The bug is:
(1) -> radicalSolve([x-y],[x,y])
(1) [[x= x]]
Type:
List(List(Equation(Expression(Integer))))
(2) -> radicalRoots([x-y],[x,y])
(2) [[x]]
Type:
List(List(Expression(Integer)))
(3) -> solve([x-y],[x,y])
(3) [[x= %A,y= %A]]
Type:
List(List(Equation(Fraction(Polynomial(Integer)))))
Clearly result (1) is wrong, and it's easy to make it return "[[x= y]]",
however, that depends on the meaning of 'radicalRoots':
radicalRoots : (L RF, L SY) -> L L RE
++ radicalRoots(lrf, lvar) finds the roots expressed in terms of
++ radicals of the list of rational functions lrf
++ with respect to the list of symbols lvar.
In the case of "radicalRoots([x-y],[x,y])" returns "[[x]]",
when equations of lrf are indeterminate, returns with
respect to the *reverse* order of lvar.
If so, the patch is:
diff --git a/src/algebra/solverad.spad b/src/algebra/solverad.spad
index c836157..fc6dec4 100644
--- a/src/algebra/solverad.spad
+++ b/src/algebra/solverad.spad
@@ -276,7 +277,7 @@ RadicalSolvePackage(R) : Cat == Capsule where
makeEq(nres : L RE, lv : L SY) : L EQ RE ==
- [equation(x :: RE, r) for x in lv for r in nres]
+ [equation(x :: RE, r) for x in reverse lv for r in nres]
After patch:
(1) -> radicalSolve([y-x],[x,y])
(1) [[y= x]]
Type:
List(List(Equation(Expression(Integer))))
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