Hi Joachim, To answer your question the following operations can be implemented:
A)Under the group theory module: 1) an algorithm to check if a set is a group(abelian also)... if True what is the Identity element,inverse of each element etc eg. >>> G.isgroup() >>> G.isabelian() 2) an algorithm to check if a subset of a group is a subgroup eg >>> A.issubgroup(G) if True then if A is a normal subgroup of G I can also implement a method to create left and right cosets of a subgroup. 3) If a ∈ G, what is the order of a... is 'a' a generator for G eg. >>> a.order(G) 4) if H and K are two subgroups the define HK... check if HK is a subgroup of G >>> HK.issubgroup(G) 5) if H is a subgroup of G then define the quotient group G/H as the set of all right cosets 6) Homomorphism: If G and H are two groups and if Φ is a mapping between them then is Φ a homomorphism... if True what is the Kernel of Φ 7) Is Φ a 1-1 map(isomorphic) I think some work on permutation groups has already been done... I could implement whatever is not there right now Also all the above operations can be implemented for a Ring B)Under vector spaces: 1) an algo to check if a set V is a vector space over a field F 2) if Φ is mapping between two vactor spaces then is it a homomorphism and 1-1 3) Find the basis of V and hence find dimension(V). Similarly finding dimension of a vector subspace 4) Then if B is a basis I can implement the Gram Shmidt process as Krestanov said to get an orthonormal basis for V These are few of the operations that I have though of right now... I am sure many more can be implemented which can be added to the above list. I am trying to figure out what all I can implement from field theory. Please let me know if u think of anything more Thnx, Gaurav On Mon, Mar 19, 2012 at 1:29 AM, Joachim Durchholz <j...@durchholz.org> wrote: > Am 18.03.2012 20:17, schrieb krastanov.ste...@gmail.com: > > I might be wrong, however the way I understand the question by Joachim >> is rather what useful functionality those objects would bring? >> > > That, and the examples that you mentioned, were what I was after. > > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to sympy@googlegroups.com. > To unsubscribe from this group, send email to sympy+unsubscribe@** > googlegroups.com <sympy%2bunsubscr...@googlegroups.com>. > For more options, visit this group at http://groups.google.com/** > group/sympy?hl=en <http://groups.google.com/group/sympy?hl=en>. > > -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.