Examples of magmas¶
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sage.categories.examples.magmas.Example¶
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class
sage.categories.examples.magmas.FreeMagma(alphabet='a', 'b', 'c', 'd')¶ Bases:
sage.structure.unique_representation.UniqueRepresentation,sage.structure.parent.ParentAn 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')
This is the free magma generated by:
sage: M.magma_generators() Family ('a', 'b', 'c', 'd') sage: 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
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class
Element¶ Bases:
sage.structure.element_wrapper.ElementWrapperThe class for elements of the free magma.
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wrapped_class¶ alias of
builtins.str
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an_element()¶ Return an element of the magma.
EXAMPLES:
sage: F = Magmas().example() sage: F.an_element() '(((a*b)*c)*d)'
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magma_generators()¶ Return the generators of the magma.
EXAMPLES:
sage: F = Magmas().example() sage: F.magma_generators() Family ('a', 'b', 'c', 'd')
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product(x, y)¶ Return the product of
xandyin the magma, as perMagmas.ParentMethods.product().EXAMPLES:
sage: F = Magmas().example() sage: F('a') * F.an_element() '(a*(((a*b)*c)*d))'
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class