- GiNaC-list - ginac.de

Re: [GiNaC-list] [GiNaC-devel] Symbolic Integration of exponential functions
by Matthias Reis 27 Apr '15

27 Apr '15

Dear Matthias, thanks a lot for your work. However, I have implemented a numeric workaround that does not need symbolic integration a few weeks ago. Since this approach works and I am running out of time with my PhD, I will unfortunately not be able to look further into ginac. At some point in the future maybe. Best regards and thanks again, Matthias Am Mon, 27 Apr 2015 16:27:43 +0200 schrieb Matthias Dellweg <dellweg(a)tp1.uni-duesseldorf.de>: > Am Mon, 27 Apr 2015 11:37:39 +0100 > schrieb "Vladimir V. Kisil" <kisilv(a)maths.leeds.ac.uk>: > > > Dear All, > > > > What is easy to do is to add to function class a primitive > > feature analogously to their knowledge of derivatives. Then, > > integral::eval_integ() may call such methods to evaluate simple > > integrals of plain functions. > > > > If this looks reasonable to be included in GiNaC, then I may write > > such a patch. > > > > Best wishes, > > Vladimir > > >>>>> On Sat, 14 Mar 2015 17:35:10 +0100, Matthias Reis > > >>>>> <matthias.reis(a)biologie.hu-berlin.de> said: > > > > MR> Dear all, as far as I understand, ginac cannot integrate > > MR> anything other than polynomials. How hard would it be (for > > MR> me maybe) to implement exponentials? What needs to be done? > > MR> This feature would be great for me. I just need to > > MR> integrate simple e^{x * constant} terms. > > > > MR> Best regards, Matthias > > Dear Matthias, > i have an implementation ready that integrates expressions like > step(x-a)*x^5*exp(b*x). > You can find it at https://bitbucket.org/mdellweg/ginac.git . > It just can not be done in the way described above, since it needs to > know stuff outside of exp(...). > I would love to hear comments on this. > Kindest regards, Matthias

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Symbolic Integration of exponential functions
by Matthias Reis 27 Apr '15

27 Apr '15

Dear all, as far as I understand, ginac cannot integrate anything other than polynomials. How hard would it be (for me maybe) to implement exponentials? What needs to be done? This feature would be great for me. I just need to integrate simple e^{x * constant} terms. Best regards, Matthias

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Re: [GiNaC-list] Piecewise function
by Vincent Huber 22 Apr '15

22 Apr '15

Dear Dr. Kisil Thank you for your answer I'll carefully read. Pr. C. Prud'homme has hacked our GiNaC fork to let people use this kind of expression. https://github.com/feelpp/feelpp/commit/547c08b66e5b6019ab258477ab19a329cdf… Now, the one that parse the string "(x<0.5)*1000+(x>0.5)*10:x:y" will find in the source file: f[0] = 10.0*(a[0]>5.0000000000000000e-01)+1000.0*(a[0]<5.0000000000000000e-01); Thank again for your quick answer ! All the best, VH 2015-04-22 18:50 GMT+02:00 Vladimir V. Kisil <kisilv(a)maths.leeds.ac.uk>: > Dear Vincent, > > You are right that GiNaC expression do not admit boolean > terms directly. However with your example you can proceed as follow (I > do understand that your actual target is much more complicated): > > 1. Use the step function from GiNaC: > > f=2*x*step(x)+3*x*step(-x). > > [but for x=0 you need take care as step(0)=.5] > > Of course, if you have a hundred points where the function changes the > expression, this becomes much more complicated > > 2. Define your own function of three variables S(a,b,x) such that > S(a,b,x)=1 for a<x<b and zero otherwise. GiNaC tutorial > contains a demonstration how make a user-defined function. Then, any > piece-wise function F will be a sum of terms f_i(x)*S(a_i,_b_i,x) > where f_i is the expression for F on [a_i,b_i] (assuming disjoint > partition. > > 3. Finally, you may derive your own class from GiNaC::basic to hold > your piece-wise function (again, GiNaC tutorial gives an example). As > I see it shall have two lists: one with points of the partition, > another with the respective expression. Then you add your custom > methods to operate this class. > > > The approaches are given in the order of increasing complexity, but > the efficiently shall grow in the same direction. > > Best wishes, > Vladimir > -- > Vladimir V. Kisil http://www.maths.leeds.ac.uk/~kisilv/ > Book: Geometry of Mobius Transformations http://goo.gl/EaG2Vu > Software: Geometry of cycles http://moebinv.sourceforge.net/ > >>>>> On Wed, 22 Apr 2015 16:47:13 +0200, Vincent Huber < > vincent.huber(a)cemosis.fr> said: > > VH> Hello Dr. Kisil, > > VH> The question from C. Trophime is not about evaluating the > VH> function but to define it. Feel++ <http://www.feelpp.org> is a > VH> Finite Element library that main goal is to solve the > VH> variational problem a(u,v)=f(v) that arises from a lot of > VH> physical problems. > > VH> We use GiNaC to dynamically define the right hand side of our > VH> problem, or our boundaries conditions and whatever can be > VH> expressed with it. > > VH> The question - I guess - can be explained like that : I would > VH> like to define > > VH> - > > VH> f(x) = 2*x if x>0 - > > VH> f(x) = 3*x if x<=0. > > VH> Thus, basically, I would like to write > > > VH> ex MyEx = (x<=0)?3*x:2*x > > VH> To my best knowledge, boolean expression are not handled in > VH> GiNaC, isn’t it ? > > VH> all the best, > > VH> Vincent H. -- Docteur Ingénieur de recherche CeMoSiS > VH> <http://www.cemosis.fr> - vincent.huber(a)cemosis.fr Tel: +33 (0)3 > VH> 68 8*5 02 06* IRMA - 7, rue René Descartes 67 000 Strasbourg > > VH> ---------------------------------------------------- > VH> Alternatives: > > VH> ---------------------------------------------------- > VH> _______________________________________________ GiNaC-list > VH> mailing list GiNaC-list(a)ginac.de > VH> https://www.cebix.net/mailman/listinfo/ginac-list > -- Docteur Ingénieur de recherche CeMoSiS <http://www.cemosis.fr> - vincent.huber(a)cemosis.fr Tel: +33 (0)3 68 8*5 02 06* IRMA - 7, rue René Descartes 67 000 Strasbourg

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Piecewise function
by Vincent Huber 22 Apr '15

22 Apr '15

Hello Dr. Kisil, The question from C. Trophime is not about evaluating the function but to define it. Feel++ <http://www.feelpp.org> is a Finite Element library that main goal is to solve the variational problem a(u,v)=f(v) that arises from a lot of physical problems. We use GiNaC to dynamically define the right hand side of our problem, or our boundaries conditions and whatever can be expressed with it. The question - I guess - can be explained like that : I would like to define - f(x) = 2*x if x>0 - f(x) = 3*x if x<=0. Thus, basically, I would like to write ex MyEx = (x<=0)?3*x:2*x To my best knowledge, boolean expression are not handled in GiNaC, isn’t it ? all the best, Vincent H. -- Docteur Ingénieur de recherche CeMoSiS <http://www.cemosis.fr> - vincent.huber(a)cemosis.fr Tel: +33 (0)3 68 8*5 02 06* IRMA - 7, rue René Descartes 67 000 Strasbourg

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Piecewise function
by Christophe Trophime 12 Mar '15

12 Mar '15

Hi, I am using GiNac within a Finite Element Library Feel++. I would to define piecewise function in GiNaC. Is this possible with latest version? Thank for any hints Best regard C. Trophime Christophe TROPHIME Research Engineer CNRS - LNCMI 25, rue des Martyrs BP 166 38042 GRENOBLE Cedex 9 FRANCE Tel : +33 (0)4 76 88 90 02 Fax : +33 (0) 4 76 88 10 01 Office U 19 M@il : christophe.trophime(a)lncmi.cnrs.fr

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Manipulation with matrice
by Fmant Dolch 08 Mar '15

08 Mar '15

Hi. In tutorial said there is lst_to_matrix method to create matrix from list of lists. If i want to change some rows in matrice, do i need firsst change list of lists then convert to matrix or there is some direct way to do it?

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list differentiation
by soppon 01 Mar '15

01 Mar '15

Hi. Here two programs. dif1 return 0 for list1 and working well for list2, dif2 return the rigth answer, but if you change table argument x to y on line 12, then get segmentation fault. What should i do?

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list input
by soppon 01 Mar '15

01 Mar '15

Hi. I'm trying to use list as input. List as output prints {expr1,expr2,..}, list.nops() is varying. When I write list as: parser reader; somelist=reader(cin); where input to cin: {expr1,expr2,..} at the end shift-D It returns somelist={expr1,expr2,..}, somelist.nops()=1. When accessing the 2nd and higher element of list, program gets segmentation fault.

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how to match symmetric function
by Zhao Li 14 Feb '15

14 Feb '15

We have a self defined function “LMT” by DECLARE_FUNCTION_2P( LMT ); REGISTER_FUNCTION( LMT, set_symmetry(sy_symm(0,1)) ); Its two arguments are symmetric to each other. And we want to make the substitution in the expressions, LMT(mu1,mu2)*LMT(mu2,mu3) -> LMT(mu1,mu3). Therefore we made an exmap by exmap replacement; replacement.insert(ex2( LMT(wild(1),wild(2))*LMT(wild(2),wild(3)), LMT(wild(1),wild(3)) )); However, it sometimes does not work for ex testexpr = LMT(rho1,rho2)*LMT(rho2,rho3); cout << “before subs, testexpr = “ << testexpr << endl; testexpr = testexpr.subs( replacement, subs_options::algebraic ); cout << “after subs, testexpr = “ << testexpr << endl; The subs here mostly fails. Then we realised GiNaC will change to the canonical form for LMT, so we insert all cases of combinations by exmap replacement; replacement.insert(ex2( LMT(wild(1),wild(2))*LMT(wild(2),wild(3)), LMT(wild(1),wild(3)) )); replacement.insert(ex2( LMT(wild(2),wild(1))*LMT(wild(2),wild(3)), LMT(wild(1),wild(3)) )); replacement.insert(ex2( LMT(wild(1),wild(2))*LMT(wild(3),wild(2)), LMT(wild(1),wild(3)) )); replacement.insert(ex2( LMT(wild(2),wild(1))*LMT(wild(3),wild(2)), LMT(wild(1),wild(3)) )); But this still does not work sometimes. Then we got that GiNaC may also change the form of matching expression of LMT(wild(1),wild(2)). What we can have now is only turn off symmetry property for LMT function, but we worry it may generate difficulty in the future. So is there some option or algorithm for the symmetric function matching? Thanks. Best Regards, Zhao

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Performance of simplify_indexed on long chains of Dirac matrices
by Vladyslav Shtabovenko 26 Jan '15

26 Jan '15

Dear all, I'm wondering about the performance of simplify_indexed applied to a long chain of Dirac matrices in D dimensions. For example, simplifying g^i1 g^i2 g^i3 g^i4 g^i5 g^i6 g^i7 g^i8 g^i9 g^i1 g^i2 g^i3 g^i4 g^i5 g^i6 g^i7 g^i8 g^i9 requires about 15 seconds on my machine. Is this something one would normally expect with GiNaC, or am I lacking some essential optimizations? I'm using Fedora 20 64-bit with newest GiNaC from the Git repository. The machine is an i5-3570 with 16GB RAM. The source code --------------------------------------------------------------------- #include <iostream> #include <ginac/ginac.h> using namespace std; using namespace GiNaC; int main() { symbol D("D"); varidx i1(symbol("i1"), D), i2(symbol("i2"), D), i3(symbol("i3"), D), i4(symbol("i4"), D), i5(symbol("i5"), D), i6(symbol("i6"), D), i7(symbol("i7"), D), i8(symbol("i8"), D), i9(symbol("i9"), D); cout << (simplify_indexed(dirac_gamma(i1)* dirac_gamma(i2)* dirac_gamma(i3)* dirac_gamma(i4)* dirac_gamma(i5)* dirac_gamma(i6)* dirac_gamma(i7)* dirac_gamma(i8)* dirac_gamma(i9)* dirac_gamma(i1.toggle_variance())* dirac_gamma(i2.toggle_variance())* dirac_gamma(i3.toggle_variance())* dirac_gamma(i4.toggle_variance())* dirac_gamma(i5.toggle_variance())* dirac_gamma(i6.toggle_variance())* dirac_gamma(i7.toggle_variance())* dirac_gamma(i8.toggle_variance())* dirac_gamma(i9.toggle_variance()) )).expand() << endl; return 0; } --------------------------------------------------------------------- is compiled and run via c++ test.cpp -o test -Ofast -lcln -lginac -Wl,-rpath,/usr/local/lib time ./test Cheers, Vladyslav

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