[fricas-devel] zeroOf

[Riccardo GUIDA]

Hi

The function zeroOf(p) zeroOf(p,x), with p a polynomial at first sight seems more harmful than useful: if there are no radical solution to p=0 it should be equivalent to rootOf, which return a generic solution, while if there are radicals solution it returns one solution (which one?????).

What would be its use case? Is it really wise to leave it exposed?

ric

PS zerosOf is OK.

[Waldek Hebisch]

Post by Riccardo GUIDA
The function zeroOf(p) zeroOf(p,x), with p a polynomial at first sight seems more harmful than useful: if there are no radical solution to p=0 it should be equivalent to rootOf, which return a generic solution, while if there are radicals solution it returns one solution (which one?????).
What would be its use case? Is it really wise to leave it exposed?
ric
PS zerosOf is OK.

Actually, all of them can be criticised. Correct use of 'zeroOf'
is in cases where you do not care which root you get. There
are at least two scenarios when this is the case:
- you need just one solution, for example seeking for change
of variables satiafying some algebraic constraints
- polynomial is irreducible (than radical solution represents
_all_ solutions when you vary radicals)

'rootsOf' and 'zerosOf' are potentially confusing because user
could expect that we build a splitting field, but in fact
the result may lie in rather strage ring with zero divisors.
In other words, result has some uses, but may be incorrect
from point of view of mathematicial not aware of limited
work done by those functions.

Note also that 'if possible' in description of 'zeroOf'
means 'if the code manages to find expression in terms
of radicals'.

Concerning exposure, ATM constructors are either exposed
or not. Expression is exposed, so all its operations
are exposed.