Solving radical inequalities
Can this be solved in Sage?
x-4>sqrt(x-2)
The standard solve method does not work, and neither does solve_ineq.
1 Answer
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.
Your Answer
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Asked: 13 years ago
Seen: 1,200 times
Last updated: Jul 04 '11
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
Yes, I noticed WA could solve it.
solve_ineq even fires an error here
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`.
Can you post your answer as an "answer" to "Can this be solved in Sage"?