How to simplify this trigonometric expression with Maple? I only know the way with  identify command, which is difficult to call mathematically correct:

restart;
Expr:=arctan((1-tan(20*Pi/180))/(1-tan(25*Pi/180)));
evalf[15](Expr);
identify(%);

I do not underand why these two gives different results

restart;
mysol:= exp(sqrt( y(x)^2/x^2+1)) = _C1*x;
ode:=diff(y(x),x) = (y(x)^2+(x^2+y(x)^2)^(1/2)*x)/x/y(x);

And now case A:

simplify(odetest(mysol,ode)) assuming x>0;

                  0

But case B

res:=odetest(mysol,ode):
simplify(res) assuming x>0;

      #does not give zero

Why is putting the result in a variable first makes it give a different result?

What should one do so both case A and B give 0 ?

It looks like scoping issue of assuming. But this is really confusing, I did not expect that putting an intermediate result in a variable first will make a difference.

Maple 2020.2, Physis 897

I'm new to maple ,I have a series of data  which are independent of angle to polarplot. the first coordinate is r, and the second coordinate is f(r,theta). what I want is  to color the figure according to the value of f(r,theta), like the figure below.

the data is listed as follow: 

[[0., 3.], [0.2000000000e-1, 2.960601340], [0.4000000000e-1, 2.922410774], [0.6000000000e-1, 2.885436547], [0.8000000000e-1, 2.849687068], [.1000000000, 2.815170918], [.1200000000, 2.781896852], [.1400000000, 2.749873799], [.1600000000, 2.719110871], [.1800000000, 2.689617363], [.2000000000, 2.661402758], [.2200000000, 2.634476731], [.2400000000, 2.608849150], [.2600000000, 2.584530087], [.2800000000, 2.561529812], [.3000000000, 2.539858808], [.3200000000, 2.519527764], [.3400000000, 2.500547591], [.3600000000, 2.482929415], [.3800000000, 2.466684589], [.4000000000, 2.451824698], [.4200000000, 2.438361556], [.4400000000, 2.426307219], [.4600000000, 2.415673985], [.4800000000, 2.406474402], [.5000000000, 2.398721271], [.5200000000, 2.392427650], [.5400000000, 2.387606862], [.5600000000, 2.384272500], [.5800000000, 2.382438431], [.6000000000, 2.382118800], [.6200000000, 2.383328042], [.6400000000, 2.386080879], [.6600000000, 2.390392334], [.6800000000, 2.396277732], [.7000000000, 2.403752707], [.7200000000, 2.412833211], [.7400000000, 2.423535514], [.7600000000, 2.435876220], [.7800000000, 2.449872265], [.8000000000, 2.465540928], [.8200000000, 2.482899838], [.8400000000, 2.501966977], [.8600000000, 2.522760694], [.8800000000, 2.545299706], [.9000000000, 2.569603111], [.9200000000, 2.595690390], [.9400000000, 2.623581418], [.9600000000, 2.653296473], [.9800000000, 2.684856242], [1., 2.718281828]]

A torus can be defined parametrically by:

where θ, φ are angles which make a full circle, so that their values start and end at the same point, R is the distance from the center of the tube to the center of the torus, r  is the radius of the tube.

R:=10:
r:=5:
plot3d( [ ( R+r(u,v)*cos(v))*sin(u),
          ( R+r(u,v)*cos(v))*cos(u),
            r*sin(v)
        ],
            u=0..2*Pi,
            v=0..2*Pi,style=patchnogrid,
            scaling=constrained,
          scaling=constrained,
coordinateview=[-15..15, -15..15,-5..5],
lightmodel=light3, viewpoint = circleleft);

I set range [-5..5] of the Z axis，but  the range of  Z axis tickmarks  in the above image maybe in [-4.5..4.5] .

How to have tickmarks included at -5 and 5 on the Z axis?

How I can determine coefficiants a0,a1,a2,b0,b1,b2?

Thanks

equation.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/equation.mw .
 

Download equation.mw

Hello. Please help me find the value of the integral.

Integral.mw

I have tried:

algsubs(Uo/sqrt(GoHo)=Fr, Go Ho/ Uo^2)

(where I want it to yield the answer `1/Fr^2`)

but it just returns:

Go Ho/ Uo^2

I have only just starting using maple , but as far as I can see other possible functions may be solve or eliminate but I believe they aren't relevant here..?

Many thanks for your help !

HOW I CAN FIND A , B DIRECTLY?

NOT BY WRITING RELATION 5?

A.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/A.mw .
 

Download A.mw

How to write names on an drawing P1, P2, P3, Pn... I try
textplot({seq([(coordinates(point(P[i]))), cat("P", i)], i = 0 .. 5)}, 'align' = {'above', 'left'}):;
i got the message : wrong number of arguments that i don't how correct. Thank you.

Hi,

I would be really grateful if someone can help me in solving the below attached problem in maple.

Thanks in advance.

In Latex 897 correct Latex is generated for the following code. In 905, wrong Latex is generated. This is different from the other cases I posted about (links below) and new issue.

In 897, the Latex generated for this example compiles with no error

restart;
sol:=(Vector(2, [x__1(t),x__2(t)])) = (Vector(2, [2^(3/4)*3^(1/4)*(exp(2^(3/4)*3^(1/4)*t)*_C1-exp(-2^(3/4)*3^(1/4)*t)*_C2-sin(2^(3/4)*3^(1/4)*t)*_C3+cos(2^(3/4)*3^(1/4)*t)*_C4),2*6^(1/2)*(exp(2^(3/4)*3^(1/4)*t)*_C1+exp(-2^(3/4)*3^(1/4)*t)*_C2-sin(2^(3/4)*3^(1/4)*t)*_C4-cos(2^(3/4)*3^(1/4)*t)*_C3)]));
Latex(sol)

Now compiling the Latex gives

\documentclass[11pt]{article}
\usepackage{amsmath}
\usepackage{maplestd2e}  

\begin{document}
\[
\left[\begin{array}{c}x_{1} \! \left(t \right) \\x_{2} \! \left(t \right) \end{array}\right]
 = 
\left[\begin{array}{c}2^{\frac{3}{4}} 3^{\frac{1}{4}} \left({\mathrm e}^{2^{\frac{3}{4}} 3^{\frac{1}{4}} t} \mathit{\_C1} -{\mathrm e}^{-2^{\frac{3}{4}} 3^{\frac{1}{4}} t} \mathit{\_C2} -\sin \! \left(2^{\frac{3}{4}} 3^{\frac{1}{4}} t \right) \mathit{\_C3} +\cos \! \left(2^{\frac{3}{4}} 3^{\frac{1}{4}} t \right) \mathit{\_C4} \right) \\2 \sqrt{6}\, \left({\mathrm e}^{2^{\frac{3}{4}} 3^{\frac{1}{4}} t} \mathit{\_C1} +{\mathrm e}^{-2^{\frac{3}{4}} 3^{\frac{1}{4}} t} \mathit{\_C2} -\sin \! \left(2^{\frac{3}{4}} 3^{\frac{1}{4}} t \right) \mathit{\_C4} -\cos \! \left(2^{\frac{3}{4}} 3^{\frac{1}{4}} t \right) \mathit{\_C3} \right) \end{array}\right]
\]
\end{document}

In 905

The Latex(sol) gives

\documentclass[11pt]{article}
\usepackage{amsmath}
\usepackage{maplestd2e}  

\begin{document}
\[
\left[\begin{array}{c}x_{1} \! \left(t \right) 
\\
 x_{2} \! \left(t \right) \end{array}\right]
 = 
\left[\begin{array}{c}2^{\frac{3}{4}} 3^{\frac{1}{4}} 
\\
\left({\mathrm e}^{2^{\frac{3}{4}} 3^{\frac{1}{4}} t} \textit{\_C1} -{\mathrm e}^{-2^{\frac{3}{4}} 3^{\frac{1}{4}} t} \textit{\_C2} -
\\
\sin \! \left(2^{\frac{3}{4}} 3^{\frac{1}{4}} t \right) \textit{\_C3} +\cos \! \left(2^{\frac{3}{4}} 3^{\frac{1}{4}} t \right) \textit{\_C4} \right) 
\\
 2 \sqrt{6}\, 
\\
\left({\mathrm e}^{2^{\frac{3}{4}} 3^{\frac{1}{4}} t} \textit{\_C1} +{\mathrm e}^{-2^{\frac{3}{4}} 3^{\frac{1}{4}} t} \textit{\_C2} -
\\
\sin \! \left(2^{\frac{3}{4}} 3^{\frac{1}{4}} t \right) \textit{\_C4} -\cos \! \left(2^{\frac{3}{4}} 3^{\frac{1}{4}} t \right) \textit{\_C3} \right) \end{array}\right]
\]
\end{document}

Which when compiled using texlive lualatex gives error. There is a missing \right. 

>lualatex foo5.tex
This is LuaHBTeX, Version 1.12.0 (TeX Live 2020)
 restricted system commands enabled.
(./foo5.tex
LaTeX2e <2020-10-01> patch level 2
.....
..Defaults to "dvips" Driver
(/usr/local/texlive/2020/texmf-dist/tex/latex/graphics/epsfig.sty (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics/graphicx.sty (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics/keyval.sty) (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics/graphics.sty (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics/trig.sty) (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics-cfg/graphics.cfg) (/usr/local/texlive/2020/texmf-dist/tex/latex/graphics-def/dvips.def))))
Defining Automatic Style Generation Macros
Defining Maple Spreadsheet Environments
Maple Spreadsheet and Table Support
) (/usr/local/texlive/2020/texmf-dist/tex/latex/l3backend/l3backend-luatex.def) (./foo5.aux) (/usr/local/texlive/2020/texmf-dist/tex/latex/base/ts1cmr.fd)
! Missing \right. inserted.
<inserted text>
\right .
l.14 \\

?

Maple 2020.2, Physics 905

Fyi, the issues I know about in Latex()  as of now are these 4

https://www.mapleprimes.com/questions/231398-Regression-In-Latex-Between-897-And?sq=231398

https://www.mapleprimes.com/questions/231397-Latex-Latex-Generates-Command-Not-In

https://www.mapleprimes.com/questions/231273-Why-Latex-Fail-To-Convert-Solution

https://www.mapleprimes.com/questions/231262-Latex-Generates-Wrong-Latex-For-This-Example

FYI,

I was testing Physics 905 to see if this bug reported in https://www.mapleprimes.com/questions/231262-Latex-Generates-Wrong-Latex-For-This-Example

But I found that now Maple generates a new command called \munderset  while in 897 it used to be  \Mapleunderset

So the problem was not fixed. In addition now it uses a command called \munderset which is not in any of Maple style files and not a standard Latex macro name. 

Replacing \munderset back to \Mapleunderset now the same error that was generated in the above linked to question, using the same exact code shown there.

So I think this new command should remain \Mapleunderset unless there is a new Maple syle file used which is not part of Maple 2020.2? 

To reproduce this, please run the same code posted in the above link. No need to duplicate it here again, and you will see this problem.

Maple 2020.2, Physics 905

In the following code,  

Although the lines in the figure include asterisk or points, the symbols don't appear in the legends.

restart:
f1:=x->x^2:
f2:=x->x^2-0.08:
N:=10: ptsize:=8: th:=1:
(a,b) := 0,2:
p1:=plot(f1(x),x=a..b,color=red,thickness=th,legend=f1(x),style=pointline,symbol=solidcircle,symbolsize=ptsize,adaptive=false,numpoints=N+1):
p2:=plot(f2(x),x=a..b,color=blue,thickness=th,legend=f2(x),style=pointline,symbol=asterisk,symbolsize=ptsize+4,adaptive=false,numpoints=N+1):

plots:-display(p1,p2);

For example; what is your method for showing asterisk, point etc. in the legends as in the following picture?

Hello!

I would appreciate any help on how to do computations on Maple of the following problem. 

Say we have 3 generators x,y,z and I define a map on polynomials in three variables over rational numbers L: Q[x,y,z] -> Q[x,y,z] on the generators, for example L(x)=xy, L(y)=1, L(z)=z^2. 

Then I need to compute L(xy+yz) and it needs to compute it using linearity and derivation (Leibniz rule):

L(x)y+xL(y)+L(y)z+yL(z)=xy^2+x+z+yz^2. 

I have in mind a recursive algorithm but I don't know enough syntacsys to implement it. 

P.S.: I need to compute Poisson brackets on a polynomial algebra for which there is no special way of doing it, right? So I though it must be easier for each basis element to come up with a linear map and extend it via derivations to know its action. 

Hi,

I was trying to differentiate an equation with two random variables with respect to my decision variable. But it took 4-5 hrs still MAPLE could not evaluate nor show an error.

 Later I want to find q* from the FOC and wish to substitute it back into the equation. I will be grateful if someone please help me in doing both.

doubt_1.mw

Thanks in Advance