MaplePrimes - answers and comments on Question, finding the range that two functions are approximately equal within a certain percent.

Solve an inequality

longrob — Mon, 27 Jun 2011 02:34:13 Z

I'm not sure what you mean by "within a certain percentage". A percentage of what ? Leaving that aside, would something like this achieve what you want ?

f:=x^2:g:=x:

iq:=abs(f-g)<1:

solve(iq,x):

convert(%,list);

[Open(1/2-(1/2)*sqrt(5)), Open((1/2)*sqrt(5)+1/2)]

Another way

Markiyan Hirnyk — Mon, 27 Jun 2011 12:16:21 Z

I tried to follow the request of the questioner using the fsolve command. I took f := sin(x) and g := sin(1.1*x) on x=0..2*Pi . Here is the result:

We see the answer: the union of [0,1.99653630] and [4.260603701,4.694353420]

Download range1.mw

It is not so simple

Markiyan Hirnyk — Mon, 27 Jun 2011 10:27:05 Z

In many cases your suggestion does not work. For example,

> restart; f := sin(x):
> g := sin(1.1*x):
> iq := abs(f-g) < 0.1e-2:
> solve({iq, x > 0, x < 2*Pi}, allsolutions);

Warning, solutions may have been lost

@Markiyan Hirnyk Obviously it depends

longrob — Mon, 27 Jun 2011 11:28:48 Z

@Markiyan Hirnyk

Obviously it depends on the particular functions, but since the poster didn't specify any, it's hard to know what he wants. I find it's usually best to start simple, particularly when the poster says he is new to Maple.

It may be hard to provide code that works for all possible scenarios (sinusoids, complex-valued functions etc)

Edit: mapleprimes cutting off part of the reply

Edit

Markiyan Hirnyk — Mon, 27 Jun 2011 13:19:41 Z

@longrob

Concerning the edit, see a screenshot screenshot.doc

One more variant

Markiyan Hirnyk — Mon, 27 Jun 2011 12:54:07 Z

Here we take into consideration the relative deviation:

Download range4.mw

The answer: the union of [0,1.963413044] and [4.282687073,4.694320635].

If the number of the solutions is big, then in order to find that a simple code is needed.

PS. If you have only a graph of two functions, then such a problem seems to be veeeery hard.

Edit. PS was combined with the code so PPS became PS and range3.mw was replaced by range4.mw .