Is there a reason quadratic-solutions only provides real solutions?

[dieggsy]

Why not quadratic-solutions providing all solutions, including complex, and quadratic-real-solutions, quadratic-real-natural-solutions, etc. or something like that?

[soegaard]

No reason, apart from nobody requesting that feature.

Also I see that the naïve solution formula is used [1].
Are you interested in adding quadratic-complex-solutions
and in the process maybe switch to the better formulas [2]?

[1] https://github.com/racket/math/blob/master/math-lib/math/private/number-theory/quadratic.rkt#L19
[2] https://people.csail.mit.edu/bkph/articles/Quadratics.pdf

[soegaard]

More notes on the choice of formulas here: https://math.stackexchange.com/questions/866331/numerically-stable-algorithm-for-solving-the-quadratic-equation-when-a-is-very/2007723

[dieggsy]

@soegaard I forget where this comes from, I once implemented this in chicken scheme, and I think is supposed to be more numerically stable, as well as accepting complex coefficients.

I think the source was a book titled something like "modern computer algebra", but I can't seem to find it at the moment.

EDIT: The book is "Numerical recipes: the art of scientific computing"

[dieggsy]

Looking over it again, I think my formula is the same as your PDF, except the check for which formula to use extends to complex numbers as well.