On Tue, Oct 7, 2008 at 12:07 AM, Alan Bromborsky <[EMAIL PROTECTED]> wrote:
>
> 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.
Like below?
In [1]: var("x1 x2 x3")
Out[1]: (x₁, x₂, x₃)
In [2]: A = Function("A")(x1, x2, x3)
In [3]: B = Function("B")(x1, x2, x3)
In [4]: f = A*B
In [5]: diff(f, x1)
Out[5]:
d d
A(x₁, x₂, x₃)⋅───(B(x₁, x₂, x₃)) + B(x₁, x₂, x₃)⋅───(A(x₁, x₂, x₃))
dx₁ dx₁
Ondrej
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