14
$\begingroup$

I have a quite complex list of equations and inequalities I combine to a boundary condition for my cost function. After investigation of two days I found the bug (I really name it a bug!). One of my equations gets simplified to False, which is not the desired result!

This is one inequality which drives me crazy!

eq = 0.0055356626 + 0.000029 x + 0.000034 y <= 1000.;

All coefficients are machine numbers:

MachineNumberQ /@ Select[Level[eq, {-1}], Head[#] == Real &]
(* {True, True, True, True} *)

Because my variables are real numbers and greater than zero, I have added this assumption to my list of inequalities and equations.

On my system (Win7,64bit, Mathematica 10.1.0 for Microsoft Windows (64-bit) (March 24, 2015))

Simplify[eq, Assumptions -> {x>0, y>0}]

yields False!

Simplify[eq]

just yields 1. x+1.17241 y<=3.44826*10^7, which is ok.

I have tried different settings for ComplexityFunction, but I still get False!

Running

TableForm@Table[Simplify[eq/.x_Real:>n*x,Assumptions->{x>0,y>0}],{n,1,20}]

gives an interesting result:

False
False
False
False
1. x+1.17241 y<=3.44826*10^7
False
False
False
1. x+1.17241 y<=3.44826*10^7
1. x+1.17241 y<=3.44826*10^7
False
False
True
False
True
False
True
1. x+1.17241 y<=3.44826*10^7
True
1. x+1.17241 y<=3.44826*10^7

I really don't understand this! What can I do? Is there something totally wrong with my equation setup?

I have restarted the Kernel twice and tested this on two computers: I get the same result.

Could anyone please verify this on other OS and version? Thanks!

UPDATE

Wolframalpha also shows False, but the evaluation seems to involve complex numbers:

Wolframalpha

UPDATE 2

Using the Assumption {x>=0, y>=0} is working fine ?!

Improve this question
$\endgroup$
6
  • 1
    $\begingroup$ V8 returns True, and V9 and V10 return False (Win8.1-64). IMHO the result should be neither True nor False. Looks like a bug indeed. Have you contacted [email protected]? $\endgroup$
    – Sjoerd C. de Vries
    Jul 1, 2015 at 16:16
  • $\begingroup$ Not yet. I will contact them soon. BTW, FullSimplify gives the same result. $\endgroup$
    – 32u-nd
    Jul 1, 2015 at 16:31
  • $\begingroup$ Confirmed on Linux. v8.0 gives True, v9.0, 10.0, 10.1 gives False. $\endgroup$
    – jkuczm
    Jul 1, 2015 at 22:39
  • $\begingroup$ Note that Refine[eq, {x>0, y>0}] gives slightly different results, and not all correct. Another workaround seems to be to use arbitrary precision numbers: N@Simplify[SetPrecision[eq, $MachinePrecision], Assumptions -> {x > 0, y > 0}]. (V10.1, Mac OSX) $\endgroup$
    – Michael E2
    Jul 2, 2015 at 3:45
  • 3
    $\begingroup$ Support case #3373364 $\endgroup$
    – 32u-nd
    Jul 2, 2015 at 6:46

1 Answer 1

Reset to default
5
$\begingroup$

Extended comment:

$Version

"10.1.0 for Mac OS X x86 (64-bit) (March 24, 2015)"

eq = 0.0055356626 + 0.000029 x + 0.000034 y <= 1000.;

eq // Simplify
  1. x + 1.17241 y <= 3.44826*10^7

Use of assumptions reproduces the problem:

Simplify[eq, {x > 0, y > 0}]

False

However, use of Rationalize avoids the problem with using assumptions

Simplify[eq // Rationalize[#, 0] &, {x > 0, y > 0}]

616842869 (29 x + 34 y) <= 616839454366000000

Which is equivalent to the original

% // N // Simplify
  1. x + 1.17241 y <= 3.44826*10^7
Improve this answer
$\endgroup$
1
  • $\begingroup$ Thanks for your suggestion. It's easier for me to add the SetPrecision approach from Michael E2 to my specific problem, but your answer is totally correct. In parallel, I will wait for the support case to be finished. $\endgroup$
    – 32u-nd
    Jul 6, 2015 at 12:51

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.