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Substitution of indexed expressions
by Z S 16 Nov '09

16 Nov '09

I am new to ginac, and I want to simplify some expected values of indexed expressions. As a toy example, I wanted to simplify E[\sum_{i,j} A.i.j ^ 2] where it is known that E[A.i.j * A.i.j] = 1. The answer should be N + E[ \sum{i,j} A.i.j \sum_{k != i,l != j} A.k.l]. I tried to use the following program but it doesnt work. Any help would be greatly appreciated as I need to implement similar but more involved expressions. Thanks! #include <iostream> #include <ginac/ginac.h> using namespace std; using namespace GiNaC; int main() { symbol N("N"); symbol i_sym("i"), j_sym("j"); idx i(i_sym, N), j(j_sym, N); symbol A("A"); ex e = indexed(A,i,j) * indexed(A,i,j); cout << "e = "<< e<< endl; cout << "Free indices = " << exprseq(e.get_free_indices()) << "\n"; // I want to substitute A.i.j * A.i.j = 1, for any i,j // The following gives a run time error //ex e3 = subs(e,indexed(A,wild(),wild()) * indexed(A,wild(),wild()) == 1); // The following doesnt substitute/simplify anything idx i0(wild(),N), i1(wild(),N); ex e3 = subs(e,indexed(A,i0,i1) * indexed(A,i0,i1) == 1); cout << "e3 = " << e3 << endl; cout << "Free indices = " << exprseq(e3.get_free_indices()) << "\n"; }

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GiNaC release 1.5.5
by Jens Vollinga 04 Nov '09

04 Nov '09

Hi everybody, the last release, 1.5.4, didn't have the correct library versioning. This release fixes the problem. GiNaC 1.5.5 is out and available. The changes are: * Correct libtool versioning. As always, this release can be downloaded from http://www.ginac.de/Download.html Best wishes, Jens

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Release GiNaC 1.5.4
by Jens Vollinga 02 Nov '09

02 Nov '09

Hi everybody, GiNaC 1.5.4 is out and available. The changes are: * Default parser now can again read in user defined classes. * Add mul::info() and add::info() support for numeric info_flags (GiNaC now can detect that the sum or product of a number of positive expressions is again a positive expression). * Fixed cast that caused compile error on 64bit machines. * Fixed incorrect uses of STL iterators. * Removed subdirectory debian. * Output LaTeX-symbols using \mathrm, instead of \mbox. As always, this release can be downloaded from http://www.ginac.de/Download.html Best wishes, Jens

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substitute for step ( wild ( ) ) function derivative
by jros 17 Sep '09

17 Sep '09

Hello, If I derive step I obtain D[0](step). I want to substitute for D[0](step)--> 0 to get a particular behavior. What should I do? (e.subs(D[0](step)(wild()) == 0) can't be understand diff(step(wild()),wild()) neither. Any clues. By the way I'm assuming that the step function is the Heaviside function ( step(x)=0 if x<0; 1 otherwise I'm assuming a real argument) . Thank you in advance. Javier

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Ordering and pattern matching
by Chris Kelly 01 Sep '09

01 Sep '09

Dear all, I am new to GiNaC and am currently trying to get to grips with the clifford algebra classes. I am trying to perform the simple substitution: A_mu gamma_mu B_nu gamma_nu = A_mu A_nu delta_mu,nu (Euclidean space). The problem i am having is that the pattern match is not consistent over repeated use of the executable: sometimes the pattern will match, at other times it will not. It looks to me that this is related to the ordering of the expressions. Here is some example code: ------------------------------ ----------------------------------------------------------------------------------------------------- #include<iostream> #include<vector> #include<sstream> #include<ginac/ginac.h> using namespace std; using namespace GiNaC; //Aim is to identify A_mu gamma_mu B_nu gamma_nu == A_mu B_nu delta_mu,nu int main(){ ex metric = unit_matrix(4); idx i(symbol("i"),4) , j(symbol("j"),4); ex al_i = clifford_unit(i,metric); //Use generalised clifford gamma matrices for euclidean space ex al_j = clifford_unit(j,metric); //Create generic 'slashed' symbols with euclidean metric ex s1 = indexed(symbol("A"),i)*al_i; ex s2 = indexed(symbol("B"),j)*al_j; //Form the product ex prod = s1*s2; cout << s1*s2 << endl; //Attempt to match to patterns idx w1(wild(1),4), w2(wild(2),4); indexed in2_w1 = indexed(wild(2),w1); indexed in3_w2 = indexed(wild(3),w2); ex al_w1 = clifford_unit(w1,metric); ex al_w2 = clifford_unit(w2,metric); ex spat2_w1 = in2_w1*al_w1; ex spat3_w2 = in3_w2*al_w2; ex mpat = spat2_w1 * spat3_w2; cout << "MATCHING TO PATTERN: " << mpat << endl; cout << prod.match(mpat) << endl; ex mpat2 = in2_w1 * in3_w2 * al_w1 * al_w2; cout << "MATCHING TO PATTERN: " << mpat2 << endl; cout << prod.match(mpat2) << endl; ex mpat3 = in3_w2 * in2_w1 * al_w1 * al_w2; cout << "MATCHING TO PATTERN: " << mpat3 << endl; cout << prod.match(mpat3) << endl; return 0; } ----------------------------------------------------------- The output of this example is as follows: B.j*(e.i*e.j)*A.i <----- matching this against pattern MATCHING TO PATTERN: (e.($1)*e.($2))*$3.($2)*$2.($1) 0 MATCHING TO PATTERN: (e.($1)*e.($2))*$3.($2)*$2.($1) 0 MATCHING TO PATTERN: (e.($1)*e.($2))*$3.($2)*$2.($1) 0 So the expressions seem to all be reordered consistently, but in a different ordering to the object to which we wish to match. If i then add more code, reproducing the above code for the first pattern but using different wildcard indices: ----------------------------------------------------------- //Create new indices, perhaps hash ordering will be correct for these? idx w4(wild(4),4), w5(wild(5),4); indexed in2_w4 = indexed(wild(2),w4); indexed in3_w5 = indexed(wild(3),w5); ex al_w4 = clifford_unit(w4,metric); ex al_w5 = clifford_unit(w5,metric); ex spat2_w4 = in2_w4*al_w4; ex spat3_w5 = in3_w5*al_w5; ex mpat4 = spat2_w4 * spat3_w5; cout << "MATCHING TO PATTERN: " << mpat4 << endl; cout << prod.match(mpat4) << endl; ---------------------------------------------------------- The output sometimes (but not always) matches: First run: (object to match output as B.j*(e.i*e.j)*A.i ) MATCHING TO PATTERN: $2.($4)*(e.($4)*e.($5))*$3.($5) 0 Second run: (object to match output as (e.i*e.j)*B.j*A.i ) MATCHING TO PATTERN: (e.($4)*e.($5))*$3.($5)*$2.($4) 1 Third run: (object to match output as B.j*(e.i*e.j)*A.i ) <---- notice this is the same as the first run MATCHING TO PATTERN: (e.($4)*e.($5))*$3.($5)*$2.($4) 1 So for some reason the pattern matching is ordering dependent in a way that cannot be controlled. Strangely even if the pattern matches for a given run, the substitution code ------------------------------------------------- //Pattern sometimes matches, try a substitution for identity ex ident = in2_w4 * in3_w5 * delta_tensor(w4,w5); cout << "SUBSTITUTION RESULT:" << prod.subs(mpat4==ident) << endl; cout << "SUBSTITUTION RESULT (ALGEBRAIC):" << prod.subs(mpat4==ident,subs_options::algebraic) << endl; -------------------------------------------------- always seems to fail (or is ignored?) Second run: (object to match output as (e.i*e.j)*B.j*A.i ) SUBSTITUTION RESULT:(e.i*e.j)*B.j*A.i SUBSTITUTION RESULT (ALGEBRAIC):(e.i*e.j)*B.j*A.i Third run: (object to match output as B.j*(e.i*e.j)*A.i ) SUBSTITUTION RESULT:B.j*(e.i*e.j)*A.i SUBSTITUTION RESULT (ALGEBRAIC):B.j*(e.i*e.j)*A.i Does anyone know how to solve these issues? Thanks, Chris K

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Ordering and pattern matching
by Chris Kelly 26 Aug '09

26 Aug '09

Dear all, I am new to GiNaC and am currently trying to get to grips with the clifford algebra classes. I am trying to perform the simple substitution: A_mu gamma_mu B_nu gamma_nu = A_mu A_nu delta_mu,nu (Euclidean space). The problem i am having is that the pattern match is not consistent over repeated use of the executable: sometimes the pattern will match, at other times it will not. It looks to me that this is related to the ordering of the expressions. Here is some example code: ----------------------------------------------------------------------------------------------------------------------------------- #include<iostream> #include<vector> #include<sstream> #include<ginac/ginac.h> using namespace std; using namespace GiNaC; //Aim is to identify A_mu gamma_mu B_nu gamma_nu == A_mu B_nu delta_mu,nu int main(){ ex metric = unit_matrix(4); idx i(symbol("i"),4) , j(symbol("j"),4); ex al_i = clifford_unit(i,metric); //Use generalised clifford gamma matrices for euclidean space ex al_j = clifford_unit(j,metric); //Create generic 'slashed' symbols with euclidean metric ex s1 = indexed(symbol("A"),i)*al_i; ex s2 = indexed(symbol("B"),j)*al_j; //Form the product ex prod = s1*s2; cout << s1*s2 << endl; //Attempt to match to patterns idx w1(wild(1),4), w2(wild(2),4); indexed in2_w1 = indexed(wild(2),w1); indexed in3_w2 = indexed(wild(3),w2); ex al_w1 = clifford_unit(w1,metric); ex al_w2 = clifford_unit(w2,metric); ex spat2_w1 = in2_w1*al_w1; ex spat3_w2 = in3_w2*al_w2; ex mpat = spat2_w1 * spat3_w2; cout << "MATCHING TO PATTERN: " << mpat << endl; cout << prod.match(mpat) << endl; ex mpat2 = in2_w1 * in3_w2 * al_w1 * al_w2; cout << "MATCHING TO PATTERN: " << mpat2 << endl; cout << prod.match(mpat2) << endl; ex mpat3 = in3_w2 * in2_w1 * al_w1 * al_w2; cout << "MATCHING TO PATTERN: " << mpat3 << endl; cout << prod.match(mpat3) << endl; return 0; } ----------------------------------------------------------- The output of this example is as follows: B.j*(e.i*e.j)*A.i <----- matching this against pattern MATCHING TO PATTERN: (e.($1)*e.($2))*$3.($2)*$2.($1) 0 MATCHING TO PATTERN: (e.($1)*e.($2))*$3.($2)*$2.($1) 0 MATCHING TO PATTERN: (e.($1)*e.($2))*$3.($2)*$2.($1) 0 So the expressions seem to all be reordered consistently, but in a different ordering to the object to which we wish to match. If i then add more code, reproducing the above code for the first pattern but using different wildcard indices: ----------------------------------------------------------- //Create new indices, perhaps hash ordering will be correct for these? idx w4(wild(4),4), w5(wild(5),4); indexed in2_w4 = indexed(wild(2),w4); indexed in3_w5 = indexed(wild(3),w5); ex al_w4 = clifford_unit(w4,metric); ex al_w5 = clifford_unit(w5,metric); ex spat2_w4 = in2_w4*al_w4; ex spat3_w5 = in3_w5*al_w5; ex mpat4 = spat2_w4 * spat3_w5; cout << "MATCHING TO PATTERN: " << mpat4 << endl; cout << prod.match(mpat4) << endl; ---------------------------------------------------------- The output sometimes (but not always) matches: First run: (object to match output as B.j*(e.i*e.j)*A.i ) MATCHING TO PATTERN: $2.($4)*(e.($4)*e.($5))*$3.($5) 0 Second run: (object to match output as (e.i*e.j)*B.j*A.i ) MATCHING TO PATTERN: (e.($4)*e.($5))*$3.($5)*$2.($4) 1 Third run: (object to match output as B.j*(e.i*e.j)*A.i ) <---- notice this is the same as the first run MATCHING TO PATTERN: (e.($4)*e.($5))*$3.($5)*$2.($4) 1 So for some reason the pattern matching is ordering dependent in a way that cannot be controlled. Strangely even if the pattern matches for a given run, the substitution code ------------------------------------------------- //Pattern sometimes matches, try a substitution for identity ex ident = in2_w4 * in3_w5 * delta_tensor(w4,w5); cout << "SUBSTITUTION RESULT:" << prod.subs(mpat4==ident) << endl; cout << "SUBSTITUTION RESULT (ALGEBRAIC):" << prod.subs(mpat4==ident,subs_options::algebraic) << endl; -------------------------------------------------- always seems to fail (or is ignored?) Second run: (object to match output as (e.i*e.j)*B.j*A.i ) SUBSTITUTION RESULT:(e.i*e.j)*B.j*A.i SUBSTITUTION RESULT (ALGEBRAIC):(e.i*e.j)*B.j*A.i Third run: (object to match output as B.j*(e.i*e.j)*A.i ) SUBSTITUTION RESULT:B.j*(e.i*e.j)*A.i SUBSTITUTION RESULT (ALGEBRAIC):B.j*(e.i*e.j)*A.i Does anyone know how to solve these issues? Thanks, Chris K

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Ordering of expressions
by Luigi Capozza 12 Aug '09

12 Aug '09

Dear people, I have the following issue with the canonicalization of expressions. If I run many times the same program without changing anything, I get the output for the same expression ordered in different ways. As far as I understand, that seems to depend on the hash value that is assigned to each symbol, which happens to be different every time I run the program. Here is an example (example.cxx): ------------------------------------------ #include <iostream> #include "ginac/ginac.h" using namespace std; using namespace GiNaC; int main() { symbol x("x"),y("y"),z("z"); ex Ex1 = 2*(x + y); ex Ex2 = z*(x + y); cout<<x.gethash()<<endl <<y.gethash()<<endl <<z.gethash()<<endl; cout<<Ex1<<endl <<Ex2<<endl; return 0; } ------------------------------------------ And here is the output I get (I am running on Ubuntu 8.04.1 with the GCC 4.2.4 compiler): -------------------------------------------------- =>g++ -lginac example.cxx -o example =>example 2178355982 851138097 3818887508 2*y+2*x (y+x)*z =>example 3784401678 2457183793 1129965908 2*y+2*x (y+x)*z =>example 2632340238 1305122353 4272871764 2*y+2*x (y+x)*z =>example 3711329038 2384111153 1056893268 2*y+2*x z*(y+x) => ... -------------------------------------------------- With more complicated expressions also the run time can vary from execution to execution up to a factor of 2 or more. Is this normal or am I doing something wrong? I saw that the hash value is calculated in a fairly sophisticated manner but is it eventually possible to set it by hand? Thanks in advance. Regards, Luigi

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Release GiNaC 1.5.3
by Jens Vollinga 30 Jul '09

30 Jul '09

Hi everybody, GiNaC 1.5.3 is out and available. The changes are: * The parser now understands user-defined functions by default. The parsed identifier names can now contain underscores. As always, this release can be downloaded from http://www.ginac.de/Download.html Best wishes, Jens

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(no subject)
by Michael Hoffmann 30 Jul '09

30 Jul '09

Hello, i'm using Ubuntu 9.04 with g++. I installed Ginac with Synaptik (.deb Packeges), I also installed cln pakeges. But it doesn't works! :) Here is the bug message: g++ -o simple_function simple_function.o -lginac simple_function.o: In function `__static_initialization_and_destruction_0': /usr/local/include/ginac/archive.h:174: undefined reference to `GiNaC::unarchive_table_t::unarchive_table_t()' /usr/local/include/ginac/archive.h:174: undefined reference to `GiNaC::unarchive_table_t::~unarchive_table_t()' simple_function.o: In function `__static_initialization_and_destruction_0': /usr/local/include/ginac/lst.h:45: undefined reference to `GiNaC::lst_unarchiver::lst_unarchiver()' /usr/local/include/ginac/lst.h:45: undefined reference to `GiNaC::lst_unarchiver::~lst_unarchiver()' simple_function.o: In function `__static_initialization_and_destruction_0': /usr/local/include/ginac/constant.h:80: undefined reference to `GiNaC::constant_unarchiver::constant_unarchiver()' /usr/local/include/ginac/constant.h:80: undefined reference to `GiNaC::constant_unarchiver::~constant_unarchiver()' simple_function.o: In function `__static_initialization_and_destruction_0': /usr/local/include/ginac/fail.h:44: undefined reference to `GiNaC::fail_unarchiver::fail_unarchiver()' /usr/local/include/ginac/fail.h:44: undefined reference to `GiNaC::fail_unarchiver::~fail_unarchiver()' simple_function.o: In function `__static_initialization_and_destruction_0': /usr/local/include/ginac/integral.h:82: undefined reference to `GiNaC::integral_unarchiver::integral_unarchiver()' /usr/local/include/ginac/integral.h:82: undefined reference to `GiNaC::integral_unarchiver::~integral_unarchiver()' simple_function.o: In function `__static_initialization_and_destruction_0': /usr/local/include/ginac/matrix.h:178: undefined reference to `GiNaC::matrix_unarchiver::matrix_unarchiver()' /usr/local/include/ginac/matrix.h:178: undefined reference to `GiNaC::matrix_unarchiver::~matrix_unarchiver()' simple_function.o: In function `__static_initialization_and_destruction_0': /usr/local/include/ginac/numeric.h:206: undefined reference to `GiNaC::numeric_unarchiver::numeric_unarchiver()' /usr/local/include/ginac/numeric.h:206: undefined reference to `GiNaC::numeric_unarchiver::~numeric_unarchiver()' simple_function.o: In function `__static_initialization_and_destruction_0': ... i don't understand what he needs, cause i have the same system (Ubuntu 9.04) and the same installation of Ginac at work and it works. I already tried to uninstall and to install new one more time - nothing changes! Please HELP!!!

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a function without any arguments with GiNaC?
by Michael Hoffmann 27 Jul '09

27 Jul '09

Hallo, how can I make a function without any arguments with GiNaC? I just need a function returned a symbolic matrix. It's the same matrix every time. How I have to declare such a function? minimal example: #include <stdio.h> #include <stdlib.h> #include <iostream> #include <math.h> #include <ginac/ginac.h> using namespace std; using namespace GiNaC; REGISTER_FUNCTION (symbolic_matrix, dummy()); { symbol a("a"), b("b"), c("c"); GiNaC::matrix D(2,2), E(2,2); D = a, b, 0, c; E = sin(a), cos(b), -sin(c), cos(a); GiNaC::ex h = D.mul(E) ; return h; } Thank you very match, Michael Hoffmann P.S. : sorry for my english!

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