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Solving radical inequalities

asked 2011-06-09 21:15:16 -0500

Eviatar Bach gravatar image

Can this be solved in Sage?

x-4>sqrt(x-2)

The standard solve method does not work, and neither does solve_ineq.

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I've been playing around with this question for a while now. I tried maxima's fourier elimination package with no success. I can't find a solution in Sage. Embarrassingly, WolframAlpha has no trouble: http://www.wolframalpha.com/input/?i=x-4+%3E+sqrt%28x-2%29

benjaminfjones gravatar imagebenjaminfjones ( 2011-06-10 07:45:55 -0500 )edit

Yes, I noticed WA could solve it.

Eviatar Bach gravatar imageEviatar Bach ( 2011-06-10 12:46:41 -0500 )edit

solve_ineq even fires an error here

Juanlu001 gravatar imageJuanlu001 ( 2011-06-15 20:15:27 -0500 )edit

If you read the documentation for `solve_ineq` you'll see that if you simply call `solve_ineq` with an inequality as the argument, it passed it to Maxima assuming that it's a rational inequality (which this is certainly not). If you pass the inequality and variable as lists then it passes them to Maxima using the fourier elimination procedure which can solve some general non-linear inequalities, but not this one unfortunately. See "Case 1" and "Case 2" in the documentation for `solve_ineq`.

benjaminfjones gravatar imagebenjaminfjones ( 2011-06-16 10:46:20 -0500 )edit

Can you post your answer as an "answer" to "Can this be solved in Sage"?

Jason Grout gravatar imageJason Grout ( 2011-07-04 14:18:48 -0500 )edit

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answered 2011-07-04 14:26:40 -0500

benjaminfjones gravatar image

If you read the documentation for solve_ineq you'll see that if you call solve_ineq with an inequality as the argument, it's passed to Maxima assuming that it's a rational inequality (which this is certainly not). If you pass the inequality and variable as lists, Maxima is instructed to use the "Fourier elimination procedure" which can solve some general non-linear inequalities, but not this one unfortunately.

See "Case 1" and "Case 2" in the documentation for solve_ineq.

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Asked: 2011-06-09 21:15:16 -0500

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Last updated: Jul 04 '11