Bug introduced in 10.0 and persisting through 11.3 or later
In 11.3.0 for Microsoft Windows (64-bit) (March 7, 2018)
writing:
f[w_, x_, y_, z_] := w*x^2*y^3 - z*(w^2 + x^2 + y^2 - 1)
eqn = {D[f[w, x, y, z], w] == 0,
D[f[w, x, y, z], x] == 0,
D[f[w, x, y, z], y] == 0,
D[f[w, x, y, z], z] == 0};
sol = Solve[eqn];
Table[eqn /. sol[[n]], {n, Length[sol]}]
I get:
{{True, True, True, True}, {True, True, True, True}, {True, True, True, True}, {True, True, True, True}, {True, True, True, True}, {True, True, True, True}, {True, True, True, True}, {True, True, True, True}, {False, True, True, False}, {True, True, True, True}, {True, True, True, True}, {False, True, True, False}, {True, True, True, True}, {True, True, True, True}, {False, True, True, False}, {True, True, True, True}, {True, True, True, True}, {False, True, True, False}, {True, True, True, True}, {True, True, True, True}}
from which there are four wrong solutions.
Am I wrong or is it a Solve[]
bug?
EDIT: through the email address support@wolfram.com I contacted Wolfram Technical Support who in less than three working days have confirmed that it is a bug and have already proceeded to report to their developers.
List@ToRules@Reduce[eqn, {x, y, z, w}]
to get all valid solutions. Filter for those that only have numeric values on the RHS of->
. $\endgroup$Select[sol, And @@ eqn /. # &]
$\endgroup$12.0
bug is fixed. $\endgroup$