05/16/2008, 01:48 PM
andydude Wrote:Well, I've included an algorithm for hyperbolic iteration (the more general "complement" of parabolic iteration,At least one person works at the tetration library ... I didnt even found the time to look through your code, but it will happen
But (!) I now have Sage actually working on my new Linux machine!
Though I found out that Sage has only support for truncated powerseries.
In Maple you could define a powerseries by a function that returns for each index the coefficient, and then apply various operations on powerseries like exponentation, composition, multiplication, addition, etc (though they were sometimes very slow ...).
Cool would also be a lazy evaluation ala Haskell, which unsurprisingly has a power series module, lazy evaluation seems just to be made for power series operations.
Quote:The matrix power code for hyperbolic iteration is very specific to triangular matrices, so I'm not sure how well it could be generalized to arbitrary matrices.
The method is generally known as Matrix function and better described at Jordan matrix. In our case the function is just the power \( x^t \).
In the matrix function article there is also mentioned a method via the Cauchy integral. I wonder whether this is a link (equality?) between Kouznetsov's method and the diagonalization method.
More useful for implementing the matrix power - without needing to perform an actual diagonalization - is Aldrovandi's explanation featured by Gottfried here.
In Maple everything is already there. You just can apply any function to matrices and you have even a specialized function Matrixpower.
Quote:I found that the Sage built-in exp will only work on numeric matrices, and that the .left_eigenvectors() and .right_eigenvectors() methods are only defined on numeric matrices as well.
Usually you have symbolic eigenvalues only up to 3 or 4. Because they are the solutions of the characteristic polynomial. I guess there are only a few occasions where symbolic eigenvalues make sense.
Quote:I would very much like to work together! It would also help the project be more robust with more eyes making sure the code is rightI have a look at it soon. Btw I would really be keen on having a public git project here or here or here. How about registering one?
