Texas Instruments TI-89 Tip List page 405

x2 = 1.1085 5630 2169 9
x3 = 2.1404 2730 947
and we want to find x3. Various permutations of the constraints give these results:
x>2 and x<2.2
2<x and x<2.2
x>low and x<high
low<x and x<high
low<x and high>x
x>low and high>x
If the constraints are numbers, then the conditional ordering is immaterial; nSolve() returned the correct
bounded root. However, if the constraints are local variables, then we must order the conditional
expression such that the independent variable occurs first.
solve() gives similar interesting results:
x>2 and x<2.2
2<x and x<2.2
x>low and x<high
low<x and x<high
low<x and high>x
x>low and high>x
Indpendent variable local declaration
In what may be a related situation, nSolve() results seem to depend on whether or not the independent
variable is declared local. I will use this program as an example:
solvebug(vf)
Func
©Demonstrate nSolve() failure with constraints
©29dec01/dburkett@infinet.com
Local vfs,tapx,t
© Find estimate tapx for solution
ln(1000*(vf-.015))→vfs
polyeval({3.618919682914,⁻31.003830334444,76.737472978603,⁻68.237201523917,262.4613974175
1,84.916629306139},vfs)+polyeval({⁻3.9287348339733⁻7,5.9179552041553⁻5,⁻0.0036896155610
467,0.12308990642018,⁻2.7560332337098,0},1/vfs)→tapx
© Find solution, with bounds from tapx
nSolve(vfts120(t)=vf,t)|t≥tapx-.4 and t≤min({tapx+.4,705.47})
EndFunc
and vfts120() looks like this:
vfts120(ts)
func
© This expression is all one program line.
polyeval({6.177102005557⁻14,⁻3.724921779392⁻11,9.3224938547231⁻9,⁻1.239459227407⁻6,
x3 returned
x3 returned
x3 returned
x1 returned - incorrect!
x1 returned - incorrect!
x3 returned
x3 returned
x3 returned
x3 returned
undef<0 and x = x2 or undef<0 and x = x1 or x = x3
(long solution time, also warning More solutions may exist)
undef<0 and x = x2 or undef<0 and x = x1 or x = x3
(even longer solution time, and warning More solutions may exist)
x3 returned
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