Hello there, I could need some help on how to store matrices over the universal cyclotomic field (UCF). Every element is stored as a linear combination of elements in the Zumbroich basis [1], which is similar to the standard basis for the cyclotomic field, but which makes it easy to convert elements from one cyclotomic field to another. For the cyclotomic field of a given order and degree, storing a matrix is done in matrix_cyclo_dense as follows:
" given an n x m matrix over a cyclotomic field of degree d, we store a d x (nm) matrix over QQ, each column of which corresponds to an element of the original matrix. This can be retrieved via the _rational_matrix method " The problem is that, even though every element in the UCF has a fixed degree, the elements in the matrix might all have different degrees; moreover I cannot predict the degree, especially not when adding or multiplying such matrices. Is there a fast way to store the data as a 2-dim array with entries being dictionaries with keys being basis elements in the Zumbroich basis, and with rational values? Any other suggestions? Thanks for your help, Christian [1] "Integral bases for subfields of cyclotomic fields" by Thomas Breuer ( AAECC 8, 279--289 (1997) ) -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
