## 454 Reputation

19 years, 43 days

## Isn't it too complicated?...

I have no idea if this is the "best" solution, but it looks a lot simpler to me:

`with(plots): with(plottools):`

`A := polygon([[(1/4)*sqrt(2), (1/4)*sqrt(2)], [-(1/4)*sqrt(2), (1/4)*sqrt(2)], [-(1/4)*sqrt(2), -(1/4)*sqrt(2)], [(1/4)*sqrt(2), -(1/4)*sqrt(2)]], color = "DarkMagenta"):B := implicitplot([x^2+y^2 = 1/4], x = -1/2 .. 1/2, y = -1/2 .. 1/2, coloring = ["Crimson", "HotPink"], filledregions = true, axes = none):C := implicitplot([x^2+y^2 = 1/2], x = -(1/2)*sqrt(2) .. (1/2)*sqrt(2), y = -(1/2)*sqrt(2) .. (1/2)*sqrt(2), coloring = ["IndianRed", "DarkOrange"], filledregions = true, axes = none):E := implicitplot([x^2+y^2 = 1], x = -1 .. 1, y = -1 .. 1, coloring = ["gold", "yellow"], filledregions = true, axes = none):`

`F := curve([[1, -1], [1, 1], [-1, 1], [-1, -1], [1, -1]], style = line, thickness = 2):G := curve([[(1/2)*sqrt(2), -(1/2)*sqrt(2)], [(1/2)*sqrt(2), (1/2)*sqrt(2)], [-(1/2)*sqrt(2), (1/2)*sqrt(2)], [-(1/2)*sqrt(2), -(1/2)*sqrt(2)], [(1/2)*sqrt(2), -(1/2)*sqrt(2)]], style = line, thickness = 2):H := curve([[1/2, -1/2], [1/2, 1/2], [-1/2, 1/2], [-1/2, -1/2], [1/2, -1/2]], style = line, thickness = 2):`

and then

`display(A,B,C,E);`

or

`display(A,B,C,E,F,G,H);`

## Isn't it too complicated?...

I have no idea if this is the "best" solution, but it looks a lot simpler to me:

`with(plots): with(plottools):`

`A := polygon([[(1/4)*sqrt(2), (1/4)*sqrt(2)], [-(1/4)*sqrt(2), (1/4)*sqrt(2)], [-(1/4)*sqrt(2), -(1/4)*sqrt(2)], [(1/4)*sqrt(2), -(1/4)*sqrt(2)]], color = "DarkMagenta"):B := implicitplot([x^2+y^2 = 1/4], x = -1/2 .. 1/2, y = -1/2 .. 1/2, coloring = ["Crimson", "HotPink"], filledregions = true, axes = none):C := implicitplot([x^2+y^2 = 1/2], x = -(1/2)*sqrt(2) .. (1/2)*sqrt(2), y = -(1/2)*sqrt(2) .. (1/2)*sqrt(2), coloring = ["IndianRed", "DarkOrange"], filledregions = true, axes = none):E := implicitplot([x^2+y^2 = 1], x = -1 .. 1, y = -1 .. 1, coloring = ["gold", "yellow"], filledregions = true, axes = none):`

`F := curve([[1, -1], [1, 1], [-1, 1], [-1, -1], [1, -1]], style = line, thickness = 2):G := curve([[(1/2)*sqrt(2), -(1/2)*sqrt(2)], [(1/2)*sqrt(2), (1/2)*sqrt(2)], [-(1/2)*sqrt(2), (1/2)*sqrt(2)], [-(1/2)*sqrt(2), -(1/2)*sqrt(2)], [(1/2)*sqrt(2), -(1/2)*sqrt(2)]], style = line, thickness = 2):H := curve([[1/2, -1/2], [1/2, 1/2], [-1/2, 1/2], [-1/2, -1/2], [1/2, -1/2]], style = line, thickness = 2):`

and then

`display(A,B,C,E);`

or

`display(A,B,C,E,F,G,H);`

## Thank you....

@Alejandro Jakubi Thank you for this comment. I think many users would like to be able to turn the automatic simplification off sometimes.

## Thank you....

@Alejandro Jakubi Thank you for this comment. I think many users would like to be able to turn the automatic simplification off sometimes.

## Not exactly....

Thank you for this possibility, however it would be nice if it could look like this:

`some_simplifications(5^2 * 5^(1/2)) = 5^(5/2)`

## Not exactly....

Thank you for this possibility, however it would be nice if it could look like this:

`some_simplifications(5^2 * 5^(1/2)) = 5^(5/2)`

I found similar question asked earlier where Robert Israel gave this solution. I remember I saw it somewhere else some time ago. Since then I am using it from time to time (it is also the second solution I had put into the question). I wondered why `implicitplot` is so ineffective. Never mind, for me it means to use `plottols[transform]` to color the regions.

I found similar question asked earlier where Robert Israel gave this solution. I remember I saw it somewhere else some time ago. Since then I am using it from time to time (it is also the second solution I had put into the question). I wondered why `implicitplot` is so ineffective. Never mind, for me it means to use `plottols[transform]` to color the regions.

and it gets even worse (the color of both "parts" is the same in this case).

and it gets even worse (the color of both "parts" is the same in this case).

## Not working in Maple 16....

In Maple 15 it works fine and I get

However, in Maple 16 I get

## Not working in Maple 16....

In Maple 15 it works fine and I get

However, in Maple 16 I get

## timming...

@dohashi May I ask why I am getting the following timmings?

`restart;p1 := proc(N)      local i, result;       for i from 1 to N       do          result[i] := 2*i-1      end;       op(result); end:  p2 := proc(N)      local i, result;       for i from 1 to N       do          result[i] := 2*i;      end;       op(result); end:  st:=time(): Threads:-Task:-Start( passed, Task=[p1,10^5], Task=[p2,10^5] ): time()-st;                            ` 1.592

2) Doing it sequentially:

`restart;st := time(): for i to 10^5 do results[i] := 2*i-1 end do: for i from 10^5+1 to 2*10^5 do results[i] := 2*i end do: op(result): time()-st;                            ` 0.858

My computer has 4 cores, Win 7 (64bit) and Maple 15.01. I would expect the timmigs vice versa.

Edit: OK, I now probably understand from your last sentence in the previous comment. However, I tried this approach to solve a different problem (5000 independent cycles in a for-loop) and got similar timmings (around 500s sequentially, around 800s parallel). A little disappointing...

## timming...

@dohashi May I ask why I am getting the following timmings?

`restart;p1 := proc(N)      local i, result;       for i from 1 to N       do          result[i] := 2*i-1      end;       op(result); end:  p2 := proc(N)      local i, result;       for i from 1 to N       do          result[i] := 2*i;      end;       op(result); end:  st:=time(): Threads:-Task:-Start( passed, Task=[p1,10^5], Task=[p2,10^5] ): time()-st;                            ` 1.592

2) Doing it sequentially:

`restart;st := time(): for i to 10^5 do results[i] := 2*i-1 end do: for i from 10^5+1 to 2*10^5 do results[i] := 2*i end do: op(result): time()-st;                            ` 0.858

My computer has 4 cores, Win 7 (64bit) and Maple 15.01. I would expect the timmigs vice versa.

Edit: OK, I now probably understand from your last sentence in the previous comment. However, I tried this approach to solve a different problem (5000 independent cycles in a for-loop) and got similar timmings (around 500s sequentially, around 800s parallel). A little disappointing...

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