Hello, I came back...
I define the following one-parameter functions and their derivatives
x,y,l,L = var('x,y,l,L')
d5 = function('d5',nargs=1)
def d3partderiv(self,*args,**kwds): arg = args[0]; return
L*L*d5(arg);
d3 = function('d3',derivative_func=d3partderiv)
def d1partderiv(self,*args,**kwds): arg = args[0]; return -( d3(arg)
+d1(arg) )/arg
d1 = function('d1',derivative_func=d1partderiv)
The derivatives work correctly:
diff(d1(x^2),x) ---> -2*(d3(x^2) + d1(x^2))/x
diff(d3(x^2),x) ---> 2*L^2*x*d5(x^2)
but the Taylor expansion of d1(x) to second order gives
taylor( d1(x), x, 0, 2) ---> 1/2*x^2*D[0, 0](d1)(0) + x*D[0](d1)(0)
+ d1(0)
I don't understand why but :
sage: add (diff (d1(x^2), x, k)*x^k/factorial(k) for k in [0..2]) #
seems right.
You recode the taylor function...
F.
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