Le lundi 13 mars 2006 à 11:37 +0100, Francois Maltey a écrit : > Hello, > > I continue to test my classical exercices with axiom. > > I can't play with eigenvalue / eigenvector for Matrix Float.
It's not possible, you have to coerce your Matrix Float to Matrix Fraction Integer. The '::' operator will call rationalApproximation in the Float package (see src/algebra/float.spad.pamphlet). After you can obtain Float results. For example if A is a Float Matrix: complexEigenvectors(A::MATRIX FRAC INT,1.e-20) returns all (Complex Float) eigenvalues and eigenvectors. realEigenvectors(a::MATRIX FRAC INT,1.e-20) returns real (Float) eigenvalues and eigenvectors > > I can compute det (M - x (1)_n), > but I can't find root of a Polynomial Float, is it possible ? I assume you want the numerical roots (mail subject). It's possible to use the computationally expensive algorithm in the ComplexRootFindingPackage, so if pol is a polynomial Float: complexZeros(pol,1.e-15)$ComplexRootFindingPackage(FLOAT,UP(x, COMPLEX FLOAT)) It's also possible if you coerce your Polynomial Float to FRAC POLY INT. To do so, you have to initially coerce it to POLY FRAC INT (it will call, as above, rationalApproximation) and after to FRAC POLY INT. This coercion involves a "commutation" coded in the interpreter (in src/interp,i-coerfn.boot.pamphlet) that coerces for example POLY FRAC INT to FRAC POLY INT or COMPLEX FRAC INT to FRAC COMPLEX INT. So qpol := pol::POLY FRAC INT::FRAC POLY INT realRoots(qpol,1.e-20) returns real (Float) roots. and complexRoots(qpol,1.e-20) returns all the roots (Complex Float) In these examples the results are computed to precision eps=1.e-20. You can change its type (to rational, the result will be expressed as rational number) or its value, see src/algebra/numeigen.spad.pamphlet and src/algebra/numsolve.spad.pamphlet. Cheers, Greg PS: The attachement contains an axiom session (with ')set output length 110) with all the examples above. > Have a good day ! > > François. > > > _______________________________________________ > Axiom-math mailing list > [email protected] > http://lists.nongnu.org/mailman/listinfo/axiom-math > _______________________________________________ Axiom-math mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-math
