hurwitz: make entry algebras "configurable."

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

diff --git a/mjo/matrix_algebra.py b/mjo/matrix_algebra.py
index 5b8b267f5120a4a319f77777885b19731437f518..c38e8556203243536fc0af87078840f82e2d57cb 100644 (file)
--- 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
             +-----+-----+
@@ -37,7 +37,7 @@ class MatrixAlgebraElement(IndexedFreeModuleElement):
             l[i][j] += v*e
         return l
 
-    def __repr__(self):
+    def _repr_(self):
         r"""
         Display this matrix as a table.
 
@@ -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()
@@ -232,10 +232,38 @@ class MatrixAlgebra(CombinatorialFreeModule):
     ncols = nrows
 
     def product_on_basis(self, mon1, mon2):
+        r"""
+
+        SETUP::
+
+            sage: from mjo.hurwitz import Octonions
+            sage: from mjo.matrix_algebra import MatrixAlgebra
+
+        TESTS::
+
+            sage: O = Octonions(QQ)
+            sage: e = O.gens()
+            sage: e[2]*e[1]
+            -e3
+            sage: A = MatrixAlgebra(2,O,QQ)
+            sage: A.product_on_basis( (0,0,e[2]), (0,0,e[1]) )
+            +-----+---+
+            | -e3 | 0 |
+            +-----+---+
+            | 0   | 0 |
+            +-----+---+
+
+        """
         (i,j,e1) = mon1
         (k,l,e2) = mon2
         if j == k:
-            return self.monomial((i,l,e1*e2))
+            # If e1*e2 has a negative sign in front of it,
+            # then (i,l,e1*e2) won't be a monomial!
+            p = e1*e2
+            if (i,l,p) in self.indices():
+                return self.monomial((i,l,p))
+            else:
+                return -self.monomial((i,l,-p))
         else:
             return self.zero()
 
@@ -250,7 +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 |
@@ -294,29 +322,3 @@ class MatrixAlgebra(CombinatorialFreeModule):
             return self
         else:
             return self.from_list(elt)
-
-
-class HurwitzMatrixAlgebraElement(MatrixAlgebraElement):
-    def is_hermitian(self):
-        r"""
-
-        SETUP::
-
-            sage: from mjo.matrix_algebra import HurwitzMatrixAlgebra
-
-        EXAMPLES::
-
-            sage: A = HurwitzMatrixAlgebra(QQbar, ZZ, 2)
-            sage: M = A([ [ 0,I],
-            ....:         [-I,0] ])
-            sage: M.is_hermitian()
-            True
-
-        """
-        return all( self[i,j] == self[j,i].conjugate()
-                    for i in range(self.nrows())
-                    for j in range(self.ncols()) )
-
-
-class HurwitzMatrixAlgebra(MatrixAlgebra):
-    Element = HurwitzMatrixAlgebraElement