# TypeError 'unable to simplify to float approximation' while trying to define an integral operator

Hello, I am trying to define an integral operator acting on a subspace of $L^2(\mathbb{R})$ that depends of time using sage. Being more explicit $W(t)$ takes a real function $f$ and returns another function $g$ defined by \begin{equation} W(t)f(x)=g(x)=\int_{-\infty}^{+\infty}K(x,y,z)f(y)\text{d}y \end{equation} This is the code I came up with

def W(t):
def dummy2(f):
def dummy3(x):
integrand(y)=f(y)*K(x,y,t)
return numerical_integral(integrand,-Infinity,+Infinity,algorithm='qag')
return dummy3
return dummy2


With $K$ a reasonable function of $x,y,t$ However I am getting the following error

TypeError: unable to simplify to float approximation


I am pretty sure it's related to the types passed to numerical_integrand What could be a solution? Or a better way to implement it? Thank you all

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The code looks fine. (Maybe change to integrand = lambda y: f(y)*K(x,y,t)). What is the function $K$ and the call that yields the error? Note $K$ must return a constant which has a floating point approximation, and hence cannot contain symbolic variables (though you could work around this by considering them as formal variables).

I still get an error, I defined K as

K(x,y,t)=1/(x^2+y^2+t^2+1)


How can I define them as formal variables?

Sort by » oldest newest most voted You don't have to define any formal variables in that case. You still haven't specified what call is giving you an error. An example of a correct call is W(0)(lambda x: 1)(1) (here $t=0, f(x) = 1, x = 1$) which gives the result without error.

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