GroupTheory`
GroupTheory`
GTGroupQ
Details and Options
- A set
of elements 
is called group if the four group axioms are satisfied: - a) Closure: There exists an operation called multiplication which associates with every pair of elements
and 
of 
to another Element 
of 
. - b) Associativity: For any three elements
, 
and 
of 
the "associative law" is valid. - c) Identity element: There exists an Element
which is contained in 
such that for every element 
. - d) Inverse element: For each element
there exists an inverse Element 
which is also contained in 
such that: 
. - The input can be of type symbol, matrix, quaternion or Euler angles (compare GTEulerAnglesQ, GTQuaternionQ and GTSymbolQ).
-
GOMethod "Numeric" Specifies the method to determine if a given list of elements is a group. - See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 3.1.
Examples
open allclose allOptions (1)
GOMethod (1)
GTGroupQ calculates the multiplication table of a list of elements and determines if the resulting elements are members of the initial list. This evaluation can in general be performed numerically. For small groups the time difference between numerical and analytical evaluation is negligible. However, the difference becomes more prominent for large groups or highly dimensional group representations.
For double groups typical square root expressions slow down an analytic evaluation.
