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 --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sympy?hl=en -~----------~----~----~----~------~----~------~--~---