March 2002 - GiNaC-list

GiNaC 1.0.8 now available
by Christian Bauer 31 Mar '02

31 Mar '02

Hello! Following our recent trend of Sunday evening releases we are proud to announce the immediate availability of GiNaC 1.0.8 which you can get from ftp://ftpthep.physik.uni-mainz.de/pub/GiNaC Changes include, but are not limited to - Improvements in memory usage of the expand() methods. Hm, wait... that's the only change!? <searches CVS logs> Aha, sorting of vector<expair> is a little faster, and the namespace fix for is_ex_the_function() is in. Alas, long gone now are the days of 0.9.x where changelog pages filled screen after screen... Bye, Christian -- / Coding on PowerPC and proud of it \/ http://www.uni-mainz.de/~bauec002/

1 0

Adding another infix operator?(programing)
by Mark Stankus 21 Mar '02

21 Mar '02

Hello, I am new to ginac. I have a computer algebra program which uses the infix operator "**" for a noncommutative multiplication (for example, a**b where a and b are symbols, but are thought of as representing matrices). (See http://math.ucsd.edu/~ncalg for more.) Is it possible/easy/hard to add a "**" infix operator to ginac? If so, where do I start looking in the code to do this. I would like to link my code up with ginac in the future. Mark Stankus mstankus(a)calpoly.edu

2 1

And GiNaC-1.0.7 shall be made legion...
by Richard B. Kreckel 18 Mar '02

18 Mar '02

Its numbers shall be increased a thousand thousand fold. The din of a million keyboards like unto a great storm shall cover the earth, and the followers of Mammon shall tremble. adapted from The Book of Mozilla, 3:31 (Red Letter Edition)

1 0

Behavior of the function 'has'
by Tatiana Zolo 13 Mar '02

13 Mar '02

I do not understand the behavior of the function 'has' in some case. I show you the problem with ginsh: > has(2^x*3^x, $0^x); 1 > has(2^x*3^x*4^x, $0^x); 1 > has(2^x*3^x, $0^x*$1^x); 1 > has(2^x*3^x*4^x, $0^x*$1^x); 0 > has(2^x*3^x*4^x, $0^x*$1^x*$2^x); 1 I would expect that also has(2^x*3^x*4^x, $0^x*$1^x); answers 'true' because I see $0^x*$1^x as a subexpression of 2^x*3^x*4^x. Same thing without to use wildcard. > has(2^x*3^x*4^x, 2^x); 1 > has(2^x*3^x*4^x, 2^x*3^x); 0 > has(2^x*3^x*4^x, 2^x*3^x*4^x); 1 Regards Tatiana Zolo

2 1

canonical ordering
by Garnet Kin-Lic Chan 11 Mar '02

11 Mar '02

Hi, I have been extending GiNaC in various ways, but something I haven't yet fathomed is the canonical ordering that automatically happens. For example, I derived a class from indexed, whose compare_same_type simply calls the inherited::compare_same_type, yet the ordering of products in my class was different from that of the usual indexed objects. What determines and triggers the canonical ordering? Perhaps this could also be explained somewhere in the reference. sincerely, Garnet

2 1

matrix^0, matrix.exp() and latex output of matrices
by Alexander Heide 08 Mar '02

08 Mar '02

Here are some remarks and questions about matrices in GiNaC. Have a look at this code: #include <iostream> #include <ginac/ginac.h> using namespace std; using namespace GiNaC; int main() { matrix A(2, 2, lst(0, 1, 1, 0)); A.print(print_latex(std::cout)); cout << endl; cout << evalm(exp(A)) << endl; cout << pow(A, 0).evalm() << endl; cout << A.pow(0) << endl; return 0; } The programm prints out: [[0,1],[1,0]] exp([[0,1],[1,0]]) 1 and then runs forever (or until someone presses CTRL-C or turns off the computer or whatever). To have a nice matrix in LaTeX I would expect something like \left(\begin{array}{ccc}0&1\\1&0\end{array}\right) in the first line of the output. In the second line the expression keeps unevaluated because of a lacking method matrix matrix::exp(void) const; The third line should be [[1,0],[0,1]] as well as the the fourth line. And finally I have a (probably stupid) question: To construct an identity 2 x 2 matrix, I want to use ex I = diag_matrix((lst(1, 1)); (More convenient would be a function like 'ex idenity_matrix(unsigned n)') Now I want to add E to another matrix A, for instance A = matrix(2, 2, lst(1, 0, 0, 1)); This works: evalm(A + E) This works not: A.add(E), because E ist not a matrix object. My question is: How con I convert E to a matrix object? I've consulted the tutorial, but I couldn't find an answer to this question.

2 1

What is a polynomial in x?
by Roberto Bagnara 08 Mar '02

08 Mar '02

We have some doubts on the handling of polynomials under GiNaC. The question we need to be answered is: what is, for GiNaC, a polynomial in a variable x? That is, for which class of expressions are the functions degree, ldegree, coeff, lcoeff, tcoeff... guaranteed to work? If this class is not the class of all expressions, it would be nice to have a function or method recognizing it so that one can do things like if (is_a_polynomial(e, x)) { // Here it is safe to use degree(e, x), ... } While we are trying to write code that depends only on the guarantees GiNaC offer, we would like to take the occasion of improving GiNaC's documentation (that is, if you answer nicely we will contribute a couple of paragraph for the section of the manual dealing with polynomials ;-) All the best Tatiana Zolo Roberto Bagnara -- Prof. Roberto Bagnara Computer Science Group Department of Mathematics, University of Parma, Italy http://www.cs.unipr.it/~bagnara/ mailto:bagnara@cs.unipr.it

3 5

degree of non-expanded polynomials
by Alessandro Zaccagnini 06 Mar '02

06 Mar '02

I have been experimenting with GiNaC, and I found that on page 46, section 5.5.2, of the manual (version 1.0.6) that degree() works reliably also on non-expanded polynomials. But the following program seems to prove that it is not the case. #include <iostream> #include <ginac/ginac.h> using namespace std; using namespace GiNaC; typedef GiNaC::ex GExpr; typedef GiNaC::symbol GSymbol; int main() { GSymbol x("x"); GExpr h_a = numeric(1,2) * x * (x-1); GExpr h_b = - (x+1) * (x-1); GExpr h_c = numeric(1,2) * x * (x+1); GExpr p = h_a + h_b + h_c; std::cout << "p = " << p << " degree " << p.degree(x) << std::endl; p = p.expand(); std::cout << "p = " << p << " degree " << p.degree(x) << std::endl; return 0; } This is the output that I obtained (from version 1.0.5): p = 1/2*(1+x)*x+1/2*(-1+x)*x+(-1+x)*(-1-x) degree 2 p = 1 degree 0 Best wishes Alessandro Zaccagnini The purrs developers team at the University of Parma

2 1

LaTeX output of indexed objects
by Alexander Heide 06 Mar '02

06 Mar '02

I encountered problems while playing with GiNaC. I want to produce LaTeX output of an indexed object. Consider the following code: #include <iostream> #include <ginac/ginac.h> using namespace std; using namespace GiNaC; int main() { symbol i_sym("i"), j_sym("j"); idx i(i_sym, 4), j(j_sym, 4); symbol A("A"); indexed(A, i, j).print(print_latex(std::cout)); return 0; } This prints out: {A}_{_{i} _{j} } If I try to latex this piece of latex code I get an error message: ! Double subscript. I think instead of the above expression, print_latex() should yield: {A}_{{i} {j} }

2 1

Problems with expand()
by Tatiana Zolo 05 Mar '02

05 Mar '02

We have a few questions about GinaC's behaviour. For our purposes, it would be useful to have a slightly more general form of expand that takes care of non-ambiguous iterated exponentials, as in the case (2^x)^3 which we would like to see in the form 2^(3*x) or even 8^x We understand that there are cases when this should not be done automatically, but we believe that this is an instance when there is no harm in simplifying since 2 is a positive real number and there is no question of complex numbers being involved. A "real" version of expand would be very useful for us. Do you plan to add these features to a future release of GiNaC? Thank you very much. Best wishes Alessandro Zaccagnini Tatiana Zolo purrs developers, at the University of Parma, Italy

2 1