Size of my matrix is (90, 36) with entries are around 2^1000. What is the fastest method to compute Hermite Normal Form?
In my matrix number of rows greater than number of columns. That is A= random_matrix(ZZ, 90, 36). Then how can I calculate transformation matrix of LLL? On 28 December 2010 22:32, luisfe <lftab...@yahoo.es> wrote: > On Dec 28, 5:27 pm, Santanu Sarkar <sarkar.santanu....@gmail.com> > wrote: > > Is there any faster method to compute Hermite Normal Form > > of a matrix A and corresponding transformation matrix? I use > > A.hermite_form(transformation=true). However it is very slow. > > > > Also is there any transformation matrix corresponding to the LLL > algorithm. > > What are the size/shape of your problem? If you just want the > hermite_form you can use A.hermite_form(algorithm = ...), where the > algorithms available can be checked in A.echelon_form. > > If you need transformation = true. Then the method will always be a > padic one, that is asymptotically fast, but may be slow for small > matrices. > > Concerning the question of LLL. I may be wrong, but I think that there > is not right now a built-in method to obtain the transformation > matrix. You could solve the linear system of equations > > sage: A = random_matrix(ZZ, 25, 50) > sage: B = A.LLL() > sage: trans_matrix = A \ B > sage: A * trans_matrix == B > True > > -- > To post to this group, send email to sage-support@googlegroups.com > To unsubscribe from this group, send email to > sage-support+unsubscr...@googlegroups.com<sage-support%2bunsubscr...@googlegroups.com> > For more options, visit this group at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org > -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
