From 37ab2f97b6f8b64360045a1db4c74b6c38651317 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Mon, 8 Mar 2021 21:43:34 -0500 Subject: [PATCH] hurwitz: make entry algebras "configurable." --- mjo/hurwitz.py | 114 ++++++++++++++++++++++++++++++------------ mjo/matrix_algebra.py | 20 ++++---- 2 files changed, 93 insertions(+), 41 deletions(-) diff --git a/mjo/hurwitz.py b/mjo/hurwitz.py index 75e8568..a1a6af0 100644 --- a/mjo/hurwitz.py +++ b/mjo/hurwitz.py @@ -315,7 +315,7 @@ class HurwitzMatrixAlgebraElement(MatrixAlgebraElement): EXAMPLES:: - sage: A = HurwitzMatrixAlgebra(QQbar, ZZ, 2) + sage: A = HurwitzMatrixAlgebra(2, QQbar, ZZ) sage: M = A([ [ 0,I], ....: [-I,0] ]) sage: M.is_hermitian() @@ -344,13 +344,13 @@ class HurwitzMatrixAlgebra(MatrixAlgebra): """ Element = HurwitzMatrixAlgebraElement - def __init__(self, entry_algebra, scalars, n, **kwargs): + def __init__(self, n, entry_algebra, scalars, **kwargs): from sage.rings.all import RR if not scalars.is_subring(RR): # Not perfect, but it's what we're using. raise ValueError("scalar field is not real") - super().__init__(entry_algebra, scalars, n, **kwargs) + super().__init__(n, entry_algebra, scalars, **kwargs) def entry_algebra_gens(self): r""" @@ -382,15 +382,15 @@ class HurwitzMatrixAlgebra(MatrixAlgebra): sets of generators have cartinality 1,2,4, and 8 as you'd expect:: - sage: HurwitzMatrixAlgebra(AA, AA, 2).entry_algebra_gens() + sage: HurwitzMatrixAlgebra(2, AA, AA).entry_algebra_gens() (1,) - sage: HurwitzMatrixAlgebra(QQbar, AA, 2).entry_algebra_gens() + sage: HurwitzMatrixAlgebra(2, QQbar, AA).entry_algebra_gens() (1, I) sage: Q = QuaternionAlgebra(AA,-1,-1) - sage: HurwitzMatrixAlgebra(Q, AA, 2).entry_algebra_gens() + sage: HurwitzMatrixAlgebra(2, Q, AA).entry_algebra_gens() (1, i, j, k) sage: O = Octonions() - sage: HurwitzMatrixAlgebra(O, AA, 2).entry_algebra_gens() + sage: HurwitzMatrixAlgebra(2, O, AA).entry_algebra_gens() (e0, e1, e2, e3, e4, e5, e6, e7) """ @@ -414,16 +414,32 @@ class OctonionMatrixAlgebra(HurwitzMatrixAlgebra): SETUP:: - sage: from mjo.hurwitz import OctonionMatrixAlgebra + sage: from mjo.hurwitz import Octonions, OctonionMatrixAlgebra EXAMPLES:: sage: OctonionMatrixAlgebra(3) Module of 3 by 3 matrices with entries in Octonion algebra with base ring Algebraic Real Field over the scalar ring Algebraic Real Field - sage: OctonionMatrixAlgebra(3,QQ) - Module of 3 by 3 matrices with entries in Octonion algebra with base - ring Rational Field over the scalar ring Rational Field + + :: + + sage: OctonionMatrixAlgebra(3,scalars=QQ) + Module of 3 by 3 matrices with entries in Octonion algebra with + base ring Rational Field over the scalar ring Rational Field + + :: + + sage: O = Octonions(RR) + sage: A = OctonionMatrixAlgebra(1,O) + sage: A + Module of 1 by 1 matrices with entries in Octonion algebra with + base ring Real Field with 53 bits of precision over the scalar + ring Algebraic Real Field + sage: A.one() + +---------------------+ + | 1.00000000000000*e0 | + +---------------------+ :: @@ -439,8 +455,8 @@ class OctonionMatrixAlgebra(HurwitzMatrixAlgebra): :: - sage: A1 = OctonionMatrixAlgebra(1,QQ) - sage: A2 = OctonionMatrixAlgebra(1,QQ) + sage: A1 = OctonionMatrixAlgebra(1,scalars=QQ) + sage: A2 = OctonionMatrixAlgebra(1,scalars=QQ) sage: cartesian_product([A1,A2]) Module of 1 by 1 matrices with entries in Octonion algebra with base ring Rational Field over the scalar ring Rational Field (+) @@ -456,11 +472,12 @@ class OctonionMatrixAlgebra(HurwitzMatrixAlgebra): True """ - def __init__(self, n, scalars=AA, prefix="E", **kwargs): - super().__init__(Octonions(field=scalars), + def __init__(self, n, entry_algebra=None, scalars=AA, **kwargs): + if entry_algebra is None: + entry_algebra = Octonions(field=scalars) + super().__init__(n, + entry_algebra, scalars, - n, - prefix=prefix, **kwargs) class QuaternionMatrixAlgebra(HurwitzMatrixAlgebra): @@ -482,11 +499,27 @@ class QuaternionMatrixAlgebra(HurwitzMatrixAlgebra): Module of 3 by 3 matrices with entries in Quaternion Algebra (-1, -1) with base ring Algebraic Real Field over the scalar ring Algebraic Real Field - sage: QuaternionMatrixAlgebra(3,QQ) + + :: + + sage: QuaternionMatrixAlgebra(3,scalars=QQ) Module of 3 by 3 matrices with entries in Quaternion Algebra (-1, -1) with base ring Rational Field over the scalar ring Rational Field + :: + + sage: Q = QuaternionAlgebra(RDF, -1, -1) + sage: A = QuaternionMatrixAlgebra(1,Q) + sage: A + Module of 1 by 1 matrices with entries in Quaternion Algebra + (-1.0, -1.0) with base ring Real Double Field over the scalar + ring Algebraic Real Field + sage: A.one() + +-----+ + | 1.0 | + +-----+ + :: sage: A = QuaternionMatrixAlgebra(2) @@ -501,8 +534,8 @@ class QuaternionMatrixAlgebra(HurwitzMatrixAlgebra): :: - sage: A1 = QuaternionMatrixAlgebra(1,QQ) - sage: A2 = QuaternionMatrixAlgebra(2,QQ) + sage: A1 = QuaternionMatrixAlgebra(1,scalars=QQ) + sage: A2 = QuaternionMatrixAlgebra(2,scalars=QQ) sage: cartesian_product([A1,A2]) Module of 1 by 1 matrices with entries in Quaternion Algebra (-1, -1) with base ring Rational Field over the scalar ring @@ -519,11 +552,14 @@ class QuaternionMatrixAlgebra(HurwitzMatrixAlgebra): True """ - def __init__(self, n, scalars=AA, **kwargs): - # The -1,-1 gives us the "usual" definition of quaternion - from sage.algebras.quatalg.quaternion_algebra import QuaternionAlgebra - Q = QuaternionAlgebra(scalars,-1,-1) - super().__init__(Q, scalars, n, **kwargs) + def __init__(self, n, entry_algebra=None, scalars=AA, **kwargs): + if entry_algebra is None: + # The -1,-1 gives us the "usual" definition of quaternion + from sage.algebras.quatalg.quaternion_algebra import ( + QuaternionAlgebra + ) + entry_algebra = QuaternionAlgebra(scalars,-1,-1) + super().__init__(n, entry_algebra, scalars, **kwargs) class ComplexMatrixAlgebra(HurwitzMatrixAlgebra): @@ -545,10 +581,24 @@ class ComplexMatrixAlgebra(HurwitzMatrixAlgebra): sage: ComplexMatrixAlgebra(3) Module of 3 by 3 matrices with entries in Algebraic Field over the scalar ring Algebraic Real Field - sage: ComplexMatrixAlgebra(3,QQ) + + :: + + sage: ComplexMatrixAlgebra(3,scalars=QQ) Module of 3 by 3 matrices with entries in Algebraic Field over the scalar ring Rational Field + :: + + sage: A = ComplexMatrixAlgebra(1,CC) + sage: A + Module of 1 by 1 matrices with entries in Complex Field with + 53 bits of precision over the scalar ring Algebraic Real Field + sage: A.one() + +------------------+ + | 1.00000000000000 | + +------------------+ + :: sage: A = ComplexMatrixAlgebra(2) @@ -563,8 +613,8 @@ class ComplexMatrixAlgebra(HurwitzMatrixAlgebra): :: - sage: A1 = ComplexMatrixAlgebra(1,QQ) - sage: A2 = ComplexMatrixAlgebra(2,QQ) + sage: A1 = ComplexMatrixAlgebra(1,scalars=QQ) + sage: A2 = ComplexMatrixAlgebra(2,scalars=QQ) sage: cartesian_product([A1,A2]) Module of 1 by 1 matrices with entries in Algebraic Field over the scalar ring Rational Field (+) Module of 2 by 2 matrices with @@ -579,6 +629,8 @@ class ComplexMatrixAlgebra(HurwitzMatrixAlgebra): True """ - def __init__(self, n, scalars=AA, **kwargs): - from sage.rings.all import QQbar - super().__init__(QQbar, scalars, n, **kwargs) + def __init__(self, n, entry_algebra=None, scalars=AA, **kwargs): + if entry_algebra is None: + from sage.rings.all import QQbar + entry_algebra = QQbar + super().__init__(n, entry_algebra, scalars, **kwargs) diff --git a/mjo/matrix_algebra.py b/mjo/matrix_algebra.py index 94a8410..c38e855 100644 --- a/mjo/matrix_algebra.py +++ b/mjo/matrix_algebra.py @@ -18,7 +18,7 @@ class MatrixAlgebraElement(IndexedFreeModuleElement): EXAMPLES:: - sage: M = MatrixAlgebra(QQbar,RDF,2) + sage: M = MatrixAlgebra(2, QQbar,RDF) sage: A = M.monomial((0,0,1)) + 4*M.monomial((0,1,1)) sage: A +-----+-----+ @@ -50,7 +50,7 @@ class MatrixAlgebraElement(IndexedFreeModuleElement): EXAMPLES:: - sage: MatrixAlgebra(ZZ,ZZ,2).zero() + sage: MatrixAlgebra(2,ZZ,ZZ).zero() +---+---+ | 0 | 0 | +---+---+ @@ -71,7 +71,7 @@ class MatrixAlgebraElement(IndexedFreeModuleElement): EXAMPLES:: - sage: A = MatrixAlgebra(ZZ,ZZ,2) + sage: A = MatrixAlgebra(2,ZZ,ZZ) sage: A([[1,2],[3,4]]).list() [1, 2, 3, 4] @@ -88,7 +88,7 @@ class MatrixAlgebraElement(IndexedFreeModuleElement): EXAMPLES:: - sage: M = MatrixAlgebra(ZZ,ZZ,2)([[1,2],[3,4]]) + sage: M = MatrixAlgebra(2,ZZ,ZZ)([[1,2],[3,4]]) sage: M[0,0] 1 sage: M[0,1] @@ -117,7 +117,7 @@ class MatrixAlgebraElement(IndexedFreeModuleElement): sage: entries = MatrixSpace(ZZ,2) sage: scalars = ZZ - sage: M = MatrixAlgebra(entries, scalars, 2) + sage: M = MatrixAlgebra(2, entries, scalars) sage: I = entries.one() sage: Z = entries.zero() sage: M([[I,Z],[Z,I]]).trace() @@ -139,7 +139,7 @@ class MatrixAlgebraElement(IndexedFreeModuleElement): sage: set_random_seed() sage: entries = QuaternionAlgebra(QQ,-1,-1) - sage: M = MatrixAlgebra(entries, QQ, 3) + sage: M = MatrixAlgebra(3, entries, QQ) sage: M.random_element().matrix_space() == M True @@ -167,7 +167,7 @@ class MatrixAlgebra(CombinatorialFreeModule): The existence of a unit element is determined dynamically:: - sage: MatrixAlgebra(ZZ,ZZ,2).one() + sage: MatrixAlgebra(2,ZZ,ZZ).one() +---+---+ | 1 | 0 | +---+---+ @@ -177,7 +177,7 @@ class MatrixAlgebra(CombinatorialFreeModule): """ Element = MatrixAlgebraElement - def __init__(self, entry_algebra, scalars, n, prefix="A", **kwargs): + def __init__(self, n, entry_algebra, scalars, prefix="A", **kwargs): category = MagmaticAlgebras(scalars).FiniteDimensional() category = category.WithBasis() @@ -245,7 +245,7 @@ class MatrixAlgebra(CombinatorialFreeModule): sage: e = O.gens() sage: e[2]*e[1] -e3 - sage: A = MatrixAlgebra(O,QQ,2) + sage: A = MatrixAlgebra(2,O,QQ) sage: A.product_on_basis( (0,0,e[2]), (0,0,e[1]) ) +-----+---+ | -e3 | 0 | @@ -278,7 +278,7 @@ class MatrixAlgebra(CombinatorialFreeModule): EXAMPLES:: - sage: A = MatrixAlgebra(QQbar, ZZ, 2) + sage: A = MatrixAlgebra(2, QQbar, ZZ) sage: A.from_list([[0,I],[-I,0]]) +----+---+ | 0 | I | -- 2.43.2