which I circumvented by commenting out references to #include <locale> in three files. 2) ginsh_parser.yy: This currently is my show stopper. if g++ -DHAVE_CONFIG_H -I. -I. -I.. -I./../ginac -I../ginac - DIN_GINAC -I/usr/local/include -g -O2 -MT ginsh_parser.o -MD -MP - MF ".deps/ginsh_parser.Tpo" -c -o ginsh_parser.o ginsh_parser.cc; \ then mv -f ".deps/ginsh_parser.Tpo" ".deps/ginsh_parser.Po"; else rm - f ".deps/ginsh_parser.Tpo"; exit 1; fi ginsh_parser.yy:48:6: error: missing binary operator before token "wrapper" ginsh_parser.yy:54:6: error: missing binary operator before token "wrapper" ginsh_parser.yy:837:6: error: missing binary operator before token "wrapper" ginsh_parser.yy:847:6: error: missing binary operator before token "wrapper" ginsh_parser.yy:899:6: error: missing binary operator before token "wrapper" ginsh_parser.yy: In function `char** fcn_completion(const char*, int, int)': ginsh_parser.yy:836: error: invalid conversion from 'const char*' to 'char*' ginsh_parser.yy:846: error: invalid conversion from 'const char*' to 'char*' make: *** [ginsh_parser.o] Error 1 My configuration: $ gcc --version powerpc-apple-darwin8-gcc-4.0.0 (GCC) 4.0.0 20041026 (Apple Computer, Inc. build 4061) Copyright (C) 2004 Free Software Foundation, Inc. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. $ gfortran --version GNU Fortran 95 (GCC 4.0.0) Copyright (C) 2005 Free Software Foundation, Inc. GNU Fortran comes with NO WARRANTY, to the extent permitted by law. You may redistribute copies of GNU Fortran under the terms of the GNU General Public License. For more information about these matters, see the file named COPYING $ bison --version GNU Bison version 1.28 cln 1.1.9 readline 5.0 patchlevel 5 gmp 4.1.4 Marius -- Marius Schamschula, Alabama A & M University, Department of Physics The Center for Hydrology Soil Climatology and Remote Sensing http://optics.physics.aamu.edu/ - http://www.physics.aamu.edu/ http://wx.aamu.edu/ - http://www.aamu.edu/hscars/ ----- End forwarded message -----

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gcd: wrong sign of cofactor (heur_gcd is broken?)
by varg＠theor.jinr.ru 04 May '05

04 May '05

Hello! This simple program fails: #include <iostream> #include <stdexcept> #include <cassert> #include <ginac/ginac.h> using namespace std; using namespace GiNaC; int main(int argc, char** argv) { symbol x("x"); symbol y("y"); ex a = pow(x,2) - pow(y,2); ex b = pow(x,4) - pow(y, 4); ex ca, cb; cout << "GCD(" << a << ", " << b << ") = "; ex ab_gcd = gcd(a, b, &ca, &cb, false); cout << ab_gcd << endl; assert((a-ca*ab_gcd).expand().is_zero()); assert((b-cb*ab_gcd).expand().is_zero()); return 0; } Documentation (normal.cpp:1256) says \begin{quote} /* * Compute GCD (Greatest Common Divisor) of multivariate * polynomials a(X) and b(X) in Z[X]. Optionally also compute * the cofactors of a and b, defined by a = ca * gcd(a, b) * and b = cb * gcd(a, b). */ \end{quote} so this behaviour is probably a bug. I've got a patch to fix it (see attachment #1), but I'm not sure if it is correct. Relevant part of gdb session is attached too. P.S. I use GiNaC 1.3.1 from CVS, g++-3.4 from Debian testing. -- Best regards, Alexei

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