Gathering points to obtain Maltese cross...

restart:with(LinearAlgebra):with(plots):with(geometry):with(plottools): On appelle alpha la moitié de l'angle de rotation de la roue menée par tour de roue menante. alpha=Pi/n en radians? soit Pi/8 pour 8 rainures.. On a alors les relations suivantes entre l'entaxe E, le rayon de la roue ùenante R1 et le rayon de la roue menée R2 : R1=E.sin(alpha), R2=E*cos(alpha) Intersection du cercle (O,R2) avec la droite tan(phi)x-r/cos(phi), on obtient les coordonnées de P3 sol:=allvalues(solve([tan(phi)*x-r/cos(phi)=y,y^2+x^2=R2^2],[x,y])): Intersection de 2 cercles sol1:=allvalues(solve([(x-E)^2+y^2=(R-a)^2,y^2+x^2=R2^2],[x,y])): Coordonnées des points du pourtour de l'élément de croix Oo:=point([0,0]): phi:=Pi/8:R2:=5:r:=1/4:E:=R2/cos(phi):evalf(%):R:=R2*tan(phi):evalf(%):a:=0.5: P1:=point([(R2/2-r)*cos(phi),(R2/2-r)*sin(phi)]): P2:=point([(R2/2)*cos(phi)+r*sin(phi),(R2/2)*sin(phi)-r*cos(phi)]): xP2:=(R2/2)*cos(phi)+r*sin(phi):yP2:=(R2/2)*sin(phi)-r*cos(phi): xP1:=(R2/2-r)*cos(phi):yP1:=(R2/2-r)*sin(phi): Equation paramétrique du segment OP1 (t varie de 0 à 1) ; x1:=t*(0-xP1)+xP1: y1:=t*(0-yP1)+yP1: n1:=5: dt:=1/(n1-1):#t varie entre 0 et 1 for i to n1 do tau:=(i-1)*dt: xx[i]:=evalf(subs(t=tau,x1)): yy[i]:=evalf(subs(t=tau,y1)): #print(i,xx[i],yy[i]); od: Equation paramétrique du quart de cercle P1P2 de la rainure (t varie de 0 à 1) x2:=R2/2*cos(phi)+r*cos(t):#attention au sens de rotation du parcours de l'objet y2:=R2/2*sin(phi)+r*sin(t): n2:=6: dt:=Pi/2/(n2-1):#arc de Pi/2 for i to n2 do tau:=phi-Pi+(i-1)*dt: xx[i]:=evalf(subs(t=tau,x2)): yy[i]:=evalf(subs(t=tau,y2)): od: for i to n2 do Vector[row]([i,xx[i],yy[i]]) od: droite:=plot((tan(phi)*x-r/cos(phi),x=0..3),linestyle=dot,color=blue): sol: xP3:=evalf(subs(op(1,sol),x)):yP3:=evalf(subs(op(1,sol),y)): xP2:yP2: xP4:=evalf(subs(op(1,sol1),x)):yP4:=evalf(subs(op(1,sol1),y)): xP5:=E-(R-a):yP5:=0: x3:=t*(xP3-xP2)+xP2: y3:=t*(yP3-yP2)+yP2: n3:=10: dt:=1/(n3-1):#t varie entre 0 et 1 for i to n3 do tau:=(i-1)*dt: xx[i+n2]:=evalf(subs(t=tau,x3)): yy[i+n2]:=evalf(subs(t=tau,y3)): od: for i to n3 do Vector[row]([i,xx[i],yy[i]]) od: x4:=xP5+R-a+(R-a)*cos(t):#attention au sens de rotation du parcours de l'objet y4:=(R-a)*sin(t): n4:=11: eta:=arcsin(yP4/(R-a)): dt:=(-eta)/(n2-1)/2:#arc de Pi/2 for i to n4 do tau:=(Pi+eta)+(i-1)*dt:#recherche de tau ? xx[i+n2+n3]:=evalf(subs(t=-tau,x4)): yy[i+n2+n3]:=evalf(subs(t=-tau,y4)): od: for i to n4 do Vector[row]([i,xx[i],yy[i]]) od: n:=n2+n3+n4; n := 27 for i to n do Vector[row]([i,xx[i],yy[i]]) od: figure:=NULL: for i from 0 to n do xx:=0:yy:=0: figure:=figure,[xx[i],yy[i]]: #print(i,xx[i],yy[i]); od: polygonplot([figure],scaling=constrained,color=yellow,view=[-0.1..5,-0.1..3]): for i to n do X[i]:=xx[i]: Y[i]:=yy[i] od: d1:=plottools[disk]([xP1,yP1],0.05,color=blue): d2:=plottools[disk]([xP2,yP2],0.05,color=red): d3:=plottools[disk]([xP3,yP3],0.05,color=green): d4:=plottools[disk]([xP4,yP4],0.05,color=green): d5:=plottools[disk]([xP5,yP5],0.05,color=green): fig:=pointplot([figure],scaling=constrained): Po:=pointplot([[xP1,yP1],[xP2,yP2],[xP3,yP3]],color = blue, symbol = asterisk): Cir:=plot([R2*cos(t),R2*sin(t),t=0..Pi/2],color=black): Arc:=plot([E+(R-a)*cos(t),(R-a)*sin(t),t=3*Pi/4..Pi],linestyle=dot,color=blue): textplot({[1, 2, "one point in 2-D"], [3, 2, "second point in 2-D"]}): texte:=textplot([[xP1-0.2,yP1,"P1"],[xP2,yP2-0.3,"P2"],[xP3+0.2,yP3+0.2,"P3"], [xP4+0.2,yP4+0.1,"P4"],[xP5-0.2,yP5+0.2,"P5"]]): display({Arc,Cir,d1,d2,d3,d4,d5,Po,fig,droite,texte},scaling=constrained,view=[-1..7,-1..6]): with(plottools): printlevel:=3: Miroir : symétrie par rapport à l'axes des x for i from 0 to n/2 do tt:=yy[i]: yy[i]:=yy[n-i+1]: yy[n-i+1]:=tt: tt:=xx[i]: xx[i]:=xx[n-i+1]: xx[n-i+1]:=tt od: for i from 0 to n-1 do xx[2*n-i]:=xx[i]: yy[2*n-i]:=-yy[i]: #print(i,xx[i],yy[i]) od: Poly:=NULL: for i from 0 to 2*n-1 do xx:=0:yy:=0: Poly:=Poly,[xx[i],yy[i]]:od: polygonplot([Poly],color=yellow,scaling=constrained): pointplot([Poly],color = blue, scaling=constrained,symbol = asterisk,view=[-1..5,-3..3]): Rotation unassign('xt','yt'): #gc(): zt:=8:#8 rainures ou faisceaux xt:=Vector(63,[]): yt:=Vector(63,[]): xt:=Vector((2*n-1),zt,[]): yt:=Vector((2*n-1),zt,[]): j:=0: for k from 0 to zt-1 do j:=0: phi:=2*Pi*k/zt: cs:=cos(phi): sn:=sin(phi): for kk from 1 to 2*n-1 do j:=j+1: xt[j][k]:=evalf(xx[kk]*cs-yy[kk]*sn): yt[j][k]:=evalf(xx[kk]*sn+yy[kk]*cs): od: od: N1:=j: points:=seq(seq([xt[i][j], yt[i][j]], j=0..zt-1), i=1..2*n-1): p_cross:= pointplot([points], scaling = constrained, color = black,linestyle=solid, filled=[yellow]): polygonplot([points], color = yellow, scaling = constrained); NULL; display([p_cross]);#How to draw this cross with a line without points. Thank you.

How do I open .mw files?...

Hey all! I recently reinstalled my PC and therefore had to reinstall Maple. I did so and it worked out great, however, minor problem. My PC doesn't recognise .mw files as associated to Maple. I have tried a few different files, but I don't know which one to select as standard program for opening .mw files. Would anyone by chance know which file is the "opener" file, if that´s what that's called.
Thank you for the help in advance :D

(PS: I do know that I can just open the file through Maple by clicking files -> open and locating the file. But I'd rather access them by just doubleclicking from the directory.

are these error messages to be expected from pdsol...

I was trying Maple 2021.2 on this pde I saw on the net, and noticed it gives some error messages.

Are these to be expected and known?

 > interface(version); > Physics:-Version(); > restart;
 > PDE := diff(u(t, x, y), t) = VectorCalculus:-Laplacian(u(t,x,y),'cartesian'[x,y]); bc := D(u)(t,0,y)=0,D(u)(t,1,y)=0, u(t, x, 0)=0,u(t, x, 3)=0; ic := u(0, x, y) = f(x,y); sol := pdsolve([PDE, bc,ic], u(t,x,y))   Error, (in assuming) when calling '`assume/NormalizeBoolean`'. Received: 'invalid input: type expects 2 arguments, but received 3'

 > restart;
 > PDE := diff(u(t, x, y), t) = VectorCalculus:-Laplacian(u(t,x,y),'cartesian'[x,y]); bc := D(u)(t,1,y)=0, u(t, x, 0)=0,u(t, x, 3)=0; ic := u(0, x, y) = f(x,y); sol := pdsolve([PDE, bc,ic], u(t,x,y))   Error, (in PDEAdvisor/2nd_order/Series/ThreeVariables) invalid input: has expects 2 arguments, but received 1

 > restart;
 > pde := diff(u(t, x, y), t) = VectorCalculus:-Laplacian(u(t,x,y),'cartesian'[x,y]); bc := D(u)(t,0,y)=0,D(u)(t,1,y)=0, u(t, x, 0)=0,u(t, x, 3)=0; sol := pdsolve([pde,bc], u(t,x,y))  Error, (in PDEAdvisor/2nd_order/Series/ThreeVariables) invalid boolean expression: NULL

 >

DEplot warnings...

I have the following warnings. Could you help me fix the problem?

 > restart;
 > deS:=diff(x(t),t)=-0.5*x(t)*y(t) (1)
 > deI:=diff(y(t),t)=0.5*x(t)*y(t)-0.15*y(t) (2)
 > with(DEtools):
 > DEplot([deS,deI],[x(t),y(t)],t=0..40,x=0..1,y=0..0.6,[[x(0)=0.99,y(0)=0]])
 Warning, plot may be incomplete, the following errors(s) were issued:    incorrect number of arguments, got 51, expected 50 >
 >

Double shift in 2-D math...

I have been experiencing an error in the 2-D math text in Maple 2021. Every time I use the shift button the command seems to double. So if I for instance want to define A:=2 it will write; AA::==2 making the command useless. This only happens in 2-D math.

I have tried restarting Maple, my PC and uninstalling then installing maple 2021 again but nothing changes. This error appeared after updating maple the 6th of january 2022 to Maple 2021.2. I have a MacBook Air M1 2020.

Maple crashes using function solve...

Hello, I'm using Maple 2021.2 to approximate the solution to a differential equation using a pseudospectral expansion in the basis of Hermite polynomials. After setting up some equations, I get a non-linear system of equations that I try to solve using the Maple's function solve, but Maple suddenly crashes during the execution of this function.

My code is the following:

HN := (n, y) -> exp(-1/2*y^2)*simplify(HermiteH(n, y))/sqrt(sqrt(Pi)*2^n*n!):

u7 := a0*HN(0, y) + a1*HN(1, y) + a2*HN(2, y) + a3*HN(3, y) + a4*HN(4, y) + a5*HN(5, y) + a6*HN(6, y):

resid := diff(u7, y \$ 2) + 4*y*diff(u7, y)*u7 + 2*u7^2:

r := evalf(allvalues(RootOf(HermiteH(7, x), x)));
equations := {evalf(eval(u7, y = 0) - 1)};
for root_r in r do
if root_r != 0 then
equations := {op(equations), evalf(eval(resid, y = root_r))};
end if:
end do:

solutions := solve(equations, {a0, a1, a2, a3, a4, a5, a6}):

Does anyone have any idea about what is happening? Is there any better way of solving a non-linear system of equations?

A user wonders if they can customize Maple output to show, for example x^2 instead of x2 in 2D output.

We suggest they either set

interface(prettyprint=0);

globally, or use

lprint(x^2)

for individual outputs.

Map of US with States Shown

Maple 2021

A user wonders if there is a straightforward way to show US states with names using the WorldMap Data Set in Maple

We suggest something like the attached: map-of-us-with-states.mw

 >  What are maple initialization files...

What/Whare are the maple initialization files.

I have a problem with libname.

According to maple help, I should create/modify ~/.mapleinit.

> cat ~/.mapleinit

libname := "/usr/local/Maple2021/lib","/home/tomdean/maple/toolbox/maplev/lib","/home/tomdean/maple/toolbox/Syrup/lib";

But, when I start maple (in emacs), libname is only the first part, "/usr/local/Maple2021/lib",

Cloud Verson of Syrup not loaded in Emacs...

I installed the cloud version of Syrup with xmaple, by clicking the cloud icon, etc. It is loaded with xmaple and cmaple. But, not in maple running in emacs.

with(Syrup);
(**) Error, invalid input: with expects its 1st argument, pname, to be of type
(**)

Tom Dean

Maple Mode for Emacs...

I am attempting to use maplev mode for emacs. Ubuntu 20.04.3, Emacs 26.3, maplev-mode from git, release-2.36-59-g142c03. maple 2021.

I copied mload from an older computer and added a line to define maple, after the original maple definition line.

MAPLE=\${MAPLE:-maple} # Maple script

I compiled and installed maplev-mode. I had to touch doc/version.texi because the file did not exist. But, otherwise, I saw no errors.

maplev-mode seems to load when I edit a .mpl file.

However, mint is not defined.  Where should I change to define the location of mint?

/usr/local/Maple2021/bin/mint

Tom Dean

Why one needs to give full name on local type decl...

In this example, i have a top module A. Inside it, I have module named my_RECORD (which happened to be option object) that I want to return back to caller when they call a proc.

Maple allows me to declare the proc to return my_RECORD. No problem., But when making a local variable inside the proc and using o::my_RECORD it complains  that my_RECORD does not exist.

The solution is to change o::my_RECORD to o::A:-my_RECORD

My question why it did not complain the same way on the return value on the proc?   for me, they are both semantically the same. One says the proc returns this type, and the other says the local variable is this type. So why had to do A:-my_RECORD on one but not the other?

Here is an example. Maple 2021.2 on windows 10.

 > restart;
 > interface(warnlevel=4); kernelopts('assertlevel'=2): > A:=module()  #this is the RECORD to return   local module my_RECORD()    option object;    export data::string:="";   end module;       export do_analysis:=proc()::my_RECORD;        local o::my_RECORD; #error here. But this is the same above line above?         o:=Object(my_RECORD);     o:-data:="test";     return o;           end proc; end module; > A:-do_analysis()

Error, (in do_analysis) type `my_RECORD` does not exist

 > #FIXED BELOW restart;
 > A:=module()     #this is the RECORD to return     local module my_RECORD()         option object;         export data::string:="";     end module;         export do_analysis:=proc()::my_RECORD;           local o::A:-my_RECORD;               o:=Object(my_RECORD);           o:-data:="test";           return o;             end proc; end module; > A:-do_analysis() >

Error in the documentation of the Physics Package ...

Hi, I am trying to enter into the Mini-Course Computer Algebra for Physicists from the help, but instead of going to the page I get the help page of Physics[FeynmanIntegral]. Can anyone confirm that this happens to them on Maple 2021.2?

Kevin

dsolve with timelimit hangs on first order homogen...

Correction

Please ignore this question. dsolve does hang, but I had typo in the timelimit command itself when I wrote the test. Fixing this, now it timesout OK.

Maybe someone can look why dsolve hangs on this ode. But since timelimit does work, there is a workaround.

Original question

I was checking Maple's dsolve on this textbook problem The book gives the answer in the back as When using Maple's dsolve, I found it hangs. The stange thing, is that adding timelimit() also hangs. I can understand dsolve() hanging sometimes. But what I do not understand is why with timelimit it also hangs?

I've waited 20 minutes and then gave up. As you see, the timelimit is 20 seconds. May be if I wait 2 hrs or 20 hrs or 20 days, it will finally timeout. I do not know but can't wait that long.

Do others see same problem on this ode? Does it hang for you? How about on the mac or Linux?

During this time, I see mserver.exe running at very high CPU. I restarted Maple few times, but this did not help.

Maple 2021.2 on windows 10. May be one day Maplesoft will fix timelimit so it works as expected.

 > interface(version) > Physics:-Version(); > restart;
 > ode:=x*diff(y(x),x)=y(x)*cos(ln(y(x)/x)); try    timeout(20,dsolve(ode)); catch:       print("timedout");        end try;    print("OK"); >

how to obtain this transformation using dchange?...

on DLMF page, they show this transformation on independent variable for second order ode

https://dlmf.nist.gov/1.13#Px7

About half way down the page, under Elimination of First Derivative by Change of Independent Variable section.

I tried to verify it using Maple dchange. But the problem it looks like dchange wants the old variable to be on the left side (z in this example) and the new variable (eta in this example) to be on the right side in the transformation. But on the above web page, it is the other way around. Here are my attempts

restart;
ode:=diff(w(z),z\$2)+f(z)*diff(w(z),z)+g(z)*w(z)=0;

tranformation:=eta=int(exp(-int(f(z),z)),z);

PDEtools:-dchange({tranformation},ode,known={z},unknown={eta});
PDEtools:-dchange({tranformation},ode,{eta},known={z});
PDEtools:-dchange({tranformation},ode,{eta});

All give errors

Error, (in dchange/info) missing a list with the new variables
Error, (in dchange/info) the new variables are not contained in the rhs of the direct transformation equations
Error, (in dchange/info) the new variables are not contained in the rhs of the direct transformation equations

The problem it does not seem possible to invert the transformation shown on the webpage, so that the old variable z show on the left side and the new variable (eta) on the right side.

Why is this restriction on dchange  Since one tells it which is the new variable and which is the old variable? May be I am not using dchange correctly in this example.

Any suggestion for a workaround to use dchange to verify the above result?

Here is my hand derivation (pdf file attached also) Can the above be done using dchange?

Maple 2021.2 on windows 10

sol.pdf

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