X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element_subalgebra.py;h=608cbc2ed2004235b1f0a356d4a9f89119a2f6c0;hb=432ca4fcc5ff6fef69ebbfc166cec124c83c5fd1;hp=7cf3f3702adb5832a7ef4bb86a80b24431d87a54;hpb=008446f3a13b4fc117e1adfbc66f86784a6495c9;p=sage.d.git diff --git a/mjo/eja/eja_element_subalgebra.py b/mjo/eja/eja_element_subalgebra.py index 7cf3f37..608cbc2 100644 --- a/mjo/eja/eja_element_subalgebra.py +++ b/mjo/eja/eja_element_subalgebra.py @@ -49,19 +49,18 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide W = V.span_of_basis( V.from_vector(v) for v in basis_vectors ) + fdeja = super(FiniteDimensionalEuclideanJordanElementSubalgebra, self) + fdeja.__init__(self._superalgebra, + superalgebra_basis, + category=category) + # The rank is the highest possible degree of a minimal # polynomial, and is bounded above by the dimension. We know # in this case that there's an element whose minimal # polynomial has the same degree as the space's dimension # (remember how we constructed the space?), so that must be # its rank too. - rank = W.dimension() - - fdeja = super(FiniteDimensionalEuclideanJordanElementSubalgebra, self) - return fdeja.__init__(self._superalgebra, - superalgebra_basis, - rank=rank, - category=category) + self.rank.set_cache(W.dimension()) def _a_regular_element(self): @@ -88,40 +87,6 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide return self.monomial(1) - def _element_constructor_(self, elt): - """ - Construct an element of this subalgebra from the given one. - The only valid arguments are elements of the parent algebra - that happen to live in this subalgebra. - - SETUP:: - - sage: from mjo.eja.eja_algebra import RealSymmetricEJA - sage: from mjo.eja.eja_element_subalgebra import FiniteDimensionalEuclideanJordanElementSubalgebra - - EXAMPLES:: - - sage: J = RealSymmetricEJA(3) - sage: x = sum( i*J.gens()[i] for i in range(6) ) - sage: K = FiniteDimensionalEuclideanJordanElementSubalgebra(x,False) - sage: [ K(x^k) for k in range(J.rank()) ] - [f0, f1, f2] - - :: - - """ - if elt == 0: - # Just as in the superalgebra class, we need to hack - # this special case to ensure that random_element() can - # coerce a ring zero into the algebra. - return self.zero() - - if elt in self.superalgebra(): - coords = self.vector_space().coordinate_vector(elt.to_vector()) - return self.from_vector(coords) - - - def one(self): """ Return the multiplicative identity element of this algebra. @@ -134,12 +99,12 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide SETUP:: - sage: from mjo.eja.eja_algebra import (RealCartesianProductEJA, + sage: from mjo.eja.eja_algebra import (HadamardEJA, ....: random_eja) EXAMPLES:: - sage: J = RealCartesianProductEJA(5) + sage: J = HadamardEJA(5) sage: J.one() e0 + e1 + e2 + e3 + e4 sage: x = sum(J.gens()) @@ -154,7 +119,7 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide The identity element acts like the identity over the rationals:: sage: set_random_seed() - sage: x = random_eja().random_element() + sage: x = random_eja(field=QQ).random_element() sage: A = x.subalgebra_generated_by() sage: x = A.random_element() sage: A.one()*x == x and x*A.one() == x @@ -164,7 +129,7 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide reals with an orthonormal basis:: sage: set_random_seed() - sage: x = random_eja(AA).random_element() + sage: x = random_eja().random_element() sage: A = x.subalgebra_generated_by(orthonormalize_basis=True) sage: x = A.random_element() sage: A.one()*x == x and x*A.one() == x @@ -174,7 +139,7 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide the rationals:: sage: set_random_seed() - sage: x = random_eja().random_element() + sage: x = random_eja(field=QQ).random_element() sage: A = x.subalgebra_generated_by() sage: actual = A.one().operator().matrix() sage: expected = matrix.identity(A.base_ring(), A.dimension()) @@ -185,7 +150,7 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide the algebraic reals with an orthonormal basis:: sage: set_random_seed() - sage: x = random_eja(AA).random_element() + sage: x = random_eja().random_element() sage: A = x.subalgebra_generated_by(orthonormalize_basis=True) sage: actual = A.one().operator().matrix() sage: expected = matrix.identity(A.base_ring(), A.dimension()) @@ -197,54 +162,10 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide return self.zero() else: sa_one = self.superalgebra().one().to_vector() - sa_coords = self.vector_space().coordinate_vector(sa_one) - return self.from_vector(sa_coords) - - - 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. - """ - return self._superalgebra - - - def vector_space(self): - """ - SETUP:: - - sage: from mjo.eja.eja_algebra import RealSymmetricEJA - sage: from mjo.eja.eja_element_subalgebra import FiniteDimensionalEuclideanJordanElementSubalgebra - - EXAMPLES:: - - sage: J = RealSymmetricEJA(3) - sage: x = J.monomial(0) + 2*J.monomial(2) + 5*J.monomial(5) - sage: K = FiniteDimensionalEuclideanJordanElementSubalgebra(x,False) - sage: K.vector_space() - Vector space of degree 6 and dimension 3 over... - User basis matrix: - [ 1 0 1 0 0 1] - [ 1 0 2 0 0 5] - [ 1 0 4 0 0 25] - sage: (x^0).to_vector() - (1, 0, 1, 0, 0, 1) - sage: (x^1).to_vector() - (1, 0, 2, 0, 0, 5) - sage: (x^2).to_vector() - (1, 0, 4, 0, 0, 25) - - """ - return self._vector_space + # The extra hackery is because foo.to_vector() might not + # live in foo.parent().vector_space()! + coords = sum( a*b for (a,b) + in zip(sa_one, + self.superalgebra().vector_space().basis()) ) + return self.from_vector(self.vector_space().coordinate_vector(coords))