Am 11.12.2014 um 00:40 schrieb Richard Fateman:
1994 paper by Adam Dingle and Richard Fateman
Branch Cuts in Computer Algebra, (ISSAC '94 proceedings. also search
online).
That paper assumes that everything can be refactored to logarithms plus
arithmetic.
Does that assumption hold? I could imagine that expressions containing
irreducible integrals might not be normalizable in that fashion.
When you say things about sqrt(), does it generalize to cuberoot? If it
does not, you are in trouble, or will be down the road.
What is the principal value of (1)^(1/6) ?
Not sure what you mean with that.
Several systems have RootOf( ...) expressions. e.g. RootOf(s^2=x, s).
There are 2 values for s. What systems?
Maple
Macsyma
Axiom/Fricas
Mathematica
probably others.
Not sure how that relates to the point you're making.
You think you can use sqrt because the quadratic formula says
-b+-sqrt(b^2....)
etc.
So you think you know what sqrt means.
Not sure what assumptions you assume.
But in that formula you can switch the values +- and the formula
is still valid.
Not sure what you mean with that - switching the signs means I still get
the same set of expressions.
How many other formulas do you expect to fiddle with where that is true?
Certainly not this one: sqrt(y^2) = abs(y).
That could still be handled by doing case distinctions.
This is an interesting case though, since it tells us that we need a
quantor: Are we interested in "there exists a branch where the
expression holds" or in "the expression holds in all branches"?
I think we need the former when determining all solutions to an
equation, and the latter when verifying an assumption.
So if you go off and do the wrong thing, it is probably prudent to
understand that you are doing the wrong thing.
Actually the "wrong thing" could be the right thing in specific
circumstances (experimental physics is full of this kind of stuff), but
I agree that you need to be aware of the kind of shortcut you're taking
and where the boundaries are where the approach would break.
I'm not sure what kind of "wrong thing" you are referring to in this
particular exchange though.
You paper takes a geometric approach (defining cuts as lines across the
complex plane), and I can see that that might be more appropriate than
blindly enumerating all branches, which might run into performance
issues, and would need quite a bit of algorithmic work to deal with
--
You received this message because you are subscribed to the Google Groups
"sympy" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sympy.
To view this discussion on the web visit
https://groups.google.com/d/msgid/sympy/5489C343.1000703%40durchholz.org.
For more options, visit https://groups.google.com/d/optout.
