oldk1331 wrote:
>
> The problem is about branch cuting:
>
> For Integers and Fractions, (-1/8)^(1/3) gives AlgebraicNumber
> containing (-1)^(1/3), avoids branch cuting.
>
> For numeric computing, for example Float, I think it's better
> to have signature:
> ^ : (%, Fraction Integer) -> %
> aka keep current definition of '^'.
>
> People can use "((-0.125)^(1/3))$Complex Float" to get principle
> complex value.
>
> So the patch I propose is:
>
> diff --git a/src/algebra/mkfunc.spad b/src/algebra/mkfunc.spad
> index 963e4727..431d9dab 100644
> --- a/src/algebra/mkfunc.spad
> +++ b/src/algebra/mkfunc.spad
> @@ -425,13 +425,15 @@
> (u := mkLispList rest l) case "failed" => "failed"
> ll := u::List(INF)
> streqlist?(op, ["+","*","/","-"]) => convert(concat(op, ll))@INF
> - streq?(op, "^") => gencode("EXPT", ll)
> streqlist?(op, ["exp","sin","cos","tan","atan",
> "log", "sinh","cosh","tanh","asinh","acosh","atanh","sqrt"]) =>
> gencode(upperCase string symbol op, ll)
> + -- Common Lisp's definition of "^" is different from FriCAS when
> + -- first argument is negative, so stop generating code for this case.
> + streq?(op, "^") => "failed"
> streq?(op, "nthRoot") =>
> second ll = convert(2::Integer)@INF =>gencode("SQRT",[first ll])
> - gencode("EXPT", concat(first ll, [1$INF / second ll]))
> + "failed" -- same as "^"
> streq?(op, "float") =>
> a := ll.1
> e := ll.2
>
This patch causes failure in tutchap4.input. Arguably, test
in tutchap4 is wrong, because it uses roots of negative
numbers:
S3 := eval(S,[A=1,k=1,c=0.1])
(6)
+-------+
+-------+ 0.05 t\|- 399.0 - 0.05 t
(0.5\|- 399.0 + 0.5)%e
+
+-------+
+-------+ - 0.05 t\|- 399.0 - 0.05 t
(0.5\|- 399.0 - 0.5)%e
/
+-------+
\|- 399.0
Type: Expression(Float)
However, this is wrong more or less the in the same way as
the x^(1/3) test that you try to make to work. So the change
does not look as improvement: we make one borderline case
work at expense of another borderline case...
--
Waldek Hebisch
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