BUILT-IN WOLFRAM LANGUAGE SYMBOL
returns the element of group determined by the word w in the generators of group.
- In GroupElementFromWord[group,w], the word w must be a list of nonzero integers representing generators in the list returned by GroupGenerators[group]. A positive integer in the word represents the generator, and a negative integer represents the inverse of the generator.
For a given list of group generators, this word represents the product of the first generator with itself and then with inverse of the second generator:
For the dihedral group of order 16, the word corresponds to the element:
The same result can be obtained by multiplying the generators explicitly: