## 1172 Reputation

12 years, 186 days

## A workable method to check inside or ou...

I came across this approach a couple of years ago for testing if a point is inside or oudside a polyogon.

The theory is given here Topology, Winding Numbers and Signed Area | Algebraic Calculus One | Wild Egg - YouTube

Basically you need to setup a garunteed exterior point to test with. Then ckeck is the segment from thr exterior point to the point of interest crosses any edges of the polyogon. The crossing number can be -1, 0, 1.   Sum the crossing numbers for all edges. If 0 then the point is on the outside else non zero means the point is on inside. The can handle non convex polygons.

Q is a random exterior point . P is the point of interest to check whether inside or outside.

Polygon Vertices

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Points for checking

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## As follows...

You should read the help on taylor and % as I have used that too

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The pattern is a geometric series based on

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## Half Circle plot...

This will plot the half circle.

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## local e...

Set e to be local is one way to suppress the warning.

local e

a := e^5;

e := 2;

a;
32

## A step by step approach....

This is not as efficient as the other solutions. It just shows more of the steps involved.

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## My solution corrected...

I deleted my original answer to correct my solution. This is not as efficient as @Rouben Rostamian . It just expands out the steps involved.

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## This is one way of showing what you requ...

If you have any questions just ask.

Edit:- Corrected my answer as I missed the 1/(x^4+1)

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## Use the solve or fsolve command...

`solve(x^4-x^3-3x^2-x+12,x)`

This will give you the vlues of x

if you just want numerical answers.

`fsolve(x^4-x^3-3x^2-x+12,x)`

Hope this helps

## A couple of ways...

Here are two possible ways. Solve the equation before the variables are assigned. e.g. xb:=1000

You can then assign the variables.

or

Use eval and locally give the variables values.

Note your equation has "ab" eb=ab*yb*db*x but "ab" was not assigned you used "xb" so I changed the equation to that.

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## op command. Is this what you want?...

This is a way to add elements to a list.

op[L] removes the brackets from the list. so you get 3,5,7,-6,4,2 to start with. Then ,i^2, i^3 tags on 1,1. The the [   ] reforms a  list. So after 1st loop you now have L as [3,5,7,-6,4,2,1,1]. and it continues

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## The value of exp(-2t) is very small...

`eq := 2*exp(-2*t) + 4*t = 127:`

I am not at Maple PC  at the moment.

But looking at the equation,

we see that this your equation isequivalent to exp(-2t) +2t=63.5

as a first approximation 2t=63.5

so t =31.75

exp(-2x31.75) is going to be very small. i.e 5.9000905*10^-29 (from my TI-68 calculator)

Hope that helps.

## " is " also works...

Look up the " is " command. Using it with the  " if " command works to evasluate you conditions. Plus a few corection to you code as @tomleslie did.

```potfeld := (x, y) -> 1/sqrt(y^2 + x^2);
for i to 5 do
for j to 3 do
if is(sqrt(i^2 + j^2) <> 0 and sqrt((i - 2)^2 + j^2) <> 0 and potfeld(i, j) < 3)
then
P[i, j] := plots:-arrow(<i, j>, <D[1](potfeld)(i, j), D[2](potfeld)(i, j)>);
else P[i, j] := plots:-arrow(<i, j>, <0.1, 0.1>);
end if;
end do;
end do;
Pseq := seq(seq([P[k, l]], k = 1 .. 5), l = 1 .. 3);
plots:-display(Pseq, view = [1 .. 5, 1 .. 3], scaling = constrained);```

The question you have asked requires a decent bit of study.

I googled "Transformations to hyperbolic plane in Maple"

There are probably many more.

Hyperbolic Patterns index page (umn.edu)

Hayter_Hyperbolic_report.pdf (dur.ac.uk)

Geometry of Curves and Surfaces with MAPLE - Vladimir Rovenski - Google Books

This one I did actually do several years ago.

Esher’s Limit Circle IV rendered on the complex upper half-plane | Open System - Ark's blog (arkadiusz-jadczyk.eu)

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