## 872 Reputation

3 years, 348 days

## ?...

What is the source of this plot? References ?

## Convert(f,piecewise).....

Only workaround.Convert to abs or signum(strange two white lines !) also works.

f := max(1, min(x, 2))+max(1, min(y, 2));

f2 := convert(op(1, f), piecewise)+convert(op(2, f), piecewise);

plots:-inequal(f2 <= 3, x = -5 .. 5, y = -5 .. 5, 'nolines');

f3 := convert(op(1, f), abs)+convert(op(2, f), abs);

plots:-inequal(f3 <= 3, x = -5 .. 5, y = -5 .. 5, 'nolines');

f4 := convert(op(1, f), signum)+convert(op(2, f), signum);

plots:-inequal(f4 <= 3, x = -5 .. 5, y = -5 .. 5, 'nolines');

## I am waiting your positive response. ?...

```Why you Not gives thumbs-up(votes) for correct(good) answers ?
I think you should give an award for someone else's for hard work?```

List question No Votes by you:

and more...

## Probably a bug !...

```(* "11.3.0 for Microsoft Windows (64-bit) (March 7, 2018)" *)

sol = Reduce[{4*x1 + 7*x2 + 6*x3 == 186,
Floor[(1/2)*x1] + Floor[(1/5)*x2] + Floor[(1/3)*x3] == 18,
Floor[(1/5)*x1] + Floor[(1/2)*x2] + Floor[(1/4)*x3] == 21}, {x1,
x2, x3}, Reals];
RegionPlot3D[ImplicitRegion[sol, {x1, x2, x3}], MaxRecursion -> 2, PlotPoints -> 10](* ? *)
```

Gives a empty plot. Maybe user  vv 4397 is right.

2D version:

```eq2 = {Floor[(1/2)*x1] + Floor[(1/5)*x2] +
Floor[-(2/9)*x1 - (7/18)*x2 + 1/3] - 8 == 0,
Floor[(1/5)*x1] + Floor[(1/2)*x2] +
Floor[-(1/6)*x1 - (7/24)*x2 + 3/4] - 14 == 0};
sol2 = Reduce[eq2, {x1, x2}, Reals]

RegionPlot[ImplicitRegion[sol2, {x1, x2}]](*Warning !!! MMA eat's RAM Memory. A bug ? *)

RegionPlot[ImplicitRegion[sol2, {x1, x2}],
Method -> {"DiscretizationMethod" -> "Symbolic"}, MaxRecursion -> 2,
PlotPoints -> 10](*Workaround*)```

## Remove......

Extract real solution using remove command witch user Acer mentioned:

sol := [RootFinding:-Analytic(4^x+1-x^4, x, re = -5 .. 10, im = -2 .. 2)]: remove(is, sol, nonreal);

#[2.09401285285812, -1.05356701067272, 3.98972895158790]

## LogicalExpand......

Answer looks better if you use  LogicalExpand.

```sol = Reduce[{4*x1 + 7*x2 + 6*x3 == 186,
Floor[(1/2)*x1] + Floor[(1/5)*x2] + Floor[(1/3)*x3] == 18,
Floor[(1/5)*x1] + Floor[(1/2)*x2] + Floor[(1/4)*x3] == 21}, {x1,
x2, x3}, Reals] // LogicalExpand

RegionPlot3D[ImplicitRegion[sol, {x1, x2, x3}]]```

## Weakness......

Thanks for showing Maple weakness in: inttrans(fourier(piecewise function)).

I need convert twice piecewise function :P

## Sea of bugs....

Nothing new,Maple leaks  like a sieve.Thanks for info.

## ....

Thank you for quick fix.  :)

Code for Maple below 2018 version.

Integro-Eq_Ver_3A.mw

## ....

@panke

I edited my answer and works as it should.

## Maybe......

Reading this paper on page 87 says better is Trapezoidal rule.

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## ....

I speed up computations by numeric integration.Code still requires polishing(Speed up).

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Works only in Maple 2018 and above.

## ....

I find a way to solve my problem.

Thank you for your contribution.

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