November 2004 - GiNaC-list

how to use ginac output in gsl at runtime
by Matei Stroila 21 Nov '04

21 Nov '04

Hello, Here is what I would like to do and I need a piece of advice on this. I want to use ginac to compute the gradient of a function so that I can use this gradient for the conjugate gradient method in gsl (the GNU scientific library). I succesfully computed the gradient and I can output its expression with "csrc_double" to a string. How can I use this expression in the definiton of a function at runtime? I guess other people had this problem too, to use a CAS library in conjuction with a numeric library, at runtime. Thanks a lot for any suggestion, Matei

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code: extended gcd
by Ralf Stephan 20 Nov '04

20 Nov '04

Hello, please include the following snippet. Its application domain depends on that of quo() which is univariate, currently. It is tested but not heavily so. It is not optimized. Thanks, ralf Input: x,y rational polynomials Computes u,v,d such that ux+vy = gcd(x,y). /////////// Extended GCD ex xgcd (const ex& a, const ex& b, ex& u, ex& v, const symbol& s) { const ex& x = a.normal(); const ex& y = b.normal(); if (is_exactly_a<numeric>(x) && is_exactly_a<numeric>(y) && x.info(info_flags::integer) && y.info(info_flags::integer)) { cln::cl_I cu, cv, cr; cr = cln::xgcd (cln::the<cln::cl_I>(ex_to<numeric>(x).to_cl_N()), cln::the<cln::cl_I>(ex_to<numeric>(y).to_cl_N()), &cu, &cv); u = numeric(cu); v = numeric(cv); return numeric(cr); } if (is_exactly_a<numeric>(y) && y.info(info_flags::integer)) { u = 0; v = numeric(1)/y; return 1; } if (is_exactly_a<numeric>(x) && x.info(info_flags::integer)) { v = 0; u = numeric(1)/x; return 1; } if (x.info(info_flags::rational_polynomial) && y.info(info_flags::rational_polynomial)) { ex d, p, q; d = gcd (x, y); int dx = degree(x, s), dy = degree(y, s); if (dx < dy) { p = y; q = x; } else { p = x; q = y; } ex u1,u2,u3,v1,v2,v3,w1,w2,w3; u1 = p; u2 = 1; u3 = 0; v1 = q; v2 = 0; v3 = 1; while (!v1.is_zero()) { ex Q = quo (u1, v1, s); w1 = u1 - Q*v1; w2 = u2 - Q*v2; w3 = u3 - Q*v3; u1 = v1.expand(); u2 = v2.expand(); u3 = v3.expand(); v1 = w1.expand(); v2 = w2.expand(); v3 = w3.expand(); } u = (u2 / ((u1/d).normal())).expand(); v = (u3 / ((u1/d).normal())).expand(); //cerr << "CHK: " << (u*x+v*y).expand() << endl << flush; return d; } throw invalid_argument("xgcd(): not a rational polynomial"); }

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normal() bug-or-feature
by varg＠thsun1.jinr.ru 18 Nov '04

18 Nov '04

Hello! Sometimes running normal() takes *really* long time. I've attached an example, at first glance it looks horrible, but in fact the expression equals zero. The root of the problem seems to be that gcd(e1, e2, &ca, &cb) returns cb in expanded form, as in: #include <iostream> #include <ginac/ginac.h> using namespace std; using namespace GiNaC; int main(int argc, char** argv) { symbol m1("m1"); symbol m2("m2"); symbol x("x"); ex e1 = pow(x,2)*pow(m1,2) - pow(x,2)*pow(m2,2); ex e2 = pow(pow(x,2)*pow(m1,2)-pow(x,2)*pow(m2,2),100); ex ca, cb, gc; gc = gcd(e1, e2, &ca, &cb, false); cout << c2 << endl; // this won't be just x^198*(m1^2-m2^2)^99. // (m1^2-m2^2)^99 gets expanded. cout << (e1/e2).normal() << endl; // won't print just x^(-198)*(m1^2-m2^2)^(-99), // (m1^2-m2^2)^99 gets expanded return 0; } so normal() in fact expands denominators. Is there any way to fix this bug/feature? Thanks in advance, Alexei.

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Usage question
by Michael Ahern 18 Nov '04

18 Nov '04

Hello All, I have been investigating using GiNac to solve certain equations and was unsure of what is was capable of. Although I saw the lsovle() function for solving systems of linear equations, I was baffled as how to solve a non-linear equation of the form: 0 = deriv(sqrt( (X - x*t)^2 + (Y - y*t)^2 + (Z - z*t - Gt^2)^2 )) Alternatively, if it is not capable of solving such an equation, if you knew of a C/C++ library (short of matlab) that was capable. Thanks, -Mike __________________________________ Do you Yahoo!? Meet the all-new My Yahoo! - Try it today! http://my.yahoo.com

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GiNaC 1.3.0
by Jens Vollinga 14 Nov '04

14 Nov '04

Hi, GiNaC 1.3.0 is out and available. The changes are: - No funny announcements anymore. - The Clifford classes have been generalized to allow working with Clifford algebras generated by arbitrary symmetric tensors or matrices. Also, a lot of new functions for Clifford algebras have been added, including automorphisms and Moebius transformations. [Contribution by V. Kisil] - Added some basic symbolic and numeric integration facilities. [Contribution by C. Dams] - The multiple polylogarithm Li() now evaluates numerically for arbitrary arguments. - New functions G(a,y) and G(a,s,y) added (another notation for multiple polylogarithms). As always, this release can be downloaded from ftp://ftpthep.physik.uni-mainz.de/pub/GiNaC/ Enjoy, Jens

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Re: [GiNaC-list] code: extended gcd
by CRAIGHS＠Nationwide.com 08 Nov '04

08 Nov '04

Okay. Ralf Stephan <ralf(a)ark.in-berlin.de> T To: ginac-list(a)zino.physik.uni-mainz.de Sent by: cc: ginac-list-admin(a)zino.phys ik.uni-mainz.de bcc: Subject: Re: [GiNaC-list] code: extended gcd 11/08/2004 01:49 PM Please respond to ginac-list > The Yap book is now unavailable on the web. No, the ftp server is a bit peculiar. Just try a few times. _______________________________________________ GiNaC-list mailing list GiNaC-list(a)ginac.de http://thep.physik.uni-mainz.de/mailman/listinfo/ginac-list

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Re: [GiNaC-list] code: extended gcd
by CRAIGHS＠Nationwide.com 08 Nov '04

08 Nov '04

The Yap book is now unavailable on the web.

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Inverse of complex matrix
by Jonathan Brandmeyer 05 Nov '04

05 Nov '04

Sometimes, inverting a matrix with complex values does not produce something that, when multiplied by the original, returns the identity. I have attached a program that demonstrates this for one case, which was found by altering checks/check_matricies.cpp to use complex values from sparse_tree(). Is this a known problem? Thanks, -Jonathan Brandmeyer P.S: GiNaC 1.3.0, G++ 3.3.4+ (Debian), CLN 1.1.8, Debian Sid on i386

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