[Maxima-bugs] [ maxima-Bugs-3520954 ] Solve returns [] when solutions exists

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Bugs item #3520954, was opened at 2012-04-24 03:43
Message generated for change (Comment added) made by rtoy
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Category: Lisp Core - Solving equations
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Mikael Samsøe Sørensen  (mrverify)
Assigned to: Nobody/Anonymous (nobody)
Summary: Solve returns [] when solutions exists

Initial Comment:
When exponents contain decimals with many figures you risk:

Maxima v. 5.25.1
(%i1)  solve(%e^(0.0057195*x)+%e^(-0.0057195*x)=1,x);
(%o1) []
But solutions exist. Removing a decimal in the exponents:

(%i1)  solve(%e^(0.005719*x)+%e^(-0.005719*x)=1,x);
<< expression too long ... >>

Removing 1 more returns a list of result.

A warning would be nice.

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>Comment By: Raymond Toy (rtoy)
Date: 2012-04-27 08:54

Message:
I think that if you are seeking numerical answers you should use a
numerical method.  find_root works great on this example:

find_root(112.02267*%e^(-0.0057195*x)/(1.80517*%e^(-0.0057195*x)+1)^2-1.97,x,0,1000)

 694.8021925434504

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Comment By: Mikael Samsøe Sørensen  (mrverify)
Date: 2012-04-26 13:40

Message:
Good point. I tried to find a simpler version version of the actual
equation that had the problem. But failed to see that it didn't have
soutions. here is the right equation

solve(112.02267*%e^(-0.0057195*x)/(1.80517*%e^(-0.0057195*x)+1)^2-1.97=0,x)
it has a real solution at x=694.8

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Comment By: Raymond Toy (rtoy)
Date: 2012-04-24 09:02

Message:
A warning about what?

Note also that your expression is equivalent to 2*cosh(.0057195*x)=1, which
has no solution for real x.  There is, of course, a solution for imaginary
values of x, and maxima can solve 2*cosh(.0057195*x)=1.

And maxima 5.27 appears to be finding roots of the original equation, but I
didn't wait.  For .00571, maxima returns a long list, but they're not
actually solutions because x appears on both the lhs and the rhs.  That's a
bug in solve.


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