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3 equations with 3 unknown variables - no Show Steps in Wolfram Alpha

ivan ivanov
Posted 9 years ago

Why do equations like "x^2 - y z = 14, y^2 - x z = 28, z^2 - x y = -14" not support step-by-step solutions? I don't need answer when I don`t know how this answer was reached. Fix this, plz.
POSTED BY: ivan ivanov
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Daniel, can you recommend a description of how GroebnerBasis works that can be understood by someone who doesn't have a Ph.D. in math?
POSTED BY: Frank Kampas
POSTED BY: Daniel Lichtblau

Daniel, thanks for the explanation.

I decided to plot all three equations and the solutions.

Show[ContourPlot3D[{x^2 - y z == 14 , y^2 - x z == 28 , 
   z^2 - x y == -14}, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}, 
  ContourStyle -> Opacity[0.5], Mesh -> None], 
 Graphics3D @ {PointSize[.03], {Point[{-3, -5, 1}], 
    Point[{3, 5, -1}]}}]

enter image description here
POSTED BY: Frank Kampas

This is really funny, Simon answered the question that simple, it was not that hard though, thanks for that simon. - Paramount Song
POSTED BY: kristen flindston

Answered what question? (What I am suggesting is that the actual question be reread.)
POSTED BY: Daniel Lichtblau

Well Done!
POSTED BY: Simon Cadrin
ivan ivanov
ivan ivanov
Posted 9 years ago

Yes, I mean "Show steps" button :) Thats a pity that I dont see her in Wolfram Pro Subscription. If it will be added ever, it would be fine
POSTED BY: ivan ivanov

I gather you are referring to the "Show steps" capability in Wolfram|Alpha. If so, I doubt this would be considered as broken. These are not linear equations, and the underlying method used for nonlinear equations (based on a GroebnerBasis computation) does not readily lend itself to "show steps" form. Or at least not one anyone would likely want to see let alone try to make sense of.

This does not rule out the possibility that some classes of systems have "nice" by-hand approaches. I do not know if the system above would fit into such a category but it is possible that it does.
POSTED BY: Daniel Lichtblau
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