On 2/26/15, Waldek Hebisch <[email protected]> wrote: > Abhinav Baid wrote: >> >> On 02/22/2015 06:47 PM, Waldek Hebisch wrote: >> >> > Hmm, it look that you are still converting Taylor series to >> > polynomials and computing coefficients of polynomials. Did >> > you push correct version? For applying r to elements of >> > basis you will need a little routine which expands each >> > coefficient of r into series and computes combination >> > of coefficients of r times derivaties of basis element. >> Oh, sorry. I convert the coefficients of r to Taylor Series now. [1] >> > Another remark: 'zerosOf' may be quite expensive, because >> > it produces _all_ zeros. Big advantage of van Hoej methods >> > is that usually it is enough to work with single zero. >> > So use 'zeroOf' instead of computing all zeros and discarding >> > the other ones. >> Yes, I was aware of the zeroOf function. But for the example mentioned >> in the thesis, the zeroOf function wasn't giving a radical solution even >> though 2 existed (repeated twice), but zerosOf was. So, I decided to go >> with zerosOf. > > I see. However, note that in algebraic case you may easily get > equal but differently looking answers. > >> > Actually, before computing zero you should >> > factor the characteristic polynomial and compute zero of >> > a single factor. For various reasons factorizer should be >> > passed as an extra parameter to 'find_right_factor'. >> > >> Okay, I now take the factorizer as an extra parameter. Surprisingly, >> now, zeroOf returns a radical result, so I use that as well. > > Well, using 'zeroOf' and 'zerosOf' without factoring may lead > to subtly wrong answers. In this case 'zerosOf' compensated > for lack of factoring, but that was just an accident due to > simple form of data. 'zerosOf' will produce answer in terms > of radicals if polynomial is simple enough, otherwise it will > produce "general" root of polynomial which displays as a new > symbol and behaves in proper way in subseqent calculations. > > >> [1] https://github.com/fandango-/spad/blob/master/task3.spad > > Now it looks OK. One extra remark: in other parts it is natural > to use factorizer which takes SparseUnivariatePolynomial(F). > Sorry, I'm not sure I understand. What do you mean by other parts? Does it refer to other spad code which takes a factorizer as a parameter? I could use the InnerEigenPackage code to get a characteristic polynomial of type SparseUnivariatePolynomial(F) and thus, change the factorizer domain now. Is that what you want to suggest?
> -- > Waldek Hebisch > [email protected] > > -- > You received this message because you are subscribed to a topic in the > Google Groups "FriCAS - computer algebra system" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/fricas-devel/2XuIRtc981E/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/fricas-devel. > For more options, visit https://groups.google.com/d/optout. > Thanks, Abhinav. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
