On Apr 1, 11:08 pm, dstahlke <dstah...@gmail.com> wrote: > Given tables defining the addition and multiplication operations for a > finite ring, is there a way to construct such a Ring() in Sage? > > For example: > > add_tab = Matrix([ > [0, 1, 2, 3], > [1, 0, 3, 2], > [2, 3, 0, 1], > [3, 2, 1, 0], > ]) > > mul_tab = Matrix([ > [0, 0, 0, 0], > [0, 0, 0, 0], > [0, 0, 1, 1], > [0, 0, 1, 1], > ])
Not directly, I do not believe so. We have lots and lots of finite rings (and fields) and their tables. sage: M = MatrixSpace(Integers(6),1,1) sage: M.multiplication_table() * a b c d e f +------------ a| a a a a a a b| a b c d e f c| a c e a c e d| a d a d a d e| a e c a e c f| a f e d c b sage: M = MatrixSpace(Integers(2),2,2) sage: M.multiplication_table() * a b c d e f g h i j k l m n o p +-------------------------------- a| a a a a a a a a a a a a a a a a b| a b c a a f b b c c a f f b c f c| a a a b c a b c b c f b c f f f d| a d e a a k d d e e a k k d e k e| a a a d e a d e d e k d e k k k f| a b c b c f a f f a f c b c b a g| a g j a a p g g j j a p p g j p h| a b c d e f g h i j k l m n o p i| a d e b c k g i h j f n o l m p j| a a a g j a g j g j p g j p p p k| a d e d e k a k k a k e d e d a l| a g j b c p d l m e f o n i h k m| a b c g j f d m l e p i h o n k n| a g j d e p b n o c k m l h i f o| a d e g j k b o n c p h i m l f p| a g j g j p a p p a p j g j g a which is perhaps less helpful than it could be... sage: T = M.multiplication_table() sage: T.row_keys() ( [0 0] [1 0] [0 1] [0 0] [0 0] [1 1] [1 0] [1 0] [0 1] [0 1] [0 0], [0 0], [0 0], [1 0], [0 1], [0 0], [1 0], [0 1], [1 0], [0 1], [0 0] [1 1] [1 1] [1 0] [0 1] [1 1] [1 1], [1 0], [0 1], [1 1], [1 1], [1 1] ) There's something in the documentation about a list() method on T, but I don't see it. But anyway, I don't see a way to go backwards. -- 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
