On 9/16/10 10:47 AM, miquel pericas wrote:
Hi,
I'm a collaborator of the author of the previous post. Let me try to
elaborate a little on what it is we want to do
Basically we are trying to simplify some complex symbolic expressions
we have generated which include matrices and vectors as variables.
Unfortunately these formulas are too long/complex to manipulate by
hand and we we are looking for some way to do this automatically.
Sage's manual explains how to simplify expressions with some
variables: The following example is extracted from the reference
manual
sage: var(’x, y, a, b, c’)
(x, y, a, b, c)
sage: f = x*(x-1)/(x^2 - 7) + y^2/(x^2-7) + 1/(x+1) + b/a + c/a; f
(x - 1)*x/(x^2 - 7) + y^2/(x^2 - 7) + b/a + c/a + 1/(x + 1)
sage: f.combine()
((x - 1)*x + y^2)/(x^2 - 7) + (b + c)/a + 1/(x + 1)
We want to do exactly the same, but in our case variables a,b,c, etc
would be vectors and matrices. Our question is: is it possible to use
sage to perform this kind of simplification with matrices and vectors?
Or, what is probably the same question, how can I generate variables
that are matrices and vectors?
It sounds like the thread I linked to in an earlier message on this
thread contains code that would do things like you are asking about.
http://groups.google.com/group/sage-devel/browse_thread/thread/cafb486c79a2eb3c/d0bb78d09a4fb52a
For example, here is an example from that thread:
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
Of course, you can deal with a vector by declaring a 3 by 1 matrix, for
example:
sage: load('matrix.sage')
sage: Alg = SymbolicMatrixAlgebra(QQ)
sage: A = Alg.matrix("A",3,3)
sage: b = Alg.matrix("b",3,1)
sage: x = Alg.matrix("x",3,1) # a column vector
sage: A*x + A^2*x+A^3*x+A*b
A A A x + A A x + A b + A x
The code isn't complete, but it does do things like not assume matrices
commute, handle inverses and transposes, etc. I would love it if the
code was polished and included in Sage. I would probably make good use
of it too.
Thanks,
Jason
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