natural_basis=natural_basis)
+ def _a_regular_element(self):
+ """
+ Override the superalgebra method to return the one
+ regular element that is sure to exist in this
+ subalgebra, namely the element that generated it.
+
+ SETUP::
+
+ sage: from mjo.eja.eja_algebra import random_eja
+
+ TESTS::
+
+ sage: set_random_seed()
+ sage: J = random_eja().random_element().subalgebra_generated_by()
+ sage: J._a_regular_element().is_regular()
+ True
+
+ """
+ if self.dimension() == 0:
+ return self.zero()
+ else:
+ return self.monomial(1)
+
+
def _element_constructor_(self, elt):
"""
Construct an element of this subalgebra from the given one.
return self.monomial(self.one_basis())
+ def natural_basis_space(self):
+ """
+ Return the natural basis space of this algebra, which is identical
+ to that of its superalgebra.
+
+ This is correct "by definition," and avoids a mismatch when the
+ subalgebra is trivial (with no natural basis to infer anything
+ from) and the parent is not.
+ """
+ return self.superalgebra().natural_basis_space()
+
+
def superalgebra(self):
"""
Return the superalgebra that this algebra was generated from.