June 2005 - GiNaC-list

[PATCH] simpler debian/*
by varg＠theor.jinr.ru 21 Jul '05

21 Jul '05

Here is yet another patch. This ought to be in the ChangeLog: * provide -dbg package (unstripped shared object with debugging symbols) * switch to CDBS, so debian/rules is *much* simpler Best regards, Alexei -- ROOT: an octopus made by nailing extra legs onto a cat.

2 3

Re: [GiNaC-list] Question
by Vladimir V. Kisil 18 Jul '05

18 Jul '05

Hi, >>>>> "JRG" == Javier Ros Ganuza <jros(a)unavarra.es> writes: JRG> I want to do algebra with cartesian (3x1) "vectors". Cartesian JRG> "vector"s are to be represented by a 3x1 Ginac vector (3-tuple) JRG> and a reference to a basis that tell us in which base the JRG> components have physical sense. Extension of GiNaC classes is not very difficult and you may implement from scratch. However it may be better to do this through the Clifford algebras in GiNaC. There are many references (e.g. books of Hestenes) on doing geometry with Clifford algebras. JRG> for example (in my particular jargon): JRG> vector1.expresion=matrix(3,1,lst(a1,b1,c1)); JRG> vector1.basis=basis_k; JRG> vector2.expresion=matrix(3,1,lst(a2,b2,c2)); JRG> vector1.basis=basis_l; This can be implemented as follows: varidx nu(symbol("nu", "\\nu"), 3), mu(symbol("mu", "\\mu"), 3); xi(symbol("xi", "\\xi"), 3), rho(symbol("rho", "\\rho"),3); basis1 = clifford_unit(mu, diag_matrix(lst(1, 1, 1))); basis2 = clifford_unit(nu, diag_matrix(lst(1, 1, 1))); vector1 = lst_to_clifford(lst(a1,b1,c1), xi, basis1); vector2 = lst_to_clifford(lst(a1,b1,c1), rho, basis2); Then the expression JRG> result=2*vector1+vector2; will be well defined and behave as expected even without reduction to the single basis. The reduction is needed only if someone try to extract its components in either basis1, basis2, or even another basis3. To this end values of all products like basis1[i]*basis2[j] (i.e. transition matrix) should be defined. Best wishes, Vladimir -- Vladimir V. Kisil email: kisilv(a)maths.leeds.ac.uk -- www: http://maths.leeds.ac.uk/~kisilv/

5 9

Re: GiNaC 1.3.1
by Chris Dams 13 Jul '05

13 Jul '05

Dear Jens, You wrote: > - Fixed a library initialization problem. Why do you think so? The safety suggested by the library_init class is still nothing more than a sham. Best wishes, Chris

3 13

matrix::solve(): how to use?
by mdias＠ift.unesp.br 12 Jul '05

12 Jul '05

Hi guys, I am tryng to solve a linear system with lsove(), with many variables being zero, so lsolve() tell that is indeterminate, but some of these entries are of interest. So, I am looking for matrix::solve and construct a matrix to solve this. Somebody have a piece of code how to make a linear system a matrix to matrix::solve ? Thanks, Marco

4 3

[PATCH] small improvements of gcd and collect_common_factors
by varg＠theor.jinr.ru 08 Jul '05

08 Jul '05

Hello! collect_common_factors does not work with powers, e.g. (in ginsh) > collect_common_factors((a*x+a*y)^2); (a*x+a*y)^2 I don't like such a behaviour, so I made the patch. With that patch, the above code actually works: > collect_common_factors((a*x+a*y)^2); a^2*(y+x)^2 To guarantee mathematical correctness, this transformation is applied to polynomial expressions only: > collect_common_factors((a*x+a*y)^n); (a*x+a*y)^n Apart from collect_common_factors hack, this patch somewhat improves worst-case performance of gcd and sr_gcd. Best regards, Alexei -- ROOT: an octopus made by nailing extra legs onto a cat.

2 3

[PATCH] build system: wipe deprecated autoconf macros
by varg＠theor.jinr.ru 30 Jun '05

30 Jun '05

Hello! This patch removes [some of the] obsolete autoconf macros, so auto* things do not complain any more. It also removes the `autogen.sh' script, since its job can be done with a simple autoreconf -i command (in fact, according to autoconf documentation, this is the recommended way to bootstrap a project). Best regards, Alexei -- ROOT: an octopus made by nailing extra legs onto a cat.

1 1

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

1 0

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} }

2 1

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

2 2

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/

3 2