Tim Lahey wrote:
>
> On Dec 17, 2008, at 8:03 PM, Jason Grout wrote:
>
>> Tim Lahey wrote:
>>> There are certainly some things you can do with general matrices and
>>> vectors, but I think doing something like defining A as an nxm matrix
>>> and allowing various operations on it is a very useful thing.
>>> Mathematica has some support for this, but I don't think it has a
>>> general solve.
>>
>> Could you maybe give an example session in Mathematica doing something
>> like this?
>>
>
> You can define a, and c as vectors and B as a matrix and then do,
>
Oh, I understood the above to mean that you could define a matrix B, for
example, without defining the elements of the matrix. I don't know how
to do that in Mathematica; maybe I'm confused. At any rate, for now,
I'll assume that you mean that you define "vectors" a and c and a
"matrix" B in Mma by specifying the entries as symbolic expressions. I
put vectors and matrix in quotes since I just ran into some trouble
trying to do an example session in Mma. To my knowledge, Mma really has
no notion of a "vector" or a "matrix", but instead has just the notion
of a list and a list of lists. This gave me problems in trying to do
what what you did below. Here, I define n to be a "vector" and try to
compute NN^T
In[2]:= n = {1, t, Cos[t]}
Out[2]= {1, t, Cos[t]}
In[3]:= b=n.Transpose[n]
Transpose::nmtx:
The first two levels of the one-dimensional list {1, t, Cos[t]}
cannot be transposed.
Instead, I assume you mean to define n as literally a column vector
(i.e., a column "matrix")?
In[6]:= n = {{1, t, Cos[t]}}//Transpose
Out[6]= {{1}, {t}, {Cos[t]}}
In[7]:= b=n.Transpose[n]
2 2
Out[7]= {{1, t, Cos[t]}, {t, t , t Cos[t]}, {Cos[t], t Cos[t], Cos[t] }}
> D[Transpose[a].B.c, c]
> or
> D[Transpose[a].B.c, a]
>
> If they conform, the operation is valid, and has a simple solution.
Pardon my ignorance, but what do you mean by a "solution"? Do you mean
that the derivatives yield a result, or that there is another solving
step which involves an equation?
I think that this might be possible in Sage using
http://trac.sagemath.org/sage_trac/ticket/3941 and
http://trac.sagemath.org/sage_trac/ticket/4493. Can you give a specific
Mathematica example session? I'll try to duplicate it in Sage.
Thanks
Jason
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