X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_subalgebra.py;h=c9abada53cf3fbd3803601fa0e7b430a0b506fd1;hb=02bb28968221a0f077b49205e2746abd8c5450d9;hp=1b86d236c390691939fd84cabb597e6b6159d406;hpb=f98ab4d7afa92a853e7ddc75cdac803d2da4fcb9;p=sage.d.git diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py index 1b86d23..c9abada 100644 --- a/mjo/eja/eja_subalgebra.py +++ b/mjo/eja/eja_subalgebra.py @@ -1,7 +1,9 @@ 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 +from mjo.eja.eja_element import (FiniteDimensionalEJAElement, + CartesianProductParentEJAElement) class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement): """ @@ -14,7 +16,6 @@ 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() @@ -27,11 +28,10 @@ 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() - sage: y.operator()(A.one()) == y + sage: x = random_eja(field=AA).random_element() # long time + sage: A = x.subalgebra_generated_by(orthonormalize=True) # long time + sage: y = A.random_element() # long time + sage: y.operator()(A.one()) == y # long time True """ @@ -70,7 +70,6 @@ class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement): 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 +83,7 @@ class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement): True """ - return self.parent().superalgebra()(self.to_matrix()) + return self.parent().superalgebra_embedding()(self) @@ -171,6 +170,7 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA): jordan_product, inner_product, field=field, + matrix_space=superalgebra.matrix_space(), prefix=prefix, **kwargs) @@ -208,24 +208,21 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA): """ 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 +230,77 @@ 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 + + + +class FiniteDimensionalCartesianProductEJASubalgebraElement(FiniteDimensionalEJASubalgebraElement, CartesianProductParentEJAElement): + r""" + The class for elements that both belong to a subalgebra and + have a Cartesian product algebra as their parent. By inheriting + :class:`CartesianProductParentEJAElement` in addition to + :class:`FiniteDimensionalEJASubalgebraElement`, we allow the + ``to_matrix()`` method to be overridden with the version that + works on Cartesian products. + + SETUP:: + + sage: from mjo.eja.eja_algebra import (HadamardEJA, + ....: RealSymmetricEJA) + + TESTS: + + This used to fail when ``subalgebra_idempotent()`` tried to + embed the subalgebra element back into the original EJA:: + + sage: J1 = HadamardEJA(0, field=QQ, orthonormalize=False) + sage: J2 = RealSymmetricEJA(2, field=QQ, orthonormalize=False) + sage: J = cartesian_product([J1,J2]) + sage: J.one().subalgebra_idempotent() == J.one() + True + + """ + pass + +class FiniteDimensionalCartesianProductEJASubalgebra(FiniteDimensionalEJASubalgebra): + r""" + Subalgebras whose parents are Cartesian products. Exists only + to specify a special element class that will (in addition) + inherit from ``CartesianProductParentEJAElement``. + """ + Element = FiniteDimensionalCartesianProductEJASubalgebraElement