#4256 raddenest failure with sqrt(sqrt(3)*%i-1)

[David Billinghurst]

raddenest - in git HEAD of 2024-01-22 - fails with sqrt(sqrt(3)*%i-1). This would be unacceptable for algsys/solve.

The correct denesting is (sqrt(3)*%i)/sqrt(2)+1/sqrt(2)

(%i1) load("raddenest")$
(%i2) eq1:sqrt(sqrt(3)*%i-1)$
(%i3) sqrtdenest(eq1);
(%o3)                        sqrt(sqrt(3) %i - 1)
(%i4) eq2:raddenest(eq1);
                                  1      sqrt(6)
(%o4)                          ─────── - ───────
                               sqrt(2)      2
(%i5) rectform(float(eq1));
(%o5)              1.224744871391589 %i + 0.7071067811865476
(%i6) rectform(float(eq2));
(%o6)                        - 0.5176380902050415
(%i7) rectform(float((sqrt(3)*%i)/sqrt(2)+1/sqrt(2)));
(%o7)              1.224744871391589 %i + 0.7071067811865475

Found while investigating feature request [#4255] which is related to algsys bug [#4252]