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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.

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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

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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

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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} }

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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

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Problem with subs
by Tatiana Zolo 28 Feb '02

28 Feb '02

We do not understand how subs works in some cases: we tried the following ginsh session > p=x+1; 1+x > subs(p,x==k-1); k > subs(p,x==x-1); -1+x > subs(p,x==x-2); -1+x > subs(p,x==x^2-1); x^2 > subs(p,x==x^2); 1+x^2 so, apparently, subs is sometimes wrong. We couldn't find anything in the documentation to explain this fact. Thank you very much. Best wishes Alessandro Zaccagnini Tatiana Zolo purrs developers, at the University of Parma, Italy

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Problems with subs
by Tatiana Zolo 28 Feb '02

28 Feb '02

We do not understand how subs works in some cases: we tried the following ginsh session > p=x+1; 1+x > subs(p,x==k-1); k > subs(p,x==x-1); -1+x > subs(p,x==x-2); -1+x > subs(p,x==x^2-1); x^2 > subs(p,x==x^2); 1+x^2 so, apparently, subs is sometimes wrong. We couldn't find anything in the documentation to explain this fact. Thank you very much. Best wishes Alessandro Zaccagnini Tatiana Zolo purrs developers, at the University of Parma, Italy

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Problem with expand()
by Tatiana Zolo 28 Feb '02

28 Feb '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

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collect TeX output
by Christophe TROESTLER 15 Feb '02

15 Feb '02

Hi, It seems that GiNaC, when (for example) collecting expressions and then printing them to LaTeX adds some braces in additions to parentheses. For example symbol x("x"), y("y"), t("t"); ex e = x*t + y*t; collect(e,t).print(GiNaC::print_latex()); ouputs t {(y+x)} Is there any way (an option?) to remove the extra braces? Indeed, they force TeX NOT to BREAK the expression (i.e., it must fit on a single line) which is problematic when the expression is long. Thanks, ChriS

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GiNaC for Win32 ?
by Herve Soulard 28 Jan '02

28 Jan '02

Hi there, I'm currently looking for a free (for now) C/C++ CAS library for the Win32 platform. GiNaC's functionnalities seem OK for me, but I'm wondering if a Win32 version exists? Do you know if I can find one ? Thanks very much for any help, Hervé Soulard.

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