Hi!

On Fri, Oct 24, 2003 at 12:59:48PM +0200, Kai Ludwig wrote:

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I'm new to GiNac. Is there a way to execute symbolic differentiation of expressions that includes differential operators ?

e.g. suppose an expression

ex F = u * dx*u

When differentiate that expression F.diff(u) it should result in the expression

dx*u + u*dx

I'm still not sure what exactly the rules are that are in effect here, but it seems that "dx" and "u" are noncommutative?

Sorry - maybe my question was not precise enough. The shortcut symbol dx means the differential operator d/dx. Applied to a function u gives du/dx. The expression I mentioned comes from functional analysis. F is an operator. I'm asking for an automatic derived expression for the (Frechet-) differential dF/du. I guess, the chain rule (thus, the product rule) also applies to such differentials. Then, dF/du = du/du * du/dx + u * d/du du/dx thus, formally dF/du = du/dx + u * d/dx That's what I meant with dx*u + u*dx ??Kai -- http://echempp.sourceforge.net Kai Ludwig Institut für Organische Chemie Auf der Morgenstelle 18 72076 Tübingen Tel.: 07071/29-73049 Mail: kai.ludwig@uni-tuebingen.de

Christian Bauer wrote:

Hi!

On Tue, Nov 18, 2003 at 06:20:30PM +0100, Kai Ludwig wrote:

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dF/du = du/du * du/dx + u * d/du du/dx

thus, formally

dF/du = du/dx + u * d/dx

Here's something hacked together that achieves the desired effect for GiNaC 1.2 (treating the dx like a function):

const unsigned TINFO_differential = 0x42420001U;

DECLARE_FUNCTION_1P(dx)

// this is ad-hockery... static ex dx_deriv(const ex & a, unsigned diff_param) { return dx(1); }

REGISTER_FUNCTION(dx, derivative_func(dx_deriv). set_return_type(return_types::noncommutative, TINFO_differential))

int main() { symbol u("u", return_types::noncommutative, TINFO_differential); ex F = u * dx(u);

cout << F << endl; // "u*dx(u)" cout << F.diff(u) << endl; // "u*dx(1)+dx(u)" }

But I don't know if that's general enough for what you have in mind.

Bye, Christian

Danke ;-) I plan to use GiNaC in a few months within our project... Maybe then I can send you results/questions_hope_not Kai

Hi, there seems to be a problem with the stl set container: int main() { GiNaC::symbol u1( "A" ); GiNaC::symbol u2( "B" ); std::set<GiNaC::symbol> spec; spec.insert(u1); spec.insert(u2); spec.insert(u3); std::set<GiNaC::symbol>::const_iterator s1 = spec.find(u1); // s2 still points to u1 ! std::set<GiNaC::symbol>::const_iterator s2 = spec.find(u2); GiNaC::ex f = pow((*s1),2) + (*s2) + 200*(*s1); std::cout << "f= " << f << std::endl; } Kai -- http://echempp.sourceforge.net Kai Ludwig Institut für Organische Chemie Auf der Morgenstelle 18 72076 Tübingen Tel.: 07071/29-73049 Mail: kai.ludwig@uni-tuebingen.de

Hi All, Just a simple question - I guess: How can I get the string of a expression ? I saw a get_name() function for symbols but nothing similar for expressions. Kai -- http://echempp.sourceforge.net Kai Ludwig Institut für Organische Chemie Auf der Morgenstelle 18 72076 Tübingen Tel.: 07071/29-73049 Mail: kai.ludwig@uni-tuebingen.de