X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_subalgebra.py;h=1286a167f4c5ede4fa45252a545fd848f3014ab9;hb=928b7d49fda98ff105c92293b5797bb7a2b9873a;hp=92fd296b3003a06e7bafb79f9d9c37d9cb6b13cb;hpb=d395668ab9c439d2ee5ec6224d2061656da5ae04;p=sage.d.git diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py index 92fd296..1286a16 100644 --- a/mjo/eja/eja_subalgebra.py +++ b/mjo/eja/eja_subalgebra.py @@ -1,4 +1,5 @@ from sage.matrix.constructor import matrix +from sage.misc.cachefunc import cached_method from mjo.eja.eja_algebra import FiniteDimensionalEJA from mjo.eja.eja_element import FiniteDimensionalEJAElement @@ -14,7 +15,6 @@ class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement): The matrix representation of an element in the subalgebra is the same as its matrix representation in the superalgebra:: - sage: set_random_seed() sage: x = random_eja(field=QQ,orthonormalize=False).random_element() sage: A = x.subalgebra_generated_by(orthonormalize=False) sage: y = A.random_element() @@ -27,7 +27,6 @@ class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement): works like it does in the superalgebra, even if we orthonormalize our basis:: - sage: set_random_seed() sage: x = random_eja(field=AA).random_element() sage: A = x.subalgebra_generated_by(orthonormalize=True) sage: y = A.random_element() @@ -51,26 +50,25 @@ class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement): 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: We can convert back and forth faithfully:: - sage: set_random_seed() sage: J = random_eja(field=QQ, orthonormalize=False) sage: x = J.random_element() sage: A = x.subalgebra_generated_by(orthonormalize=False) @@ -84,7 +82,7 @@ class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement): True """ - return self.parent().superalgebra()(self.to_matrix()) + return self.parent().superalgebra_embedding()(self) @@ -121,17 +119,18 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA): 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:: @@ -139,7 +138,6 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA): sage: B = A.one().subalgebra_generated_by() sage: B.dimension() 1 - """ def __init__(self, superalgebra, basis, **kwargs): self._superalgebra = superalgebra @@ -152,7 +150,7 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA): # 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: @@ -171,6 +169,7 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA): jordan_product, inner_product, field=field, + matrix_space=superalgebra.matrix_space(), prefix=prefix, **kwargs) @@ -200,32 +199,29 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA): ....: associative=True, ....: orthonormalize=False) sage: K(J.one()) - f1 + c1 sage: K(J.one() + x) - f0 + f1 + c0 + c1 :: """ if elt in self.superalgebra(): - return super()._element_constructor_(elt.to_matrix()) + # If the subalgebra is trivial, its _matrix_span will be empty + # but we still want to be able convert the superalgebra's zero() + # element into the subalgebra's zero() element. There's no great + # workaround for this because sage checks that your basis is + # linearly-independent everywhere, so we can't just give it a + # basis consisting of the zero element. + m = elt.to_matrix() + if self.is_trivial() and m.is_zero(): + return self.zero() + else: + return super()._element_constructor_(m) else: return super()._element_constructor_(elt) - - def matrix_space(self): - """ - Return the matrix 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 matrix basis elements to - infer anything from) and the parent is not. - """ - return self.superalgebra().matrix_space() - - def superalgebra(self): """ Return the superalgebra that this algebra was generated from. @@ -233,4 +229,39 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA): return self._superalgebra + @cached_method + def superalgebra_embedding(self): + r""" + Return the embedding from this subalgebra into the superalgebra. + + SETUP:: + + sage: from mjo.eja.eja_algebra import HadamardEJA + + EXAMPLES:: + + sage: J = HadamardEJA(4) + sage: A = J.one().subalgebra_generated_by() + sage: iota = A.superalgebra_embedding() + sage: iota + Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: + [1/2] + [1/2] + [1/2] + [1/2] + Domain: Euclidean Jordan algebra of dimension 1 over Algebraic Real Field + Codomain: Euclidean Jordan algebra of dimension 4 over Algebraic Real Field + sage: iota(A.one()) == J.one() + True + + """ + from mjo.eja.eja_operator import FiniteDimensionalEJAOperator + mm = self._module_morphism(lambda j: self.superalgebra()(self.monomial(j).to_matrix()), + codomain=self.superalgebra()) + return FiniteDimensionalEJAOperator(self, + self.superalgebra(), + mm.matrix()) + + + Element = FiniteDimensionalEJASubalgebraElement