Re: [fricas-devel] discussion: bug and description for 'radicalRoots:(L

[oldk1331]

>  Our solvers transform 
>  system of equations into triangular form.  If system is zero 
>  dimensional (has finite number of solutions) than current 
>  method works OK.  We have problem in case of higher dimensional 
>  solution set.

I noticed that too, 'triangularSystems' uses 'groebSolve' to do the
0 dimension case.  For the linear 'solve' function, there's 'checkLinear'
and 'linSolve' to deal with this high dimension situation.  But according
to your reply, similar technique doesn't apply to radicalSolve.

Still, did this patch fix this trival case and not break others?

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[fricas-devel] discussion: bug and description for 'radicalRoots:(L RF, L SY) -> L L RE'

[oldk1331]

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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