sage: idJ.inverse() == idJ
True
- The zero operator is never invertible::
+ The inverse of the inverse is the operator we started with::
sage: set_random_seed()
- sage: J = random_eja()
- sage: J.zero().operator().inverse()
- Traceback (most recent call last):
- ...
- ZeroDivisionError: input matrix must be nonsingular
+ sage: x = random_eja().random_element()
+ sage: L = x.operator()
+ sage: not L.is_invertible() or (L.inverse().inverse() == L)
+ True
"""
return ~self
SETUP::
- sage: from mjo.eja.eja_algebra import RealSymmetricEJA, random_eja
+ sage: from mjo.eja.eja_algebra import (RealSymmetricEJA,
+ ....: TrivialEJA,
+ ....: random_eja)
EXAMPLES::
sage: x.operator().is_invertible()
True
+ The zero operator is invertible in a trivial algebra::
+
+ sage: J = TrivialEJA()
+ sage: J.zero().operator().is_invertible()
+ True
+
TESTS:
The identity operator is always invertible::
sage: J.one().operator().is_invertible()
True
- The zero operator is never invertible::
+ The zero operator is never invertible in a nontrivial algebra::
sage: set_random_seed()
sage: J = random_eja()
- sage: J.zero().operator().is_invertible()
+ sage: not J.is_trivial() and J.zero().operator().is_invertible()
False
"""