matrix_algebra: add _entry_algebra_element_to_vector() method.

[sage.d.git] / mjo / hurwitz.py

diff --git a/mjo/hurwitz.py b/mjo/hurwitz.py
index 1f7c9dc3781a844d6d77a1e63168c52340bf6770..cad89ca177cbdcfbc065682d4a64af43aad6917a 100644 (file)
--- a/mjo/hurwitz.py
+++ b/mjo/hurwitz.py
@@ -319,6 +319,7 @@ class HurwitzMatrixAlgebraElement(MatrixAlgebraElement):
             sage: A = HurwitzMatrixAlgebra(2, QQbar, ZZ)
             sage: M = A([ [ I,   2*I],
             ....:         [ 3*I, 4*I] ])
+            sage: M.conjugate_transpose()
             +------+------+
             | -1*I | -3*I |
             +------+------+
@@ -626,6 +627,32 @@ class QuaternionMatrixAlgebra(HurwitzMatrixAlgebra):
             entry_algebra = QuaternionAlgebra(scalars,-1,-1)
         super().__init__(n, entry_algebra, scalars, **kwargs)
 
+    def _entry_algebra_element_to_vector(self, entry):
+        r"""
+
+        SETUP::
+
+            sage: from mjo.hurwitz import QuaternionMatrixAlgebra
+
+        EXAMPLES::
+
+            sage: A = QuaternionMatrixAlgebra(2)
+            sage: u = A.entry_algebra().one()
+            sage: A._entry_algebra_element_to_vector(u)
+            (1, 0, 0, 0)
+            sage: i,j,k = A.entry_algebra().gens()
+            sage: A._entry_algebra_element_to_vector(i)
+            (0, 1, 0, 0)
+            sage: A._entry_algebra_element_to_vector(j)
+            (0, 0, 1, 0)
+            sage: A._entry_algebra_element_to_vector(k)
+            (0, 0, 0, 1)
+
+        """
+        from sage.modules.free_module import VectorSpace
+        d = len(self.entry_algebra_gens())
+        V = VectorSpace(self.entry_algebra().base_ring(), d)
+        return V(entry.coefficient_tuple())
 
 class ComplexMatrixAlgebra(HurwitzMatrixAlgebra):
     r"""
@@ -706,3 +733,24 @@ class ComplexMatrixAlgebra(HurwitzMatrixAlgebra):
             from sage.rings.all import QQbar
             entry_algebra = QQbar
         super().__init__(n, entry_algebra, scalars, **kwargs)
+
+    def _entry_algebra_element_to_vector(self, entry):
+        r"""
+
+        SETUP::
+
+            sage: from mjo.hurwitz import ComplexMatrixAlgebra
+
+        EXAMPLES::
+
+            sage: A = ComplexMatrixAlgebra(2, QQbar, QQ)
+            sage: A._entry_algebra_element_to_vector(QQbar(1))
+            (1, 0)
+            sage: A._entry_algebra_element_to_vector(QQbar(I))
+            (0, 1)
+
+        """
+        from sage.modules.free_module import VectorSpace
+        d = len(self.entry_algebra_gens())
+        V = VectorSpace(self.entry_algebra().base_ring(), d)
+        return V((entry.real(), entry.imag()))