sage: J = RealSymmetricEJA(3)
sage: x = sum(J.gens())
sage: x
- e0 + e1 + e2 + e3 + e4 + e5
+ b0 + b1 + b2 + b3 + b4 + b5
sage: A = x.subalgebra_generated_by(orthonormalize=False)
sage: A(x)
- f1
+ c1
sage: A(x).superalgebra_element()
- e0 + e1 + e2 + e3 + e4 + e5
+ b0 + b1 + b2 + b3 + b4 + b5
sage: y = sum(A.gens())
sage: y
- f0 + f1
+ c0 + c1
sage: B = y.subalgebra_generated_by(orthonormalize=False)
sage: B(y)
- g1
+ d1
sage: B(y).superalgebra_element()
- f0 + f1
+ c0 + c1
TESTS:
TESTS:
- Ensure that our generator names don't conflict with the superalgebra::
+ Ensure that our generator names don't conflict with the
+ superalgebra::
sage: J = JordanSpinEJA(3)
sage: J.one().subalgebra_generated_by().gens()
- (f0,)
+ (c0,)
sage: J = JordanSpinEJA(3, prefix='f')
sage: J.one().subalgebra_generated_by().gens()
(g0,)
- sage: J = JordanSpinEJA(3, prefix='b')
+ sage: J = JordanSpinEJA(3, prefix='a')
sage: J.one().subalgebra_generated_by().gens()
- (c0,)
+ (b0,)
Ensure that we can find subalgebras of subalgebras::
sage: B = A.one().subalgebra_generated_by()
sage: B.dimension()
1
-
"""
def __init__(self, superalgebra, basis, **kwargs):
self._superalgebra = superalgebra
# try to "increment" the parent algebra's prefix, although
# this idea goes out the window fast because some prefixen
# are off-limits.
- prefixen = [ 'f', 'g', 'h', 'a', 'b', 'c', 'd' ]
+ prefixen = ["b","c","d","e","f","g","h","l","m"]
try:
prefix = prefixen[prefixen.index(self._superalgebra.prefix()) + 1]
except ValueError:
....: associative=True,
....: orthonormalize=False)
sage: K(J.one())
- f1
+ c1
sage: K(J.one() + x)
- f0 + f1
+ c0 + c1
::