On Tue, Mar 20, 2012 at 2:18 AM, Gaurav Sathe <gaurav.sath...@gmail.com> wrote: > 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()
Wouldn't this require knowing the operation as well? > >>> 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 ??? There are subgroups which are not normal. > > 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 I guess you mean group of all right cosets, but then the question is how do you define the multiplication table? For example, do you return the quotient group as another permutation group (isomorphic to the group of 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 ... > > 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+unsubscr...@googlegroups.com. >> For more options, visit this group at >> 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. -- 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.
