How can this alteration occur by itself and what is the point of doing so? How do I change it back to $\cup$ and $\cap$?

I'm trying to put image in my maplet interface.

I use this following code

Label(Image(cat(currentdir(),"\\Image Folder\File name.png")))

The code work as well when i run the code in worksheet. But it doesn't work since i export the worksheet to .maplet file.

Please help. Thank you

interface(prettyprint=2):
with(ListTools):
with(StringTools):
for xx from 1 to 2 do
xx := 1:
Source := FileTools[Text][ReadFile](cat("C:\\hello\\probability1-200-26042020\\home\\probability",xx,"\\probability",xx,".txt")):
openindex := [SearchAll("[",Source)]:
endindex := [SearchAll("]",Source)]:
beforefiltered := []:
for mm from 1 to nops(openindex) do
if mm > 27 then
beforefiltered := [op(beforefiltered), Chop(substring(Source, openindex[mm]..endindex[mm]))]:
end if:
od:
afterfiltered := []:
for mm in beforefiltered do
if Has(mm,"--") or Has(mm,"|") or Has(mm,"{") or Has(mm,"}") then
dummy := 0:
elif Has(mm,"Root") then
dummy := 0:
else
afterfiltered := [op(afterfiltered),mm]:
end if:
od:
afterfiltered[1];

however after chop still has new line, can not make a beautiful csv format, 

"[b(t,k)+ a
(t,k)*
x(t,k)]"

# I try to export to text first and then use Excel to use "|" as delimiter instead comma as delimiter,
#because b(t,k) has comma "," will separate to open a new column

appendto("C:\\Users\\Student\\Documents\\IQ1-200csv.txt"):
for mm in afterfiltered do
AA := parse(mm):
lprint(xx,"|","hello := [","|",AA[1],"|",AA[2],"|","]:");
od:
od:

Expect csv in format
1,b(t,k)+a(t,k)*x(t,k)
2,a(t,k)+s(t,k)*z(t,k)

Download 01.mw01.mw

i don't know why it doesn't work now.Please help
 

Download ask_maple.mw

Hello, I found this very strange behavior in Maple and I can't explain why this is not working

A little bit of context first:

1. I placed a polygon as a boundary for a section and then two polygons that correspond to inner holes to the first one.
2. Then I proceed to create a regular mesh that places N x M points spread across the region (OK here)
3. A procedure checks weather or not a Point is inside the region, on the borders or in the inner holes (OK here)
4. Then I want to select the closest (but exterior) ones so I can create a path using the mesh points.
 

Here is where I find the issue. I start at a vertex called V[1,1] and I want to arrive at V[1,2] (in the document they are blue solid points marked they are near-vertices near the original polygons). The procedure that I apply finds a path towards the V[1,2] as I was expecting but when the procedure hits the V[1,2] coordinates the while loop does not stop

The condition I wrote was:    while point<>V[1,2] do  where 'point' is correctly generated by another procedure.

This happens in a 40 by 50 mesh but with other configurations it works properly (there are also another kind of errors but it's inherent to lack of optimization in my procedures).

What baffles me is why doesn't it stop the cycle, if I test the condition outside the loop it DOES recognize the points are indeed equal. Is it something in Maple or is it something in my PC?

Thanks to anyone who can see the error or the problem because I don't understand the nature of the problem.

Not_Working.mw

Problem with pdsolve/numeric

Contextualizing:

I created a routine for solving a thermo-mechanical problem. The size of the spatial domain is a function of time and the thermo-mechanical behavior of the structure.

The solution is obtained by discretizing the time domain in n intervals. The thermo-mechanical responses are obtained at each time t[i] =t[i-1]+dt.

The material exhibits elastic and elastoplastic mechanical behavior and thus the problem was divided into two consecutive phases (phase 1 and 2).

The heat problem is nonlinear because the thermal properties are variable (termal conductivity, specific heat, and density).

The problem:

In phase 2, the pdsolve/numeric command returns an error for the solution of the heat conduction equation (equation called pde1). I believe this error is related to the derivative of thermal conductivity k(x1) (piecewise function).

I tested many alternatives (I wrote the pde1 equation in two different ways), I checked the routine many times and I don't understand the reason for the error. With each attempt, the command returns a different error.

Thanks for your attention and help.

Problem.mw

Hi everyone.

I have a 2D function and I wanna after Differentiating from it with respect to tau (at any amount of sigma value) and equaling this derivative to zero solve the infinite system of equations.

P[n](tau)==LegendreP(n - 1/2, cosh(tau)) , Q[n](tau)==LegendreQ(n - 1/2, cosh(tau)) 

are Legendre function.

Thanks in advanced

FUNCTION_f.mw

Download FUNCTION_f.mw

P1 := x^2+y^2-4:
P2 := y^2-2*x+2:

Original question is find CAD of (some y)[P1 <0 and P2 <0]

how to use maple 12 and maple 2015 to find Q1,Q2,Q3 which are projection of P1 and P2

my book show sample points are [-4,-1-sqrt(7),-3,-2,0,1,3/2,-1+sqrt(7),9/5,2,3]
but FindSamples result is not the same with my book, is it my book wrong or FindSamples function wrong?
I find result of my script is the same as book's quantifier position at 7,8,9 though sample points has little different

how to generalize my following script to multiple variables x, y, z, and more ?

and

I compare with maple 2015 result are different from my book solution, is maple 2015 more advanced version CAD? 

with(ListTools):

P1 := x^2+y^2-4:
P2 := y^2-2*x+2:

Q1 := x^2 + 2*x - 6;
Q2 := x^2 - 4;
Q3 := x - 1;

sourcesamples := sort(evalf([solve(Q1), solve(Q2), solve(Q3)]),`<`);

FindSamples:=proc(sourcesamples)
local N, P;
N:=nops(sourcesamples);
P:=proc(a,b)
local a1, b1, m1, n, m;
if a=b then error "Should be a<>b" fi;
a1,b1:=op(convert(sort([a,b],(x,y)->evalf(x)<evalf(y)),rational));
count := 0:
for n from 1 do
m1:=a1*n;
m:=`if`(type(m1,integer),m1+1,ceil(m1));
count := count + 1:
if is(m/n>a1) and is(m/n<b1) then return m/n fi;
od;
print("count=",count);
end proc:
[ceil(sourcesamples[1])-1, seq(op([sourcesamples[i],P(sourcesamples[i],sourcesamples[i+1])]), i=1..N-1),sourcesamples[N],floor(sourcesamples[N])+1];
end proc:

RemoveComplex := proc(yy)
local result, k:
result := []:
for k in yy do
if Im(k) = 0 then
result := [op(result), k]:
end if:
od:
if result = [] then
result := []:
end if:
return result:
end proc:

Joinsolution := proc(param1, param2group)
local result, k:
result := []:
for k in param2group do
result := [op(result), [param1, k]]:
od:
return result:
end proc:

CADsamples := FindSamples(sourcesamples):
CADresult1 := []:
for mm in CADsamples do
#print(mm):
if MakeUnique(RemoveComplex([solve(subs(x=mm, P1)), solve(subs(x=mm, P2))])) = [] then
CADresult1 := [op(CADresult1), op(Joinsolution(mm,[0]))];
else
CADresult1 := [op(CADresult1), op(Joinsolution(mm,FindSamples(sort(evalf(MakeUnique(RemoveComplex([solve(subs(x=mm, P1)), solve(subs(x=mm, P2))]))),`<`))))];
end if:
od:
CADresult1;

for mm in CADresult1 do
if subs(x=mm[1],subs(y=mm[2], P1)) < 0 and subs(x=mm[1],subs(y=mm[2], P2)) < 0 then
print("solution ", mm, SearchAll(mm[1],CADsamples), evalf(mm)):
end if:
od:

Compare with

with(RegularChains):
with(ChainTools):
with(MatrixTools):
with(ConstructibleSetTools):
with(ParametricSystemTools):
with(SemiAlgebraicSetTools):
with(FastArithmeticTools):
R := PolynomialRing([x,y]):
sys := [x^2+y^2-4,y^2-2*x+2]:
N := []:
P := []: 
H := [x]:
dec := RealTriangularize(sys,N,P,H,R):
proj := Projection(sys, N, P, H, 1, R);
Display(dec, R);

P := SamplePoints(sys, R);
Display(P, R);
cad := CylindricalAlgebraicDecompose(sys, R);
 

Hello everyone, my computer installed Maple 2016, 2020 and set Maple 2016 as default opening files .mw, .mws. How to change default to Maple 2020 . I tried searching on Google but not found.

Thank you very much.

How I can prove the following equation in red box.

Also, Pn(v) and qn(v) are the real combinations of half-integer Legendre functions.

For more details please see 

https://math.stackexchange.com/questions/2746660/potential-flow-around-a-torus-laplace-equation-in-toroidal-coordinates/3809487#3809487

Determine how many transitive relations there are on a set with n elements for all positive integers n with n<=7.

Custom Palettes and Palette Entries on windows Pro 7 
Read a tutorial from a user @les 185

https://www.mapleprimes.com/posts/207781-Custom-Palettes-And-Palette-Entries

Is this still valid this tutorial from 2015  in the current version of Maple ?
This seems to be userunfriendly.

This is strange.  It is true that this function (a modular form) goes to infinity as t -> 0 from the right.
But should plotting it it do this?

    |\^/|     Maple 2019 (APPLE UNIVERSAL OSX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2019
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> version();
 User Interface: 1435526
         Kernel: 1435526
        Library: 1435526
                                    1435526

> exp(-Pi*t/3)^8*JacobiTheta3(Pi*(4*I*t+1)/2,
> exp(-12*Pi*t))^8/(exp(-Pi*t/6)^4*
> JacobiTheta3(Pi*(2*I*t + 1)/2, exp(-6*Pi*t))^4);
                 Pi t 8              Pi (4 I t + 1)                8
           exp(- ----)  JacobiTheta3(--------------, exp(-12 Pi t))
                  3                        2
           ---------------------------------------------------------
                 Pi t 4              Pi (2 I t + 1)               4
           exp(- ----)  JacobiTheta3(--------------, exp(-6 Pi t))
                  6                        2

> plot(%,t=0..4);
memory used=48.4MB, alloc=45.3MB, time=0.45
Execution stopped: Stack limit reached.