def __init__(self, R, n, r):
"""
Initialize ``self``.
TESTS::
sage: S = SchurAlgebra(ZZ, 2, 2)
sage: TestSuite(S).run()
::
sage: SchurAlgebra(ZZ, -2, 2)
Traceback (most recent call last):
...
ValueError: n (=-2) must be a positive integer
sage: SchurAlgebra(ZZ, 2, -2)
Traceback (most recent call last):
...
ValueError: r (=-2) must be a non-negative integer
sage: SchurAlgebra('niet', 2, 2)
Traceback (most recent call last):
...
ValueError: R (=niet) must be a commutative ring
"""
if n not in ZZ or n <= 0:
raise ValueError("n (={}) must be a positive integer".format(n))
if r not in ZZ or r < 0:
raise ValueError(
"r (={}) must be a non-negative integer".format(r))
if not R in Rings.Commutative():
raise ValueError("R (={}) must be a commutative ring".format(R))
self._n = n
self._r = r
CombinatorialFreeModule.__init__(
self,
R,
schur_representative_indices(n, r),
prefix='S',
bracket=False,
category=AlgebrasWithBasis(R).FiniteDimensional())
