Ondrej Certik wrote:
> On Mon, Oct 6, 2008 at 11:28 PM, Alan Bromborsky <[EMAIL PROTECTED]> wrote:
>
>> Suppose I have two symbols A and B that I wish to declare implicit
>> functions of say the symbols x1, x2, and x3. Then I wish to calculate
>> the derivative of A*B with respect to x1 and x2 and x3. Can I do this
>> and if so how?
>>
>
> Yes, for example this way:
>
> In [2]: A = Function("A")
>
> In [3]: B = Function("B")
>
> In [4]: var("x1 x2 x3")
> Out[4]: (x₁, x₂, x₃)
>
> In [5]: f = A(x1, x2, x3)*B(x1, x2, x3)
>
> In [6]: f
> Out[6]: A(x₁, x₂, x₃)⋅B(x₁, x₂, x₃)
>
> In [7]: diff(f, x1)
> Out[7]:
> d d
> A(x₁, x₂, x₃)⋅───(B(x₁, x₂, x₃)) + B(x₁, x₂, x₃)⋅───(A(x₁, x₂, x₃))
> dx₁ dx₁
>
>
>
>
> Ondrej
>
> >
>
Is there anyway of suppressing the arguments so you could write f = A*B
and then d(A*B)/dx1 = dA/dx1*B+A*dB/dx1. I guess what I am saying is
that writing A(x1,x2,x3) could get very long especially if the A's and
B's are components of vectors or matrices and you are differentiating
all of them. It would be very useful to declare the independent
variables when you declare A as a function so you do not have to write
out A(x1,x2,x3) every time you use A in an expression or differentiate it.
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