Possible bug in Solve function?












15














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.






equation-solving bugs







share|improve this question




















  • 1




    You could use 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 ->.
    – Szabolcs
    Jan 5 at 22:30










  • Select[sol, And @@ eqn /. # &]
    – Bob Hanlon
    Jan 5 at 23:53






  • 5




    Next time, please do not add the bugs tag yourself on a question. The tag is only supposed to be added after your observations have been confirmed by other users.
    – J. M. is computer-less♦
    Jan 6 at 2:45
















15














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.






equation-solving bugs







share|improve this question




















  • 1




    You could use 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 ->.
    – Szabolcs
    Jan 5 at 22:30










  • Select[sol, And @@ eqn /. # &]
    – Bob Hanlon
    Jan 5 at 23:53






  • 5




    Next time, please do not add the bugs tag yourself on a question. The tag is only supposed to be added after your observations have been confirmed by other users.
    – J. M. is computer-less♦
    Jan 6 at 2:45














15












15








15


2





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.






equation-solving bugs







share|improve this question















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.






equation-solving bugs




equation-solving bugs






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 15 hours ago









Szabolcs

158k13432928




158k13432928










asked Jan 5 at 21:50









TeMTeM

1,990621




1,990621








  • 1




    You could use 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 ->.
    – Szabolcs
    Jan 5 at 22:30










  • Select[sol, And @@ eqn /. # &]
    – Bob Hanlon
    Jan 5 at 23:53






  • 5




    Next time, please do not add the bugs tag yourself on a question. The tag is only supposed to be added after your observations have been confirmed by other users.
    – J. M. is computer-less♦
    Jan 6 at 2:45














  • 1




    You could use 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 ->.
    – Szabolcs
    Jan 5 at 22:30










  • Select[sol, And @@ eqn /. # &]
    – Bob Hanlon
    Jan 5 at 23:53






  • 5




    Next time, please do not add the bugs tag yourself on a question. The tag is only supposed to be added after your observations have been confirmed by other users.
    – J. M. is computer-less♦
    Jan 6 at 2:45








1




1




You could use 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 ->.
– Szabolcs
Jan 5 at 22:30




You could use 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 ->.
– Szabolcs
Jan 5 at 22:30












Select[sol, And @@ eqn /. # &]
– Bob Hanlon
Jan 5 at 23:53




Select[sol, And @@ eqn /. # &]
– Bob Hanlon
Jan 5 at 23:53




5




5




Next time, please do not add the bugs tag yourself on a question. The tag is only supposed to be added after your observations have been confirmed by other users.
– J. M. is computer-less♦
Jan 6 at 2:45




Next time, please do not add the bugs tag yourself on a question. The tag is only supposed to be added after your observations have been confirmed by other users.
– J. M. is computer-less♦
Jan 6 at 2:45










2 Answers
2






active

oldest

votes


















5














Thanks for asking! In version 9.0 only 16 solutions are returned and they are all valid. In version 10.2 there are 20 solutions, with the extra 4 all being invalid. Contragulations! I think you found a bug. You may want to click "Help", then "Give Feedback...", and then fill out the form in your browser to report.



As another answer notes, you can always try Reduce instead which may give better results in some cases, but Solve is usually what you want.






share|improve this answer























  • Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
    – TeM
    Jan 5 at 22:11






  • 2




    @TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
    – Szabolcs
    Jan 5 at 22:31










  • @Szabolcs: Could you direct me where I can do it correctly?
    – TeM
    Jan 5 at 22:44






  • 4




    @TeM wolfram.com/support/contact
    – Szabolcs
    Jan 5 at 23:49



















4














You can use Reduce



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};

red = Reduce[eqn, Backsubstitution -> True]



$left(z=0land x=0land w=-sqrt{1-y^2}right)lor left(z=0land x=0land w=sqrt{1-y^2}right)lor left(z=0land y=0land
w=-sqrt{1-x^2}right)lor left(z=0land y=0land w=sqrt{1-x^2}right)lor (z=0land y=-1land x=0land w=0)lor (z=0land y=0land x=0land
w=-1)lor (z=0land y=0land x=0land w=1)lor (z=0land y=1land x=0land w=0)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land
x=-frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)\
lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)$




First@eqn //. {ToRules[red]}



{True, True, True, True, True, True, True, True, True, True, True,
True, True, True, True, True}







share|improve this answer





















  • Yes, of course, I had already tried. I was almost certain it was a bug from Solve, so I pointed out. Thank you very much anyway, always very kind!
    – TeM
    Jan 6 at 1:14






  • 4




    I believe Solve use the function Reduce under the hood. when you remove Backsubstitution -> True, you'll find implicit solution, somehow Solve messes up somewhere and it is definitely a bug..
    – Okkes Dulgerci
    Jan 6 at 1:18











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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes









5














Thanks for asking! In version 9.0 only 16 solutions are returned and they are all valid. In version 10.2 there are 20 solutions, with the extra 4 all being invalid. Contragulations! I think you found a bug. You may want to click "Help", then "Give Feedback...", and then fill out the form in your browser to report.



As another answer notes, you can always try Reduce instead which may give better results in some cases, but Solve is usually what you want.






share|improve this answer























  • Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
    – TeM
    Jan 5 at 22:11






  • 2




    @TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
    – Szabolcs
    Jan 5 at 22:31










  • @Szabolcs: Could you direct me where I can do it correctly?
    – TeM
    Jan 5 at 22:44






  • 4




    @TeM wolfram.com/support/contact
    – Szabolcs
    Jan 5 at 23:49
















5














Thanks for asking! In version 9.0 only 16 solutions are returned and they are all valid. In version 10.2 there are 20 solutions, with the extra 4 all being invalid. Contragulations! I think you found a bug. You may want to click "Help", then "Give Feedback...", and then fill out the form in your browser to report.



As another answer notes, you can always try Reduce instead which may give better results in some cases, but Solve is usually what you want.






share|improve this answer























  • Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
    – TeM
    Jan 5 at 22:11






  • 2




    @TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
    – Szabolcs
    Jan 5 at 22:31










  • @Szabolcs: Could you direct me where I can do it correctly?
    – TeM
    Jan 5 at 22:44






  • 4




    @TeM wolfram.com/support/contact
    – Szabolcs
    Jan 5 at 23:49














5












5








5






Thanks for asking! In version 9.0 only 16 solutions are returned and they are all valid. In version 10.2 there are 20 solutions, with the extra 4 all being invalid. Contragulations! I think you found a bug. You may want to click "Help", then "Give Feedback...", and then fill out the form in your browser to report.



As another answer notes, you can always try Reduce instead which may give better results in some cases, but Solve is usually what you want.






share|improve this answer














Thanks for asking! In version 9.0 only 16 solutions are returned and they are all valid. In version 10.2 there are 20 solutions, with the extra 4 all being invalid. Contragulations! I think you found a bug. You may want to click "Help", then "Give Feedback...", and then fill out the form in your browser to report.



As another answer notes, you can always try Reduce instead which may give better results in some cases, but Solve is usually what you want.







share|improve this answer














share|improve this answer



share|improve this answer








edited Jan 6 at 1:16

























answered Jan 5 at 22:05









SomosSomos

3628




3628












  • Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
    – TeM
    Jan 5 at 22:11






  • 2




    @TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
    – Szabolcs
    Jan 5 at 22:31










  • @Szabolcs: Could you direct me where I can do it correctly?
    – TeM
    Jan 5 at 22:44






  • 4




    @TeM wolfram.com/support/contact
    – Szabolcs
    Jan 5 at 23:49


















  • Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
    – TeM
    Jan 5 at 22:11






  • 2




    @TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
    – Szabolcs
    Jan 5 at 22:31










  • @Szabolcs: Could you direct me where I can do it correctly?
    – TeM
    Jan 5 at 22:44






  • 4




    @TeM wolfram.com/support/contact
    – Szabolcs
    Jan 5 at 23:49
















Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
– TeM
Jan 5 at 22:11




Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
– TeM
Jan 5 at 22:11




2




2




@TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
– Szabolcs
Jan 5 at 22:31




@TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
– Szabolcs
Jan 5 at 22:31












@Szabolcs: Could you direct me where I can do it correctly?
– TeM
Jan 5 at 22:44




@Szabolcs: Could you direct me where I can do it correctly?
– TeM
Jan 5 at 22:44




4




4




@TeM wolfram.com/support/contact
– Szabolcs
Jan 5 at 23:49




@TeM wolfram.com/support/contact
– Szabolcs
Jan 5 at 23:49











4














You can use Reduce



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};

red = Reduce[eqn, Backsubstitution -> True]



$left(z=0land x=0land w=-sqrt{1-y^2}right)lor left(z=0land x=0land w=sqrt{1-y^2}right)lor left(z=0land y=0land
w=-sqrt{1-x^2}right)lor left(z=0land y=0land w=sqrt{1-x^2}right)lor (z=0land y=-1land x=0land w=0)lor (z=0land y=0land x=0land
w=-1)lor (z=0land y=0land x=0land w=1)lor (z=0land y=1land x=0land w=0)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land
x=-frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)\
lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)$




First@eqn //. {ToRules[red]}



{True, True, True, True, True, True, True, True, True, True, True,
True, True, True, True, True}







share|improve this answer





















  • Yes, of course, I had already tried. I was almost certain it was a bug from Solve, so I pointed out. Thank you very much anyway, always very kind!
    – TeM
    Jan 6 at 1:14






  • 4




    I believe Solve use the function Reduce under the hood. when you remove Backsubstitution -> True, you'll find implicit solution, somehow Solve messes up somewhere and it is definitely a bug..
    – Okkes Dulgerci
    Jan 6 at 1:18
















4














You can use Reduce



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};

red = Reduce[eqn, Backsubstitution -> True]



$left(z=0land x=0land w=-sqrt{1-y^2}right)lor left(z=0land x=0land w=sqrt{1-y^2}right)lor left(z=0land y=0land
w=-sqrt{1-x^2}right)lor left(z=0land y=0land w=sqrt{1-x^2}right)lor (z=0land y=-1land x=0land w=0)lor (z=0land y=0land x=0land
w=-1)lor (z=0land y=0land x=0land w=1)lor (z=0land y=1land x=0land w=0)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land
x=-frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)\
lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)$




First@eqn //. {ToRules[red]}



{True, True, True, True, True, True, True, True, True, True, True,
True, True, True, True, True}







share|improve this answer





















  • Yes, of course, I had already tried. I was almost certain it was a bug from Solve, so I pointed out. Thank you very much anyway, always very kind!
    – TeM
    Jan 6 at 1:14






  • 4




    I believe Solve use the function Reduce under the hood. when you remove Backsubstitution -> True, you'll find implicit solution, somehow Solve messes up somewhere and it is definitely a bug..
    – Okkes Dulgerci
    Jan 6 at 1:18














4












4








4






You can use Reduce



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};

red = Reduce[eqn, Backsubstitution -> True]



$left(z=0land x=0land w=-sqrt{1-y^2}right)lor left(z=0land x=0land w=sqrt{1-y^2}right)lor left(z=0land y=0land
w=-sqrt{1-x^2}right)lor left(z=0land y=0land w=sqrt{1-x^2}right)lor (z=0land y=-1land x=0land w=0)lor (z=0land y=0land x=0land
w=-1)lor (z=0land y=0land x=0land w=1)lor (z=0land y=1land x=0land w=0)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land
x=-frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)\
lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)$




First@eqn //. {ToRules[red]}



{True, True, True, True, True, True, True, True, True, True, True,
True, True, True, True, True}







share|improve this answer












You can use Reduce



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};

red = Reduce[eqn, Backsubstitution -> True]



$left(z=0land x=0land w=-sqrt{1-y^2}right)lor left(z=0land x=0land w=sqrt{1-y^2}right)lor left(z=0land y=0land
w=-sqrt{1-x^2}right)lor left(z=0land y=0land w=sqrt{1-x^2}right)lor (z=0land y=-1land x=0land w=0)lor (z=0land y=0land x=0land
w=-1)lor (z=0land y=0land x=0land w=1)lor (z=0land y=1land x=0land w=0)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land
x=-frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)\
lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)$




First@eqn //. {ToRules[red]}



{True, True, True, True, True, True, True, True, True, True, True,
True, True, True, True, True}








share|improve this answer












share|improve this answer



share|improve this answer










answered Jan 6 at 1:09









Okkes DulgerciOkkes Dulgerci

4,1851816




4,1851816












  • Yes, of course, I had already tried. I was almost certain it was a bug from Solve, so I pointed out. Thank you very much anyway, always very kind!
    – TeM
    Jan 6 at 1:14






  • 4




    I believe Solve use the function Reduce under the hood. when you remove Backsubstitution -> True, you'll find implicit solution, somehow Solve messes up somewhere and it is definitely a bug..
    – Okkes Dulgerci
    Jan 6 at 1:18


















  • Yes, of course, I had already tried. I was almost certain it was a bug from Solve, so I pointed out. Thank you very much anyway, always very kind!
    – TeM
    Jan 6 at 1:14






  • 4




    I believe Solve use the function Reduce under the hood. when you remove Backsubstitution -> True, you'll find implicit solution, somehow Solve messes up somewhere and it is definitely a bug..
    – Okkes Dulgerci
    Jan 6 at 1:18
















Yes, of course, I had already tried. I was almost certain it was a bug from Solve, so I pointed out. Thank you very much anyway, always very kind!
– TeM
Jan 6 at 1:14




Yes, of course, I had already tried. I was almost certain it was a bug from Solve, so I pointed out. Thank you very much anyway, always very kind!
– TeM
Jan 6 at 1:14




4




4




I believe Solve use the function Reduce under the hood. when you remove Backsubstitution -> True, you'll find implicit solution, somehow Solve messes up somewhere and it is definitely a bug..
– Okkes Dulgerci
Jan 6 at 1:18




I believe Solve use the function Reduce under the hood. when you remove Backsubstitution -> True, you'll find implicit solution, somehow Solve messes up somewhere and it is definitely a bug..
– Okkes Dulgerci
Jan 6 at 1:18


















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