## 18909 Reputation

14 years, 34 days

## Re...

@tomleslie  You're right. At first everything worked fine (as in my answer above). But then when I opened the saved document, the correct result appeared not 4, but only 3 times. I repeated these experiments several times and each time the situation worsened. Sometimes from the very beginning there was an incorrect result. All this is very strange.

## Edited version...

@tomleslie  It seems my edited version works relatively stable (see above). I repeated the same 4 times.

## Help...

@denkasyan  1. Yes this is the simplest way to construct three-dimensional graph of the system of  linear  inequalities. See help on PolyhedralSets  package for details.

2. Yes.

## Not work in Maple 2017.3 32 bit...

@tomleslie  For some unknown reason, your code does not work in my Maple 2017.3 32 bit:

## Re...

@denkasyan In  PolyhedralSets  package, a body must be given by non-strict inequalities. But to build a body it does not matter. Maple simply draws the boundaries of this body as parts of the planes. In your example, the body will be part of the plane  y = -20 .

## Re...

@denkasyan  You get the set  {x<0, y=-20, z<0}

## What is the essence of the problem?...

You got some useful tips, but if you want more specific help, then you need to explain in what the essence of the problem is. And more: what do your functions B, P mean, what is loss and so on?

## Equivalent...

If I understand correctly,  until "any condition"  is equivalent to  if "any condition" then break fi , but slightly shorter. The latter variant I use very often.

## Reliable method for analytic functions...

@acer  This example shows the importance of visualization (a plot) in these methods. How else would we know a priori that the result

`Optimization:-Maximize(f, x=0..2*Pi, method = branchandbound);`

is incorrect?

If we want to solve purely programmatically (not looking at the plots), then probably the best method will be a standard approach using the first derivative:

```f:=x->sin(3*x)-cos(7*x)+sin(17*x)+cos(20*x)-sin(67*x):
R:=[RootFinding:-Analytic(diff(f(x),x), x, re=0..2*Pi, im=-1..1)];
Min=min(f~(R)[], f(0), f(2*Pi));
Max=max(f~(R)[], f(0), f(2*Pi));
```

Unfortunately  method=branchandbound  option is not very reliable. The example below shows that both the minimum and maximum are found incorrectly, which is clearly shown by the graph:

f:=sin(3*x)-cos(7*x)+sin(17*x)+cos(20*x)-sin(67*x):
plot(f, x=0..2*Pi, size=[1000,500], numpoints=1000);
Optimization:-Maximize(f, x=0..2*Pi, method = branchandbound);
Optimization:-Minimize(f, x=0..2*Pi, method = branchandbound);

DirectSearch  package successfully copes with the problem:

DirectSearch:-GlobalOptima(f, [x=0..2*Pi]);
DirectSearch:-GlobalOptima(f, [x=0..2*Pi], maximize);

[-4.82606452700204, [x = 3.59004152503469], 191]
[3.40373784598079, [x = 4.94786409954761], 162]

## Re...

@Bilawal  See another way in my answer.

## Bugs...

@Mariusz Iwaniuk  The results for  x>Pi/2  are erroneous:

F:=simplify(unapply(int(sqrt(sin(x)), x=0..T), T)) assuming T>0, T<=Pi;
F(Pi/4), F(Pi/2), F(3*Pi/4), F(Pi):
# Examples
evalf([%])[];

## Re...

@nm  Sorry, I am wrong. I had in mind a syntax error for the numerical solution. I corrected the title.

## Help...

@ahmeng  See help on  value(%)  and  emptysymbol(``)

## Explanation...

@Lali_miani  In Maple, there is a rule: if at least one number is represented as a decimal fraction, for example  0.2  in your example, then Maple calculates the entire expression approximately (by default with 10 significant digits). If you want to have a symbolic representation, then instead of 0.2 you should write 1/5, that is  sin(1/5) . But then in the output Maple just writes the same thing, since sin(1/5)  can not be exactly written in a simpler form, for example, in radicals. But with this expression it is possible to work further, for example to calculate it approximately with some accuracy or to expand in a series, etc.

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