On Tue, Oct 7, 2008 at 12:26 AM, Alan Bromborsky <[EMAIL PROTECTED]> wrote:
>
> Ondrej Certik wrote:
>> 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
>>
>> >
>>
> Yes almost, but can you suppress the (x1,x2,x3) in the output so that
> the output would be
>
> A*dB/dx1+B*dA/dx1 ?
I see. Isn't this just a way of printing the expression? E.g. a matter
of creating a new Printer class.
It's true that if you just use symbols, you'll get 0, as they don't
depend on x1:
In [1]: var("x1 A B")
Out[1]: (x₁, A, B)
In [2]: diff(A*B, x1)
Out[2]: 0
Feel free to create a new issue for that and let's start implementing it.
Ondrej
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