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I know this is a long short but I was wondering whether it is possible to substitute a combination of variables by something else. Let me explain it with an example.

Let f(x,y,z) = f(x) \sqrt(x^2+y^2+z^2) + f(y) \sqrt(x^2+y^2+z^2) + f(z) \sqrt(x^2+y^2+z^2)

As we can see the combination \sqrt(x^2+y^2+z^2) occurs very often. Is there a way I call this combination some other variable, say, w. I cannot use substitute in this case as I want to leave x,y and z alone if they dont come in this specific combination \sqrt(x^2+y^2+z^2). If it were a string I could have used find and replace. But I want to use the expression as a input later on in the notebook.

Thanks in advance.

I know this is a long short but I was wondering whether it is possible to substitute a combination of variables by something else. Let me explain it with an example.

Let f(x,y,z) = f(x) \sqrt(x^2+y^2+z^2) + f(y) \sqrt(x^2+y^2+z^2) + f(z) \sqrt(x^2+y^2+z^2)

As we can see the combination \sqrt(x^2+y^2+z^2) occurs very often. Is there a way I call this combination some other variable, say, w. I cannot use substitute in this case as I want to leave x,y and z alone if they dont come in this specific combination \sqrt(x^2+y^2+z^2). If it were a string I could have used find and replace. But I want to use the expression as a input later on in the notebook. notebook.

Edit: I came across a sympy command which is very close to what I want to do but not quite. There is a command cse in the module simplify. However, it identifies the subexpresssion by itself. As far as I could see it does not offer the flexibility for the users to identify the subexpression. Also for some reason sage expressions cannot be converted to sympy using f._sympy_() if there are "i"'s in the expression.

Thanks in advance.

I know this is a long short but I was wondering whether it is possible to substitute a combination of variables by something else. Let me explain it with an example.

Let f(x,y,z) $f(x,y,z) = f(x) \sqrt(x^2+y^2+z^2) \sqrt{x^2+y^2+z^2} + f(y) \sqrt(x^2+y^2+z^2) \sqrt{x^2+y^2+z^2} + f(z) \sqrt(x^2+y^2+z^2)\sqrt{x^2+y^2+z^2}$

As we can see the combination \sqrt(x^2+y^2+z^2) $\sqrt{x^2+y^2+z^2}$ occurs very often. Is there a way I call this combination some other variable, say, w. I cannot use substitute in this case as I want to leave x,y $x$,$y$ and z $z$ alone if they dont come in this specific combination \sqrt(x^2+y^2+z^2). $\sqrt{x^2+y^2+z^2}$. If it were a string I could have used find and replace. But I want to use the expression as a input later on in the notebook.

Edit: I came across a sympy command which is very close to what I want to do but not quite. There is a command cse in the module simplify. However, it identifies the subexpresssion by itself. As far as I could see it does not offer the flexibility for the users to identify the subexpression. Also for some reason sage expressions cannot be converted to sympy using f._sympy_() f._sympy_() if there are "i"'s in the expression.

Thanks in advance.

I know this is a long short but I was wondering whether it is possible to substitute a combination of variables by something else. Let me explain it with an example.

Let $f(x,y,z) = f(x) \sqrt{x^2+y^2+z^2} + f(y) \sqrt{x^2+y^2+z^2} + f(z) \sqrt{x^2+y^2+z^2}$

As we can see the combination $\sqrt{x^2+y^2+z^2}$ occurs very often. Is there a way I call this combination some other variable, say, w. I cannot use substitute in this case as I want to leave $x$,$y$ and $z$ alone if they dont come in this specific combination $\sqrt{x^2+y^2+z^2}$. If it were a string I could have used find and replace. But I want to use the expression as a input later on in the notebook.

Edit: I came across a sympy command which is very close to what I want to do but not quite. There is a command cse in the module simplify. However, it identifies the subexpresssion by itself. As far as I could see it does not offer the flexibility for the users to identify the subexpression. Also for some reason sage expressions cannot be converted to sympy using f._sympy_() if there are "i"'s in the expression.

Thanks in advance.