Dear Ross,
On Mon, Apr 19, 2010 at 06:38:31PM +0930, ross kyprianou wrote:
> (Im trying to finish this in 2-3 weeks to include some results in a
> paper but I understand that may not be possible)
Oops, I just noticed this deadline of yours; I hope you will still
make it! Please find attached a possible refactorisation of your code.
Here is a short extract of the doc (to be run after loading the code):
EXAMPLES::
sage: Alg = SymbolicMatrixAlgebra(QQ)
sage: A = Alg.matrix("A",3,2)
sage: B = Alg.matrix("B",2,3)
sage: C = Alg.matrix("C",2,3)
sage: D = Alg.matrix("D",3,3)
Example 1: Adding/Multiplying matrices of correct size::
sage: A * (B + C)
A B + A C
Example 2: Transposing a sum of matrices::
sage: (B + C).transpose()
C^t + B^t
Example 3: Transposing a product of matrices::
sage: (A * B).transpose()
B^t A^t
Example 4: Inverting a product of matrices::
sage: (A * B)^-1
B^-1 A^-1
Example 5: Multiplying by its inverse::
sage: D * D^-1 # todo: not implemented
I
Enjoy, and let me know how it goes!
Best,
Nicolas
--
Nicolas M. Thiéry "Isil" <[email protected]>
http://Nicolas.Thiery.name/
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from sage.structure.element import Element
from sage.combinat.free_module import CombinatorialFreeModule
# TODO: doc and tests for all of those
class SymbolicMatrix(SageObject):
def __init__(self, name, nrows, ncols, inverted = False, transposed =
False):
#Element.__init__(self, parent)
self._name = name
self._nrows = nrows
self._ncols = ncols
self._inverted = inverted
self._transposed = transposed
def _repr_(self):
result = self._name
if self._inverted:
result += "^-1"
if self._transposed:
result += "^t"
return result
def transpose(self):
result = copy(self)
result._transposed = not self._transposed
(result._nrows, result._ncols) = (self._ncols, self._nrows)
return result
def __invert__(self):
assert self._nrows == self._ncols, "Can't inverse non square matrix"
result = copy(self)
result._inverted = not self._inverted
return result
class SymbolicMatrixAlgebra(CombinatorialFreeModule):
r"""
EXAMPLES::
sage: Alg = SymbolicMatrixAlgebra(QQ)
sage: A = Alg.matrix("A",3,2)
sage: B = Alg.matrix("B",2,3)
sage: C = Alg.matrix("C",2,3)
sage: D = Alg.matrix("D",3,3)
Example 1: Adding/Multiplying matrices of correct size::
sage: A * (B + C)
A B + A C
Example 2: Transposing a sum of matrices::
sage: (B + C).transpose()
C^t + B^t
Example 3: Transposing a product of matrices::
sage: (A * B).transpose()
B^t A^t
Example 4: Inverting a product of matrices::
sage: (A * B)^-1
B^-1 A^-1
Example 5: Multiplying by its inverse::
sage: D * D^-1 # todo: not implemented
I
TODO: decide on the best output; do we want to be able to
copy-paste back? do we prefer short notations?
.. warnings::
The identity does not know it is size, so the following should
complain, but does not::
sage: D * D^-1 * A
TODO: describe all the abuses
"""
def __init__(self, R):
"""
EXAMPLES::
sage: A = AlgebrasWithBasis(QQ).example(); A
An example of an algebra with basis: the free algebra on the
generators ('a', 'b', 'c') over Rational Field
sage: TestSuite(A).run()
"""
CombinatorialFreeModule.__init__(self, R, Words(), category =
AlgebrasWithBasis(R))
def matrix(self, name, nrows, ncols):
""" TODO: doctest"""
return self.monomial(Word([SymbolicMatrix(name, nrows, ncols)]))
def _repr_(self):
"""
EXAMPLES::
sage: SymbolicMatrixAlgebra(QQ)
The symbolic matrix algebra over Rational Field
"""
return "The symbolic matrix algebra over %s"%(self.base_ring())
@cached_method
def one_basis(self):
"""
Returns the empty word, which index the one of this algebra,
as per :meth:`AlgebrasWithBasis.ParentMethods.one_basis`.
EXAMPLES::
sage: Alg = SymbolicMatrixAlgebra(QQ)
sage: Alg.one_basis()
word:
sage: A.one()
I
"""
return self.basis().keys()([])
def product_on_basis(self, w1, w2):
r"""
Product of basis elements, as per
:meth:`AlgebrasWithBasis.ParentMethods.product_on_basis`.
EXAMPLES::
sage: Alg = SymbolicMatrixAlgebra(QQ)
sage: P = Alg.matrix("P", 3, 2)
sage: Q = Alg.matrix("Q", 3, 2)
sage: R = Alg.matrix("R", 2, 2)
sage: S = Alg.matrix("S", 2, 3)
sage: P * P
Traceback (most recent call last):
...
AssertionError: Non-conformable matrices: matrix sizes are
incompatible for multiplication
sage: P * R * S
P*R*S
sage: (P+Q) * R
P*R + Q*R
sage: (P+Q) * R * S
P*R*S + Q*R*S
sage: S * (P+Q) * R
"""
if len(w1) == 0:
return self.monomial(w2)
if len(w2) == 0:
return self.monomial(w1)
assert w1[-1]._ncols == w2[0]._nrows, "Non-conformable matrices: matrix
sizes are incompatible for multiplication"
# TODO: handle cancelations between w1[-1] and w2[0]
return self.monomial(w1 + w2)
# TODO: define an_element
def _repr_term(self, t):
"""
EXAMPLES::
sage: Alg.one() # indirect doctest
I
sage: Alg.an_element() # todo: not implemented
"""
if len(t) == 0:
return 'I'
else:
return ' '.join(repr(m) for m in t)
class Element(CombinatorialFreeModule.Element):
def transpose(self):
"""
EXAMPLES::
sage: Alg = SymbolicMatrixAlgebra(QQ)
sage: A = Alg.matrix("A", 3, 2)
sage: B = Alg.matrix("B", 3, 2)
sage: C = Alg.matrix("C", 2, 2)
sage: D = Alg.matrix("D", 2, 3)
sage: x = D * (A+B) * C
sage: x
D B C + D A C
sage: x.transpose()
C^t B^t D^t + C^t A^t D^t
"""
return self.map_support(lambda w: Word(m.transpose() for m in
reversed(w)))
def __invert__(self):
"""
EXAMPLES::
sage: Alg = SymbolicMatrixAlgebra(QQ)
sage: A = Alg.matrix("A", 2, 2)
sage: B = Alg.matrix("B", 2, 2)
sage: C = Alg.matrix("C", 2, 2)
sage: D = Alg.matrix("D", 3, 2)
sage: E = Alg.matrix("E", 2, 3)
sage: ~(A*B*C)
C^-1 B^-1 A^-1
sage: ~(A*B^-1*C^-1)
C B A^-1
sage: ~(D*C*E)
Traceback (most recent call last):
...
AssertionError: Can't inverse non square matrix
sage: ~(A+B)
Traceback (most recent call last):
...
AssertionError: Can't inverse non trivial linear combinations
of matrices
"""
assert len(self) == 1, "Can't inverse non trivial linear
combinations of matrices"
(w, c) = self.leading_item()
return self.parent().term(Word(~m for m in reversed(w)), c)
