# Revision history [back]

### Symbolic Integration works only with second dummy variable

Hi there,

I am trying get an symbolic expression for the convolution $$(\psi \star f)(x) := \int\limits_{\mathbb{R}} \psi(x-y) f(y) {d y}$$

of two functions $f, \psi: \mathbb{R} \to \mathbb{R}$ as follows:

 var('y') psi = function('psi')(y) f = function('f')(y) integrate(psi(x-y)*f(y),y) 

upon which I get the error message

RuntimeError: ECL says: Error executing code in Maxima:

If I add an extra argument to the two functions and define them as $$f, \psi : \mathbb{R} \times \mathbb{R} \to \mathbb{R}$$ as follows:

 var('t') psi = function('psi')(t,y) f = function('f')(t,y) integrate(psi(t,x-y)*f(t,y),y) 

there is a surprise, it suddenly works! I get the desired symbolic expression on which I can run diff(..,x) and all the other built-in functions.

What is happening here?

### Symbolic Integration works only with second dummy variable

Hi there,

I am trying get an symbolic expression for the convolution $$(\psi \star f)(x) := \int\limits_{\mathbb{R}} \psi(x-y) f(y) {d y}$$

of two functions $f, \psi: \mathbb{R} \to \mathbb{R}$ as follows:

 var('y') var('y') psi = function('psi')(y) f = function('f')(y) integrate(psi(x-y)*f(y),y) 

upon which I get the error message

RuntimeError: ECL says: Error executing code in Maxima:

If I add an extra argument to the two functions and define them as $$f, \psi : \mathbb{R} \times \mathbb{R} \to \mathbb{R}$$ as follows:

 var('t') psi = function('psi')(t,y) f = function('f')(t,y) integrate(psi(t,x-y)*f(t,y),y) 

there is a surprise, it suddenly works! I get the desired symbolic expression on which I can run diff(..,x) and all the other built-in functions.

What is happening here?am I missing here ?

TL;DR Why does integrate(f(y)*f(y),y) return an error?

### Symbolic Integration works only with second dummy variable

TL;DR Why does integrate(f(y)*f(y),y) return an error?

Hi there,

I am trying get an symbolic expression for the convolution $$(\psi \star f)(x) := \int\limits_{\mathbb{R}} \psi(x-y) f(y) {d y}$$

of two functions $f, \psi: \mathbb{R} \to \mathbb{R}$ as follows:

 var('y') psi = function('psi')(y) f = function('f')(y) integrate(psi(x-y)*f(y),y) 

upon which I get the error message

RuntimeError: ECL says: Error executing code in Maxima:

If I add an extra argument to the two functions and define them as $$f, \psi : \mathbb{R} \times \mathbb{R} \to \mathbb{R}$$ as follows:

 var('t') psi = function('psi')(t,y) f = function('f')(t,y) integrate(psi(t,x-y)*f(t,y),y) 

there is a surprise, it suddenly works! I get the desired symbolic expression on which I can run diff(..,x) and all the other built-in functions.

What am I missing here ?

TL;DR Why does integrate(f(y)*f(y),y) return an error?

### Symbolic Integration works only with second dummy variable

TL;DR Why does integrate(f(y)*f(y),y)integrate(psi(y)*f(y),y) return an error?

Hi there,

I am trying get an symbolic expression for the convolution $$(\psi \star f)(x) := \int\limits_{\mathbb{R}} \psi(x-y) f(y) {d y}$$

of two functions $f, \psi: \mathbb{R} \to \mathbb{R}$ as follows:

 var('y') psi = function('psi')(y) f = function('f')(y) integrate(psi(x-y)*f(y),y) 

upon which I get the error message

RuntimeError: ECL says: Error executing code in Maxima:

If I add an extra argument to the two functions and define them as $$f, \psi : \mathbb{R} \times \mathbb{R} \to \mathbb{R}$$ as follows:

 var('t') psi = function('psi')(t,y) f = function('f')(t,y) integrate(psi(t,x-y)*f(t,y),y) 

there is a surprise, it suddenly works! I get the desired symbolic expression on which I can run diff(..,x) and all the other built-in functions.

What am I missing here ?

### Symbolic Integration works only with second dummy variable

TL;DR Why does integrate(psi(y)*f(y),y) return an error?

Hi there,

I am trying get an symbolic expression for the convolution $$(\psi \star f)(x) := \int\limits_{\mathbb{R}} \psi(x-y) f(y) {d y}$$

of two functions $f, \psi: \mathbb{R} \to \mathbb{R}$ as follows:

 var('y') psi = function('psi')(y) f = function('f')(y) integrate(psi(x-y)*f(y),y) 

upon which I get the error message

RuntimeError: ECL says: Error executing code in Maxima:

If I add an extra argument to the two functions and define them as $$f, \psi : \mathbb{R} \times \mathbb{R} \to \mathbb{R}$$ as follows:

 var('t') psi = function('psi')(t,y) f = function('f')(t,y) integrate(psi(t,x-y)*f(t,y),y) 

there is a surprise, it suddenly works! I get the desired symbolic expression on which I can run diff(..,x) and all the other built-in functions.

What am I missing here ?

# Symbolic Integration works only with second dummy variable

TL;DR Why does integrate(psi(y)*f(y),y) return an error?

Hi there,

I am trying get an symbolic expression for the convolution $$(\psi \star f)(x) := \int\limits_{\mathbb{R}} \psi(x-y) f(y) {d y}$$

of two functions $f, \psi: \mathbb{R} \to \mathbb{R}$ as follows:

 var('y') psi = function('psi')(y) f = function('f')(y) integrate(psi(x-y)*f(y),y) 

upon which I get the error message

RuntimeError: ECL says: Error executing code in Maxima:

If I add an extra argument to the two functions and define them as $$f, \psi : \mathbb{R} \times \mathbb{R} \to \mathbb{R}$$ as follows:

 var('t') psi = function('psi')(t,y) f = function('f')(t,y) integrate(psi(t,x-y)*f(t,y),y) 

there is a surprise, it suddenly works! I get the desired symbolic expression on which I can run diff(..,x) and all the other built-in functions.

TL;DR Why does integrate(psi(y)*f(y),y) return an error?

What am I missing here ?

# Symbolic Integration works only with second dummy variable

Hi there,

I am trying get an symbolic expression for the convolution $$(\psi \star f)(x) := \int\limits_{\mathbb{R}} \psi(x-y) f(y) {d y}$$

of two functions $f, \psi: \mathbb{R} \to \mathbb{R}$ as follows:

 var('y') psi = function('psi')(y) f = function('f')(y) integrate(psi(x-y)*f(y),y) 

upon which I get the error message

RuntimeError: ECL says: Error executing code in Maxima:

If I add an extra argument to the two functions and define them as $$f, \psi : \mathbb{R} \times \mathbb{R} \to \mathbb{R}$$ as follows:

 var('t') psi = function('psi')(t,y) f = function('f')(t,y) integrate(psi(t,x-y)*f(t,y),y) 

there is a surprise, it suddenly works! I get the desired symbolic expression on which I can run diff(..,x) and all the other built-in functions.

TL;DR Why does integrate(psi(y)*f(y),y) return an error?

What am I missing here ?

# Symbolic Integration works only with second dummy variable

Hi there,

I am trying get an symbolic expression for the convolution $$(\psi \star f)(x) := \int\limits_{\mathbb{R}} \psi(x-y) f(y) {d y}$$

of two functions $f, \psi: \mathbb{R} \to \mathbb{R}$ as follows:

 var('y') psi = function('psi')(y) f = function('f')(y) integrate(psi(x-y)*f(y),y) 

upon which I get the error message

RuntimeError: ECL says: Error executing code in Maxima:

If I add an extra argument to the two functions and define them as $$f, \psi : \mathbb{R} \times \mathbb{R} \to \mathbb{R}$$ as follows:

 var('t') psi = function('psi')(t,y) f = function('f')(t,y) integrate(psi(t,x-y)*f(t,y),y) 

there is a surprise, it suddenly works! I get the desired symbolic expression on which I can run diff(..,x) and all the other built-in functions.

TL;DR Why does integrate(psi(y)*f(y),y) return an error?

What am I missing here ?

# Symbolic Integration works only with second dummy variable

Hi there,

I am trying get an symbolic expression for the convolution $$(\psi \star f)(x) := \int\limits_{\mathbb{R}} \psi(x-y) f(y) {d y}$$

of two functions $f, \psi: \mathbb{R} \to \mathbb{R}$ as follows:

 var('y') psi = function('psi')(y) f = function('f')(y) integrate(psi(x-y)*f(y),y) 

upon which I get the error message

RuntimeError: ECL says: Error executing code in Maxima:

If I add an extra argument to the two functions and define them as $$f, \psi : \mathbb{R} \times \mathbb{R} \to \mathbb{R}$$ as follows:

 var('t') psi = function('psi')(t,y) f = function('f')(t,y) integrate(psi(t,x-y)*f(t,y),y) 

there is a surprise, it suddenly works! I get the desired symbolic expression on which I can run diff(..,x) and all the other built-in functions.

TL;DR Why does integrate(psi(y)*f(y),y) return an error?

What am I missing here ?Solution Use sympy backend for symbolic integration as in integrate(psi(x-y)*f(y),y, algorithm="sympy")