| 0 | 0 |
+---+---+
+ TESTS::
+
+ sage: MatrixAlgebra(0,ZZ,ZZ).zero()
+ []
+
"""
+ if self.nrows() == 0 or self.ncols() == 0:
+ # Otherwise we get a crash or a blank space, depending on
+ # how hard we work for it. This is what MatrixSpace(...,
+ # 0) returns.
+ return "[]"
+
return table(self.rows(), frame=True)._repr_()
if "Unital" in entry_algebra.category().axioms():
category = category.Unital()
entry_one = entry_algebra.one()
- self.one = lambda: sum( (self.monomial((i,i,entry_one))
- for i in range(self.nrows()) ),
- self.zero() )
+ self.one = lambda: self.sum( (self.monomial((i,i,entry_one))
+ for i in range(self.nrows()) ) )
if "Associative" in entry_algebra.category().axioms():
category = category.Associative()
# lies to us.
entry_basis = self.entry_algebra_gens()
- basis_indices = [(i,j,e) for j in range(n)
- for i in range(n)
+ basis_indices = [(i,j,e) for i in range(n)
+ for j in range(n)
for e in entry_basis]
super().__init__(scalars,
if hasattr(entry, 'to_vector'):
return entry.to_vector()
- from sage.modules.free_module import VectorSpace
+ from sage.modules.free_module import FreeModule
d = len(self.entry_algebra_gens())
- V = VectorSpace(self.entry_algebra().base_ring(), d)
+ V = FreeModule(self.entry_algebra().base_ring(), d)
if hasattr(entry, 'list'):
# sage matrices
(i,j,e1) = mon1
(k,l,e2) = mon2
if j == k:
- # 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))
+ # There's no reason to expect e1*e2 to itself be a monomial,
+ # so we have to do some manual conversion to get one.
+ p = self._entry_algebra_element_to_vector(e1*e2)
+
+ # We have to convert alpha_g because a priori it lives in the
+ # base ring of the entry algebra.
+ R = self.base_ring()
+ return self.sum_of_terms( (((i,l,g), R(alpha_g))
+ for (alpha_g, g)
+ in zip(p, self.entry_algebra_gens()) ),
+ distinct=True)
else:
return self.zero()
SETUP::
- sage: from mjo.matrix_algebra import MatrixAlgebra
+ sage: from mjo.hurwitz import ComplexMatrixAlgebra
EXAMPLES::
- sage: A = MatrixAlgebra(2, QQbar, ZZ)
- sage: A.from_list([[0,I],[-I,0]])
+ sage: A = ComplexMatrixAlgebra(2, QQbar, ZZ)
+ sage: M = A.from_list([[0,I],[-I,0]])
+ sage: M
+----+---+
| 0 | I |
+----+---+
| -I | 0 |
+----+---+
+ sage: M.to_vector()
+ (0, 0, 0, 1, 0, -1, 0, 0)
"""
nrows = len(entries)
# Octonions(AA).
return self.entry_algebra().from_vector(e_ij.to_vector())
- return sum( (self.monomial( (i,j, convert(entries[i][j])) )
- for i in range(nrows)
- for j in range(ncols) ),
- self.zero() )
+ def entry_to_element(i,j,entry):
+ # Convert an entry at i,j to a matrix whose only non-zero
+ # entry is i,j and corresponds to the entry.
+ p = self._entry_algebra_element_to_vector(entry)
+
+ # We have to convert alpha_g because a priori it lives in the
+ # base ring of the entry algebra.
+ R = self.base_ring()
+ return self.sum_of_terms( (((i,j,g), R(alpha_g))
+ for (alpha_g, g)
+ in zip(p, self.entry_algebra_gens()) ),
+ distinct=True)
+
+ return self.sum( entry_to_element(i,j,entries[i][j])
+ for j in range(ncols)
+ for i in range(nrows) )
+
def _element_constructor_(self, elt):
if elt in self: