Examples of magmas¶
- class sage.categories.examples.magmas.FreeMagma(alphabet=('a', 'b', 'c', 'd'))[source]¶
- Bases: - UniqueRepresentation,- Parent- An example of magma. - The purpose of this class is to provide a minimal template for implementing a magma. - EXAMPLES: - sage: M = Magmas().example(); M An example of a magma: the free magma generated by ('a', 'b', 'c', 'd') - >>> from sage.all import * >>> M = Magmas().example(); M An example of a magma: the free magma generated by ('a', 'b', 'c', 'd') - This is the free magma generated by: - sage: M.magma_generators() Family ('a', 'b', 'c', 'd') sage: a, b, c, d = M.magma_generators() - >>> from sage.all import * >>> M.magma_generators() Family ('a', 'b', 'c', 'd') >>> a, b, c, d = M.magma_generators() - and with a non-associative product given by: - sage: a * (b * c) * (d * a * b) '((a*(b*c))*((d*a)*b))' sage: a * (b * c) == (a * b) * c False - >>> from sage.all import * >>> a * (b * c) * (d * a * b) '((a*(b*c))*((d*a)*b))' >>> a * (b * c) == (a * b) * c False - class Element[source]¶
- Bases: - ElementWrapper- The class for elements of the free magma. - wrapped_class¶
- alias of - str
 
 - an_element()[source]¶
- Return an element of the magma. - EXAMPLES: - sage: F = Magmas().example() sage: F.an_element() '(((a*b)*c)*d)' - >>> from sage.all import * >>> F = Magmas().example() >>> F.an_element() '(((a*b)*c)*d)' 
 - magma_generators()[source]¶
- Return the generators of the magma. - EXAMPLES: - sage: F = Magmas().example() sage: F.magma_generators() Family ('a', 'b', 'c', 'd') - >>> from sage.all import * >>> F = Magmas().example() >>> F.magma_generators() Family ('a', 'b', 'c', 'd') 
 - product(x, y)[source]¶
- Return the product of - xand- yin the magma, as per- Magmas.ParentMethods.product().- EXAMPLES: - sage: F = Magmas().example() sage: F('a') * F.an_element() '(a*(((a*b)*c)*d))' - >>> from sage.all import * >>> F = Magmas().example() >>> F('a') * F.an_element() '(a*(((a*b)*c)*d))'