solve irrational inequality

asked 2016-04-03 21:52:36 +0100

sophia
77 ●4 ●5 ●12

updated 2016-04-05 13:36:16 +0100

slelievre
17704 ●22 ●160 ●350 http://carva.org/samue...

Is there any way to solve the following inequality for a in Sage?

(It's pretty easy to do in Maple.)

abs(-1/4*a - 1/4*sqrt(a^2 - 30*a + 17) + 1/4) < 1

Using solve doesn't work. I tried using the QEPCAD package, but on SageMathCloud, i get an error: "unable to start QEPCAD".

I tried using sympy-solve and sympy-solveset, and that didn't work either. I plan to raise questions regarding sympy on stackexchange, but if anyone has helpful guidelines on using sagemath's solve vs sympy-solve, that'd be greatly appreciated. My general experience has been that sympy-solve is a lot more capable than sagemath's solve.

Any help would be greatly appreciated. Thank you.

EDIT

Thank you for replying. I am able to use qepcad now, but the problem I'm trying to solve takes a very long time. Here is the code:

var('a')
dnf = solve(abs(-1/4*a - 1/4*sqrt(a^2 - 30*a + 17) + 1/4) <= 1, a)
qf = apply(qepcad_formula.or_, map(qepcad_formula.and_, dnf)) # reformat the solution
qf
qepcad(qf, vars='(a)') # simplify

Any help solving this would be greatly appreciated. Also, would it be possible to update the version of sympy on sagemathcloud? Thank you.

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2 Answers

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answered 2016-04-05 15:02:23 +0100

Harald Schilly
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right now, sympy 1.0 is in the anaconda distribution on smc. so you can use it over there, but that's outside of the confined world of sagemath. I've no idea how you can mix this.

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Expanding @schilly's answer a tiny bit: to use the Sympy in Anaconda on SageMathCloud, open a new Jupyter notebook in one of your SageMathCloud projects, then in the "Kernel" menu pick "Change kernel > Anaconda" (you might have a choice between Anaconda 2 and Anaconda 3). Then you can import sympy and get going.

slelievre ( 2016-04-05 15:52:48 +0100 )edit

Thank you, I am able to access the latest version of sympy now. My original question was on solving the irrational inequality above. Is that not possible in sagemath? Thanks.