On 03/17/2012 04:11 PM, David Joyner wrote:
On Sat, Mar 17, 2012 at 3:55 PM, [email protected]
<[email protected]> wrote:
Is this necessary? All groups are isomorphic to the permutation group
anyway. Groups for specific structures can make use of functionality
implemented for them (matrix group -> sympy matrices, galois -> polys)
for basic operations and can implement the mapping to the perm group
module for group theoretic operations.
This seems incorrect. Zn is abelian for example and it is not
isomorphic to any permutation group. Moreover, there are all the
continuous groups.
It is not correct to say Zn (I assume you mean the ring of integers
mod n) is not isomorphic to a permutation group. (Consider the
cyclic group generated by the n-cycle (1,2,...,n) in disjoint
cycle notation.)
Implementing Lie groups would be a relatively difficult undertaking
I think...
Besides, it will be nicer to have some abstract object that is not
tied to a concrete representation, even though it will probably just
be a wrapper for all the representations supported by sympy.
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For Lie groups you might want to look at "Geometric Algebra for
Physicists" by Doran and Lasenby section 11.3 - Lie Groups and section
11.4 - Complex Structures and Unitary Groups.
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