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
--
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