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multi index storage of expressions
by Charlls Quarra 21 Feb '07

21 Feb '07

Hi, I wanted to define a simple matrix of derivatives (i.e: a Jacobian) first as an indexed object: ex f = a*x + b*y + c*x*y + ... ex g = u*pow(x,2) + v*pow(y,2) + w*x,y + .... idx i(symbol("is") , 2) , j(symbol("js") , 2); ex Jacobian = diff( f*delta_tensor(i , 0) + g*delta_tensor(i,1) , x )*delta_tensor( 0 , j ) + diff( f*delta_tensor(i , 0) + g*delta_tensor(i,1) , y )*delta_tensor( 1 , j ); but then this failed on me (because 0 and 1 are not acceptable arguments where an idx should be expected) Why am i trying to do this as an indexed object and not with a matrix? well, because later, i would also want to make computations with an object like D( f_{i} ) / dx_{j} dx_{k} but afaik there isnt a "three indexed" matrix object in ginac, or how they are usually called, cubic arrays. correct? __________________________________________________ Preguntá. Respondé. Descubrí. Todo lo que querías saber, y lo que ni imaginabas, está en Yahoo! Respuestas (Beta). ¡Probalo ya! http://www.yahoo.com.ar/respuestas

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Re: [GiNaC-list] table and exhashmap
by Jerome BENOIT 19 Feb '07

19 Feb '07

Hi, Sheplyakov Alexei wrote: > On Mon, Feb 19, 2007 at 03:45:03PM +0800, Jerome BENOIT wrote: > >> Let be more specific. >> >> During some kind of computation I have to compute (multi-indexed) >> coefficients: >> 1] these coefficients are long to compute; >> 2] they are computed by sub set through (consuming) recurrence formulae; >> 3] these coefficients are meant to be used randomly and very often. > >> Clearly the remember machinery can be use to overcome point [1] and [3]: >> for GiNaC function this is transparent for the user. >> >> Point [2] causes me some difficulty: >> I want to compute each subset only once. > >> Hence the idea to compute each subset through a GiNaC function >> (with the remember option) which return tables, > > Why do you need _GiNaC_ function to compute coefficients? What's wrong > with C++ function, e.g. > > ex compute(const ex& data) > { > static exmap remember; > exmap::iterator i = remember.find(data); > if (i != remember.end()) > return i->second; > > ex result; > // actually compute it, making use of compute() itself > > remember.insert(exmap::value_type(data, result)); > return result; > } > >> Right now, my guess is that I have to introduce a super class >> with a exhashmap<SOMETHING> as (principal) member: I thought >> that there was a better GiNaC way to do so, but apparently not. > > Unless I'm missing something fundamental, this approach seems to be > unnecessary complicated. I am more than agree: hence my question. I guess that I still too Maple oriented. Thanks you very much, Jerome

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table and exhashmap
by Jerome BENOIT 19 Feb '07

19 Feb '07

Hello List, I am new in GiNaC and in C++ (but very familiar with another CAS and C). I would like to implement a function which returns table. Unless I missed something, there is no ready to use table object in GiNaC. My first thought was to use exhashmap<T> , but I am no more sure about it as I do not see how to proceed. Any hint is welcomes. Thanks in advance, Jerome -- Jerome BENOIT jgmbenoit_at_mailsnare_dot_net

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list of list
by Jerome BENOIT 17 Feb '07

17 Feb '07

Hello List, I am rather a newbie in GiNaC and in C++ (but I am very familiar with another CAS and with C): I have just noticed that: lst list; list = lst(lst(1,1),lst(2,4),lst(3,9)); gives a list of list as expected, whereas lst list; list = lst(1,1),lst(2,4),lst(3,9); gives the first list (namely lst(1,1)) is it a bug ? or is it a wrong thing to do ? Thanks in advance, Jerome

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Release of GiNaC 1.3.7
by Jens Vollinga 05 Feb '07

05 Feb '07

Hello everybody, GiNaC 1.3.7 is out and available. The changes are: - Fixed bug in expansion of power. - Fixed bugs in functions S() (infinite loop), H() and zeta() (wrong results). - Rebuilt bison related files with bison version 2.3 (fixes parse error bugs). - Improved power::eval(). - Improved libreadline detection. As always, this release can be downloaded from http://www.ginac.de/Download.html Best wishes, Jens

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Teaching material for GiNaC
by Chris Dams 02 Feb '07

02 Feb '07

Dear all, For the C++ course that has been held at my university, I have done two of the lectures and talked about GiNaC. For use by others in similar circumstances, you find my teaching materials attached to this course. Labeling the sections as "First hour" and "Second hour" turned out to be a bit optimistic. I used two hours for both the first and second section. Mainly because the students needed quite a bit of time for the final exercise in each section. Best wishes, Chris

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collecting on similar series expansion
by Charlls Quarra 01 Feb '07

01 Feb '07

Hi , I'm just trying out ginac for the first time. I have an expression with sumands of this type (in latex format): 1-\frac{1}{3} \frac{ p D[0](F)(q) D[0,0](F)(q) \nu \epsilon^{2} dt^{5} \delta}{m^{3}}-\frac{1}{9} \frac{ p D[0](F)(q) D[0,0](F)(q)^{2} \alpha^{2} \nu^{2} \epsilon^{2} dt^{9} \F(q) \delta \gamma}{m^{5}}-\frac{1}{18} \frac{ p^{2} D[0,0](F)(q) D[0,0,0](F)(q) \beta \alpha^{2} \epsilon^{2} dt^{8} \F(q) \delta \gamma}{m^{5}}+\frac{1}{2} \frac{ D[0](F)(q) D[0,0](F)(q) \alpha \nu \epsilon dt^{6} \F(q)}{m^{3}} .... so i want to collect terms that have the same coefficients of the form D[0..i times] (F)(q) * D[ 0.. j times] (F)(q) .... but the polynomial collect won't work. Initially i thought about substituting each D[ ] (F)(q) with a different symbol, then collect on the multivariate polynomials of these symbols and then finally substitute back the D[] expressions, however, I don't know how the collect call is supposed to receive the symbols that it must collect, the code looks like this: ex jacobian = diff( q + dq_new*dt , q )*diff( p + dp_new*dt , p ) - diff( q + dq_new*dt , p )*diff( p + dp_new*dt , q ); cout << " the jacobian of the integrator is " << expand(jacobian) << endl; exmap diff_map , inv_diff_map; symbol foo[10]; diff_map[ F(q) ] = foo[0]; inv_diff_map[ foo[0] ] = F(q); diff_map[ F(q).diff(q) ] = foo[1]; inv_diff_map[ foo[1] ] = F(q).diff(q); diff_map[ F(q).diff(q,2) ] = foo[2]; inv_diff_map[ foo[2] ] = F(q).diff(q,2); diff_map[ F(q).diff(q,3) ] = foo[3]; inv_diff_map[ foo[3] ] = F(q).diff(q,3); diff_map[ F(q).diff(q,4) ] = foo[4]; inv_diff_map[ foo[4] ] = F(q).diff(q,4); ex rord = collect( jacobian.subs( diff_map ) , { foo[0] , foo[1] , foo[2] , foo[3] , foo[4] } ); // i know this is an error in C++, but this is the idea rord = rord.subs( inv_diff_map ); cout << "reordered we obtain " << rord << endl; any thoughts on this? __________________________________________________ Preguntá. Respondé. Descubrí. Todo lo que querías saber, y lo que ni imaginabas, está en Yahoo! Respuestas (Beta). ¡Probalo ya! http://www.yahoo.com.ar/respuestas

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I'm ready for the new release.
by Chris Dams 01 Feb '07

01 Feb '07

Dear all, I applied the patch that I was talking about. The points are (1) Added a simplification rules for powers that turns (x^a)^b into x^(a*b) in the case that x is positive and a is real. (2) Improved expansion of powers. In the case that a power is raised to an integer power, we should not simply be doing (x^a)^n -> expair(x, a*n) because this is wrong if x=y^2, a=1/2 and n=2. Then we get ((y^2)^(1/2))^2 -> expair(y^2, 1), which should be expair(y, 2). Happy releasing, Chris

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retrieving wildcard replacements on C++
by Charlls Quarra 01 Feb '07

01 Feb '07

Hi, suppose the following: symbol x("x"); ex foo = A*pow(x,2) + B*x; lst ocurrences; foo.find( wild(1)*x , ocurrences ); //the wildcard replacement is B how would you retrieve the wildcard replacement in this case? in ginsh you already get a list of the wildcards replacement, but after reading various times the relevant page of the tutorial, i couldn't find how is this done in c++ cheers __________________________________________________ Preguntá. Respondé. Descubrí. Todo lo que querías saber, y lo que ni imaginabas, está en Yahoo! Respuestas (Beta). ¡Probalo ya! http://www.yahoo.com.ar/respuestas

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array expressions with symbolic index
by Zhongxing Xu 01 Feb '07

01 Feb '07

Hello, Is there something like array expression in GiNaC? I want to do symbolic computation involving array expressions related to program verification. I would like to implement a theorem prover on top of GiNaC. So I also need conditional expressions. For example: x = mem[2] + 2; y = mem[i] -3; x >= 3; Can GiNaC represent these expressions? Note that array index might be a symbolic value. Thank you. - Zhongxing Xu

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