Possible bug in Solve function?












7














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?






equation-solving bugs







share|improve this question






















  • 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
    2 hours ago










  • Select[sol, And @@ eqn /. # &]
    – Bob Hanlon
    1 hour ago
















7














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?






equation-solving bugs







share|improve this question






















  • 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
    2 hours ago










  • Select[sol, And @@ eqn /. # &]
    – Bob Hanlon
    1 hour ago














7












7








7


1





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?






equation-solving bugs







share|improve this question













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?






equation-solving bugs




equation-solving bugs






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked 3 hours ago









TeM

1,938620




1,938620












  • 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
    2 hours ago










  • Select[sol, And @@ eqn /. # &]
    – Bob Hanlon
    1 hour ago


















  • 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
    2 hours ago










  • Select[sol, And @@ eqn /. # &]
    – Bob Hanlon
    1 hour ago
















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
2 hours ago




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
2 hours ago












Select[sol, And @@ eqn /. # &]
– Bob Hanlon
1 hour ago




Select[sol, And @@ eqn /. # &]
– Bob Hanlon
1 hour ago










2 Answers
2






active

oldest

votes


















2














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.






share|improve this answer























  • Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
    – TeM
    3 hours ago










  • @TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
    – Szabolcs
    2 hours ago










  • @Szabolcs: Could you direct me where I can do it correctly?
    – TeM
    2 hours ago






  • 1




    @TeM wolfram.com/support/contact
    – Szabolcs
    1 hour ago



















1














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





















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    2 Answers
    2






    active

    oldest

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    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    2














    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.






    share|improve this answer























    • Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
      – TeM
      3 hours ago










    • @TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
      – Szabolcs
      2 hours ago










    • @Szabolcs: Could you direct me where I can do it correctly?
      – TeM
      2 hours ago






    • 1




      @TeM wolfram.com/support/contact
      – Szabolcs
      1 hour ago
















    2














    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.






    share|improve this answer























    • Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
      – TeM
      3 hours ago










    • @TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
      – Szabolcs
      2 hours ago










    • @Szabolcs: Could you direct me where I can do it correctly?
      – TeM
      2 hours ago






    • 1




      @TeM wolfram.com/support/contact
      – Szabolcs
      1 hour ago














    2












    2








    2






    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.






    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.







    share|improve this answer














    share|improve this answer



    share|improve this answer








    edited 45 mins ago

























    answered 3 hours ago









    Somos

    2727




    2727












    • Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
      – TeM
      3 hours ago










    • @TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
      – Szabolcs
      2 hours ago










    • @Szabolcs: Could you direct me where I can do it correctly?
      – TeM
      2 hours ago






    • 1




      @TeM wolfram.com/support/contact
      – Szabolcs
      1 hour ago


















    • Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
      – TeM
      3 hours ago










    • @TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
      – Szabolcs
      2 hours ago










    • @Szabolcs: Could you direct me where I can do it correctly?
      – TeM
      2 hours ago






    • 1




      @TeM wolfram.com/support/contact
      – Szabolcs
      1 hour ago
















    Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
    – TeM
    3 hours ago




    Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
    – TeM
    3 hours ago












    @TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
    – Szabolcs
    2 hours ago




    @TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
    – Szabolcs
    2 hours ago












    @Szabolcs: Could you direct me where I can do it correctly?
    – TeM
    2 hours ago




    @Szabolcs: Could you direct me where I can do it correctly?
    – TeM
    2 hours ago




    1




    1




    @TeM wolfram.com/support/contact
    – Szabolcs
    1 hour ago




    @TeM wolfram.com/support/contact
    – Szabolcs
    1 hour ago











    1














    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


























      1














      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
























        1












        1








        1






        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












        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}







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        answered 4 mins ago









        Okkes Dulgerci

        4,1551816




        4,1551816






























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