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Re: [GiNaC-list] How to differentiate from a Tensor?
by Vladimir V. Kisil 18 Jul '17

18 Jul '17

>>>>> On Fri, 14 Jul 2017 13:29:37 +0430, esarcush esarcush <esarcush(a)gmail.com> said: EE> E needs to depend on x. So, symbol A("A"), x("x"); symbol EE> i_sym("i"), j_sym("j"); idx i(i_sym, 3), j(j_sym, 3); ex e = EE> indexed(A, i, j); ex de_dx = e.diff(x); cout << de_dx << "\n"; EE> returns 0. Thus, what is the way to depend "e" on "x" like EE> undefined functions? If a dependence of A on x is not defined, try to use the step function (as one without defined derivative): ex e = indexed(step(x), i, j); This keeps track on derivatives. To maintainer: I have run into similar situation working with differential operators. Shall we add "generic" functions to GiNaC with 1, 2, 3, 4 variables? -- 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/ EE> All the bests, EE> On 7/14/17, Vladimir V. Kisil <kisilv(a)maths.leeds.ac.uk> wrote: >>>>>>> On Fri, 14 Jul 2017 12:15:49 +0430, esarcush esarcush >>>>>>> <esarcush(a)gmail.com> said: >> EE> Dear all, What is right way to have something like \( EE> \frac{\partial A^{i}_{jk}}{\partial x} \)? Indeed, I defined a EE> tensor "A~i.j.k" and want to differentiate from it with respect EE> to "x" e.g. >> >> For a GiNaC object E its derivative with respect to x is obtained >> by E.diff(x) >> -- >> 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/ >>

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Re: [GiNaC-list] Tricky way to control over dummy indices
by esarcush esarcush 14 Jul '17

14 Jul '17

On 7/15/17, esarcush esarcush <esarcush(a)gmail.com> wrote: > Agreement: Every dummy index have a hidden sigma. > > Based on the page you linked (and in common also), there are two ways > to illustrate a dummy index in a term: > 1) "j" is a dummy one iff it appears as superscript and subscript. > > 2) "j" is a dummy one iff it appears in two (or more that two) > tensor coefficients making that term. > > GiNaC is using second approach. This makes some troubles to somebodies > that are using first one. For example, I'd like to deal with some > tensorials that have in-common indices as e.g. subscripts but free (as > mentioned example). I think second approach is more physical vs first > one more diff-geometrical. ;) > > All the best, > Esa > > > > > > > > > On 7/14/17, Vladimir V. Kisil <kisilv(a)maths.leeds.ac.uk> wrote: >>>>>>> On Fri, 14 Jul 2017 22:54:35 +0430, esarcush esarcush >>>>>>> <esarcush(a)gmail.com> said: >> >> EE> Dear all, in expression >> >> EE> { indexed(A, i, j) * indexed(B, j, k) } >> >> EE> GiNaC is saying that the dummy index is "j" and "i, k" are >> EE> free. Is there a way to determine dummy indices based on >> EE> Einstein summation notation; namely all the indices in the >> EE> latter be free. >> >> My understanding of >> >> https://en.wikipedia.org/wiki/Einstein_notation >> >> is that in the above expression there is summation over j, thus it is >> not free. >> -- >> 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/ >> >

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Tricky way to control over dummy indices
by esarcush esarcush 14 Jul '17

14 Jul '17

Dear all, in expression { indexed(A, i, j) * indexed(B, j, k) } GiNaC is saying that the dummy index is "j" and "i, k" are free. Is there a way to determine dummy indices based on Einstein summation notation; namely all the indices in the latter be free. All the bests, Esa

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Re: [GiNaC-list] How to differentiate from a Tensor?
by esarcush esarcush 14 Jul '17

14 Jul '17

On 7/14/17, Vladimir V. Kisil <kisilv(a)maths.leeds.ac.uk> wrote: >>>>>> On Fri, 14 Jul 2017 12:15:49 +0430, esarcush esarcush >>>>>> <esarcush(a)gmail.com> said: > > EE> Dear all, What is right way to have something like \( > EE> \frac{\partial A^{i}_{jk}}{\partial x} \)? Indeed, I defined a > EE> tensor "A~i.j.k" and want to differentiate from it with respect > EE> to "x" e.g. > > For a GiNaC object E its derivative with respect to x is obtained by > E.diff(x) > -- > 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/ > E needs to depend on x. So, symbol A("A"), x("x"); symbol i_sym("i"), j_sym("j"); idx i(i_sym, 3), j(j_sym, 3); ex e = indexed(A, i, j); ex de_dx = e.diff(x); cout << de_dx << "\n"; returns 0. Thus, what is the way to depend "e" on "x" like undefined functions? All the bests,

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How to differentiate from a Tensor?
by esarcush esarcush 14 Jul '17

14 Jul '17

Dear all, What is right way to have something like \( \frac{\partial A^{i}_{jk}}{\partial x} \)? Indeed, I defined a tensor "A~i.j.k" and want to differentiate from it with respect to "x" e.g. All the bests, Esa

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CAS
by Robert Hai 07 Jul '17

07 Jul '17

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Min/Max functions
by Lukas Barth 30 May '17

30 May '17

Hi everyone, I'm currently evaluating whether to use GiNaC for my project where I basically need to differentiate functions containing max(…,…), some tanh(…), and some other atrocities. Now, from the documentation it looks like GiNaC does not implement max() or min(). I realize that these functions do weird things (especially when you differentiate them). Still, I was wondering if they are really not included, just missing from the documentation, or if I'm too blind to find them. Any pointers are appreciated! Regards, Lukas

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Converting an expression to std::string and back again
by Robert Hai 29 Mar '17

29 Mar '17

Dear Mailing List, for a project I need to convert a std::string to an ex, diff it and then convert it back to a std::string. For the conversion from std::string to ex I found this constructor : /** Construct example from string and a list of symbols. The input grammar is * similar to the GiNaC output format. All symbols and indices to be used * in the expression must be specified in a lst in the second argument. * Undefined symbols and other parser errors will throw an exception. */ ex(const std::string &s, const ex &l); at http://www.ginac.de/reference/classGiNaC_1_1ex.html#ace68037326c1a2b8c93a56… So I tried doing the following : symbol x("x"); ex expression; ex e("x^2",expression); std::cout << diff(e,x) << std::endl; But this leads me to this exception : std::invalid_argument: find_or_insert_symbol: symbol "x" not found Note that I tried using expression and e in diff(e,x). Unfortunately I could not find any documentation on how to convert the expression diff returns to a std::string. Thanks a lot for your help in advance ! Robert Hey

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Error on expression
by Jean-Michaël Celerier 14 Mar '17

14 Mar '17

The following code produces an error that says that it should be reported : #include<ginac/ginac.h> #include<iostream> int main(int argc, char* argv[]) { GiNaC::symtab table; table["x"] = 2.34; GiNaC::parser p(table); GiNaC::ex e = p("2*cos(x)+e^x"); GiNaC::numeric n = GiNaC::ex_to<GiNaC::numeric>(e); double x = GiNaC::ex_to<GiNaC::numeric>(n.evalf()).to_double(); std::cout << x << std::endl; return 0; } The error : terminate called after throwing an instance of 'cln::notreached_exception' what(): Internal error: statement in file real/elem/cl_R_mul.cc, line 93 has been reached!! Please send the authors of the program a description how you produced this error! Best Jean-Michaël

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compile-time calculations
by Matteo 28 Feb '17

28 Feb '17

Hello, I am currently evaluating GiNaC for use in an engineering software that we use internally. Therefore, I am still inexperienced with it and only ask for some pointers. I have read in the news feed http://www.ginac.de/News.html that new C++11 features like "constexpr" are being implemented into GiNaC. My question is: how much can be done at compile time? Background: The basic workflow that we would like to optimize is the following: 1) Design an algorithm in C++, which involves manipulation of scientific formulae 2) Elaborate the "manipulation" part in a separate environment (mostly SageMath) 3) Translate the result of the separate CAS as C++ 4) Integrate the result into the original C++ algorithm This works, but has the following disadvantages: - it requires to leave one environment (C++ IDE) to the other (CAS environment) - translating the mathematical results to C++ is tedious and error prone (although it can be automated for simple cases) - it separates the various parts of the algorithm into different documents, which makes it hard to mantain Ideally then, we would use GiNaC instead of SageMath (or other CAS) to unify the code. However, we would like to remove the runtime overhead of expression manipulation and interpretation. I am looking for something like the "compilation of expressions to function pointers", but with the addition of compile-time expression manipulation. http://www.ginac.de/tutorial/#Compiling-expressions-to-C-function-pointers The closest I have found so far is ViennaMath, but it seems still very limited in features. http://viennamath.sourceforge.net/viennamath-example-integration.html Thank you for any help!

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