On Jan 27, 2013, at 11:21 PM, "Alexey U. Gudchenko" <pr...@goodok.ru> wrote:
> > On 28.01.2013 01:08, Aaron Meurer wrote: >> On Jan 27, 2013, at 6:34 AM, "Alexey U. Gudchenko" <pr...@goodok.ru> wrote: >> >>> >>> Additionally to Stefan's answer about sympy core , I introduce the >>> example how it may be implemented concretely. >>> >>> There is the tested code in the atachment of it. >>> (I can create PR, but I don't know where will it be better to put in the >>> sympy modules) >>> >>> And there is the '__call__' magic-method used instead of the implicit >>> multiplication as aplly-like method. >>> >>>>>> Dx = DiffOperator(x) >>>>>> myD = (a*Dx + Dx**3) # construct diff operator >>>>>> myD(x**4) # apply this operator. >>> 4*a*x**3 + 24*x >>> >>> >>> For matrices it is some more complicated >>> >>>>>> I = Matrix([[0, -1], [1, 0]]) >>>>>> myD = I*Dx # construct diff >>>>>> myD(x**2) # apply >>> >>> Derivative([x**2, 0] >>> [ 0, x**2], x) >>> >>> >>> Here I don't know how Derivative can be automatically applied for the >>> Matrix expression. >> >> Well just as application of Dx isn't really multiplication, neither is >> application of the matrix operator. So a subclass of Matrix will be >> needed here. >> >> Aaron Meurer >> > > Yes, for the matrix differential operators with matrices which are > depended of the variables of differentiation we must think. > > But for the "constant" matrix (which is independent of the variable x) I > don't quite understand what kind of subclass of Matrix is needed: which > is related to differential operator or differential method of matrix itself. > > In order to avoid duplicating code, I think, we must use that for the > matrix M which is independent of the variable x the following is: > > M Dx = Dx M > > and at the same time for the applying this operator we only care that > differential operator would always be to the left of the expression A > (x) to which it is applied. > > So for the (constant) matrix differential operator myD = (M Dx) > > (M Dx) A(x) = (Dx M) A(x) = Dx (M A(x)) > > Is it right? But applying D first is probably more efficient. Aaron Meurer > > This is done automatically in presented diff_operator.py (only for the > matrices M which are independent of the variable x) > > Therefore for the (M Dx) A(x) we can compute M A(x) firstly and then > only a problem in this case, that I can't compute derivative of the > matrix expression > > diff( M*A(x), x) > > This was the question. > > In the case when M(x) is depended of x, we must of course keep it always > on the left in th expression > > M(x) Dx != Dx M(x) > > (this is not realized in attached code above) > > So a subclass of Matrix will be needed only in this case. > Or rather, internal support in DiffOperator expression must be > implemented for this case. > > > Alexey Gudchenko > >>> >>> -- >>> Alexey Gudchenko >>> >>> On 26.01.2013 02:49, ruoyu zhang wrote: >>>>>>> p = DifferentialOperator(t) >>>>>>> a * p * f(t) >>>> Derivative(f(t), t)*a >>>> >>>> p is a DifferentialOperator, when it multiply with some expression at >>>> right side, it calculates the derivative of the expression. >>> >>> -- >>> You received this message because you are subscribed to the Google Groups >>> "sympy" group. >>> To unsubscribe from this group and stop receiving emails from it, send an >>> email to sympy+unsubscr...@googlegroups.com. >>> To post to this group, send email to sympy@googlegroups.com. >>> Visit this group at http://groups.google.com/group/sympy?hl=en. >>> For more options, visit https://groups.google.com/groups/opt_out. >>> >>> >>> <diff_operator.py> > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To post to this group, send email to sympy@googlegroups.com. > Visit this group at http://groups.google.com/group/sympy?hl=en. > For more options, visit https://groups.google.com/groups/opt_out. > > -- 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 sympy+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sympy?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
