ENH: change term zero to root in newton

Is your feature request related to a problem? Please describe.

in root finding, we try to find x | f(x) == 0

here, x is sometimes called a root of the function or a zero of the function.

This request is to use the term ‘root’ instead of the term ‘zero’ because it’s technically confusing that both x and y can be seen as a “zero value”

consider the specific case of documenting the tol argument to the newton method: https://github.com/scipy/scipy/blob/v1.9.3/scipy/optimize/_zeros_py.py#L94-L370

tol is labeled as “The allowable error of the zero value.” but it is applied along the x-axis only, not to the “zero value” along the y-axis

Describe the solution you’d like.

it would be much clearer if scipy sticks to the term “root” to identify x within root-finding algorithms

Describe alternatives you’ve considered.

you could also actually apply tol to the output variable. in many cases this speeds things up although i don’t think it’s backwards compatible. it also arguably doesn’t solve the root issue 😉 of confusing parameter naming

Additional context (e.g. screenshots, GIFs)

No response

[WarrenWeckesser]

I think it would be best to focus on the consistent use of root in the root-finding functions in optimize. In other contexts, the use of zero has a long history, and I think it would be more confusing to switch to root. For example, with Bessel functions, zeros is widely used:

• https://en.wikipedia.org/wiki/Bessel_function#Zeros_of_the_Bessel_function
• https://mathworld.wolfram.com/BesselFunctionZeros.html
• Chapter XV of the classic “A treatise on the theory of Bessel functions” is “The zeros of Bessel functions”

[mdhaber]

I’d prefer to review optimize only. No rush.