## Why does Copy as image not work?...

macOS 12.3 + Maple 2021.2

* select a region on a document
* context click
* --> Copy as image

Copy as image does not put an image on the clipboard.

What is solution?

## How to implement decomposition function respect ba...

I describe my problem accurately in mws file. I have a step function

 > First step. This is f(x) function
 >
 (1)
 > Next step. I try to approximate this function f(x) using wavelet transform, and  I  want to decomposite this function, choose wavelet Haar function and scaling functon  , choose basisn funtion from multiresolution analysis of the Lebesgue space  L^2(R). I choose  such wavelet fucntion  from space MRA V0 and scaling function from space MRA V0:
 >
 (2)
 >
 (3)
 > After I try approximate initial function f(x), decomposed using such contruction:
 >
 >
 > where coeff m shows, space MRA, to which the basis function belongs, and kk shows,basis function shift (x-k)
 > i.e. I try decompose function respective to basis function, where coeffs calculate the such way:
 >
 >
 > The approximation is considered satisfactory if the following condition is  true:
 >
 >
 > For example  calculate that such way:
 >
 > if the wavelet Haar functions:
 >
 (4)
 >
 > Then vector of Haar functions compute using the follow code:
 >
 >
 > Then integrals
 >
 >
 > where  is an d-square matrix called an operational matrix of integration
 >
 >
 > And now, it's not working, so I have troubles for calculate coeffs and writing and  plotting this result, so, I have some questions: 1) How to calculate coeffs and   for my fucntion f(x) and get value of coeffs? 2) How to implement integration and write the final sum (approximation of function f(x)? 3) How to calculate
 >
 >
 > and plot initial function f(x) and approximation sum at one plot?
 > Do I understand correctly that I need to calculate this integral for my function on each interval of my function?
 >
 >
 > How to implement this procedure?

Code for calculating procs a I try ude from this source: http://www.m-hikari.com/ams/ams-2012/ams-125-128-2012/sunmonuAMS125-128-2012.pdf

I would be very grateful for any help!

## Syntax for the seq function with units...

So all I'm trying to do is a simple sequence like seq(i^2, i=1..10, 1) but with units.  The seq function is part of the Units:-Standard and Units:-Simple packages.  I couldn't find any examples with units in the help system.  For my first attempt, I tried to create a simple sequence of values with units using what is, to me, a logical syntax.  I have included the Maple input below.  I bolded the input.

with(Units:-Standard);
[*, +, -, /, <, <=, <>, =, Im, Re, ^, abs, add, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin,

arcsinh, arctan, arctanh, argument, ceil, collect, combine, conjugate, cos, cosh, cot, coth, csc, csch, csgn, diff, eval,

evalc, evalr, exp, expand, factor, floor, frac, int, ln, log,  log10, log2, max, min, mul, normal, polar, root, round, sec,

sech, seq, shake, signum, simplify, sin, sinh, sqrt, surd, tan,   tanh, trunc, type, verify]

seq(ii, ii = 1.0*Unit('m') .. 10.0*Unit('m'), 1.0*Unit('m'));

Error, (in Units:-Standard:-seq) wrong number (or type) of parameters in function seq

Can anyone show me the correct syntax for this?  Is there something in the help?  I tried it in 2021 and 2022 with the same result.

## Maple 2021.2 (for Linux) sometimes does not shown ...

I am using Maple 2021.2 on Ubuntu Linux 20.04 LTS. Sometimes the Maple after start does not show Sig in part of top Maple desktop panel. So I need to restart Maple and 2nd or 3rd start is mostly OK. After that is the situation for some time good.

See attached snapshot... Any idea what is wrong?

## infolevel gives different output depending on orde...

I set infolevel[dsolve]:=2; and first time I use it, it gives very long output. Next time I use it on same ode with same command it gives much shorter output.

Why is that and how to make it give the shorter output from first call?  This is very strange behavior.  One would expect the same output each time. The worksheet attached shows that first time it is used, the output is very long. At the end of the worksheet the call is made again with same infolevel, and now output is much smaller.

(getting error uploading worksheet. Will try again. Unable to do insert content keep getting error from this site. So I am just attaching it as link. May be due to large size of the worksheet)

infolevel_changes.mw

## The strange behavior of IsSubgraphIsomorphic requ...

The IsSubgraphIsomorphic command accepts either two undirected graphs or two directed graphs as input.  It returns true if G1 is isomorphic to some subgraph of G2. The GraphTheory [IsSubgraphIsomorphic] command was introduced in Maple 2021.

If a graph T is isomorphic to some subgraph T' of  a graph GIsSubgraphIsomorphic(T,G)  will  return true. But there is no option to return T'. That makes it hard to check manually.

I've seen  IsSubgraphIsomorphic behaving strangely lately. I want to check whether K8-P6 contains K7-K3 as its subgraph.

T:=DeleteEdge(CompleteGraph(7),{{1,2},{2,3},{3,1}},inplace= false):
G:=DeleteEdge(CompleteGraph(8),{{1,2},{2,3},{3,4},{4,5},{5,6}},inplace= false):
IsSubgraphIsomorphic(T,G)

true

I think theoretically, the result of IsSubgraphIsomorphic is not correct. I also tested it from Mathematica, and it worked as I expected.

h = EdgeDelete[ CompleteGraph[7], {1 <-> 2, 2 <-> 3, 3 <-> 1}];
g = EdgeDelete[ CompleteGraph[8], {1 <-> 2, 2 <-> 3, 3 <-> 4, 4 <-> 5, 5 <-> 6}];
IsomorphicSubgraphQ[h, g]

False

I wonder what went wrong.

PS: Subgraph isomorphism is a question I've asked before, and we can refer to the following links and code. https://www.mapleprimes.com/questions/226937-How-To--Test--A--Graph--Whether-Contains

with(GraphTheory):
with(combinat):
T:=DeleteEdge(CompleteGraph(7),{{1,2},{2,3},{3,1}},inplace= false):
G:=DeleteEdge(CompleteGraph(8),{{1,2},{2,3},{3,4},{4,5},{5,6}},inplace=false):
nE,nV := NumberOfEdges(T), NumberOfVertices(T):
# Produce all subgraphs of G which have the same number of edges and vertices as the "test" sub-graph T
U:=choose(Edges(G),nE): nops(%):
U1:=select(t -> (nops(union(t[]))=nV), U): nops(%):
gL:= Graph~(U1): nops(%):
ans:= [ seq
( if
( IsIsomorphic( T, gL[j] ),
j,
NULL
),
j=1..numelems(gL)
)
]:
if   numelems(ans)>0
then HighlightSubgraph( G, gL[ans[1]], edgestylesheet=[thickness=4, color="Red"]);
DrawGraph(G, style=spring);
fi;

These codes are due to tomleslie  and  vv. According to above codes, it seems that there is something wrong with IsSubgraphIsomorphic too.

## formatting the output generated by writeto(filenam...

I capture the output of dsolve after setting infolevel to some file so I can later read that output and put it in my own document (Latex).

Currently what I do is set infolevel, then use writeto(file_name) to send all the output that would normally go to standard output to the text file, then later do readline to read it back for further processing.

The problem is that Maple does not put the output in the file the same way as it appears on the screen when using worksheet.

For example, all newlines are lost. So everything comes out in one line in the file_name .  I am not sure why that is.

Is there an option or trick to make the output not lose the newlines? It also seems to format things differently in the file. An example will make this clear

When running this code

restart;
currentdir("... set the directory to where you want to save the file to ..");

infolevel[:-dsolve]:=5;
writeto("output_of_dsolve.txt");  #send all output to file
sol:=dsolve(diff(y(x),x)=sin(x),y(x));
close("output_of_dsolve.txt"):
writeto(terminal); #to send output back to terminal



When I open the file output_of_dsolve.txt this is what shows

Methods for first order ODEs:--- Trying classification methods ---trying a quadrature<- quadrature successful     solAssignyApplyFunction(x)equalsuminus0cosApplyFunction(x) + _C1, [

Typesetting:-mprintslash([sol := y(x) = -cos(x) + _C1],

[y(x) = -cos(x) + _C1])]



But in the worksheet, when I run the same code without writeto("output_of_dsolve.txt");  so output goes to terminal as normal, here it is how it looks like

Is there a way to keep the newlines? And why there is some extra stuff in the file that do not show on the screen? Should one change the Settings for Display before doing the above? Currently the default I have is typesetting level is "Extended". Do not know if this affects it or not.

Is the above method the only way to capture the output of dsolve from infolevel to a text file? It looks like Maple uses  in the file in place where there should be a newline (CR) inserted.

Update

I did this experiment but there is still some strange formatting coming out in the file. Here is an example

restart;

currentdir(".....");

:-infolevel[:-dsolve]:=5;
writeto("output_of_dsolve.txt");
sol:=dsolve(diff(y(x),x)=sin(x),y(x));
close("output_of_dsolve.txt"):
writeto(terminal);


And now the text file has this

Methods for first order ODEs:--- Trying classification methods ---trying a quadrature<- quadrature successfulTypesetting:-mprintslash([(sol := y(x) = -cos(x)+_C1)],[y(x) = -cos(x)+_C1])

What is Typesetting:-mprintslash at the end of the line above? it is duplicate.

And how to get rid of it? Is there another settings to set other than interface(typesetting=standard): and interface(prettyprint=0): ?

## How do I only plot certain points from a list?...

I have a set of points. I only want to plot ones with x and y less that 5 units from [0,0]. I can do it with for do loop. Can't get it to work with seq. Ideally I don't want to create another list.

 (1)

## How to switch off the Autosaving in Maple 2021?...

I have been unsuccessfully switching off the autosaving from Maple 2021. There is no "Options Dialog - General Tab". Please help me. Thank you!

## Why does this integral evaluate as "undefined"?...

int( exp(-2*r)*cos(theta)^3*r^2*sin(theta), phi=0..2*Pi, theta=0..Pi, r=0..infinity);
undefined

This integral with cos(theta) to an odd power should evaluate to zero, as found in Maple 17 [moderator: and up to Maple 2015.2] but not the most recent versions.

## Maple Freezes When Doing Multivariate Integral...

Opgave 1)
restart;
with(LinearAlgebra);
with(plots);

a = radius 1
b = radius 2
h = højde
Error, unexpected number
a := 213/2;
b := 144/2;
h := 46;
Vi definerer A_g(a,b)= areal af grundfladne, hvor a og b er de to radiusser.
r(u,v) = parametrisering af fladen i rummet
jf = Jacobi for fladen
r(u,v,w) = parametrisering af voluminet i rummet
jv = jacobi for voluminet
v(u0,u1,v0,v1,w0,w1) = voluminet af figuren
A_f(u0,u1,v0,v1) = voluminet af fladen
Error, missing operator or ;
A_g := (a, b) -> b*a*Pi;
V := (a, b, h) -> 2/3*b*a*Pi*h;
x := (u, v) -> a^cos(u)*sin(v);
y := (u, v) -> b*sin(u)*sin(v);
z := (u, v) -> h*cos(v);
r := (u, v) -> <x(u, v), y(u, v), z(u, v)>;
ru := (u, v) -> diff(r(u, v), u);
rv := (u, v) -> diff(r(u, v), v);
jac := CrossProduct(ru(u, v), rv(u, v));
jf := sqrt(jac[1]^2 + jac[2]^2 + jac[3]^2);
/
|
|               2       4
jf := |10969344 cos(u)  sin(v)
\

2
/     cos(u)\                 2           /
|/213\      |        2   /213\        4   |
+ 2116 ||---|      |  sin(u)  ln|---|  sin(v)  + |
\\ 2 /      /            \ 2 /            \
cos(u)
/213\             2   /213\
-72 |---|       sin(u)  ln|---| sin(v) cos(v)
\ 2 /                 \ 2 /

\
cos(u)       \  |
/213\             |  |
- 72 cos(u) sin(v) |---|       cos(v)|^2|^(1/2)
\ 2 /             /  /

/
|               2       4                  2       4
jf := \10969344 cos(u)  sin(v)  + 24000201 sin(u)  sin(v)

2\
/            2                            2              \ |
+ \-7668 sin(u)  sin(v) cos(v) - 7668 cos(u)  sin(v) cos(v)/ /^

(1/2)

Opgave b)

A_g(a, b);
7668 Pi

evalf(7668*Pi);
24089.73247

V(a, b, h);
235152 Pi

evalf(235152*Pi);
5
7.387517958 10

Opgave b)

Vi skal blot løse integralet for
u \in [0,2*Pi] og v \in [0,Pi/2].

V bestemmer hvor langt z skal gå. Da dette er vores højde, lader vi denne gå til 0. Men ikke længere.
Error, missing operator or ;
NULL;
int(jf, [u = -Pi .. Pi, v = 0 .. Pi/2]);
"(->)"

34384.

Opgave c)

Humlen er her, blot at definere en f(x,y,z)=z0-hældning*z, hvor:

hældning = df/dz
z0 = f(z=0)

I opgaven får vi
z=0 -> f = 20
z=46 -> f=10

Det er en fastprocentdel, så vi skal bruge eksponentialfunktion:

Hældning := (10/20)^(1/46)

Vi går så m(u,v) = f(x(u,v),y(u,v),z(u,v))

Bagefter, skal vi gange med jacobi og tage integralet.

Error, missing operator or ;

z0 := 20;
hældning := (10/20)^(1/46);
f := (x, y, z) -> 20*hældning^z;
m := (u, v) -> 20*(1/2*2^(45/46))^(46*cos(v));

NULL;
int(m(u, v)*jf, [u = 0 .. 2*Pi, v = 0 .. Pi/2]);
"(->)"

129.98 jf

NULL;
Question:
Whenever I run any of the double integrals in this script, Maple freezes out and doesn't come back. What am I doing wrong? Why does it lag so much?

## Using Layout = interactive in a DrawGraph makes it...

I want to generate several graphs  at the same time that can be dynamically adjusted.I tried to write the following code. But it seemed to keep overwriting the previous drawing of graphs in the list g. I only got the last graph K6.

with(GraphTheory):
g:=[seq(CompleteGraph(i),i=2..6)]:
DrawGraph~(g, layout = interactive, layoutoptions = [neutral_color = "pink", initial = spring])


I don't know how to generate  some graphs with dynamically modified layouts at once

## invalid latex for empty matrix...

Maple uses \begin{array}...\end{array} for the latex of a Matrix, which is all good. But for an empty matrix, it does not generate the column specification c or and so the latex when compiled gives an error. Here is an example

W:=Matrix([[]]);
latex(W)

#which gives

\left[\begin{array}{}
{}
\end{array}\right]


Compare to

W:=Matrix([[1]]);
latex(W)

#gives

\left[\begin{array}{c}
1
\end{array}\right]


Because the c is missing in the first example, this generates an error

\documentclass[12pt]{book}
\usepackage{amsmath}

\begin{document}
$\left[\begin{array}{} {} \end{array}\right]$

\end{document}
>lualatex foo.tex
This is LuaHBTeX, Version 1.13.2 (TeX Live 2021)
restricted system commands enabled.
(./foo.tex
LaTeX2e <2021-11-15>
L3 programming layer <2021-11-12>
(/usr/local/texlive/2021/texmf-dist/tex/latex/base/book.cls
Document Class: book 2021/10/04 v1.4n Standard LaTeX document class
(/usr/local/texlive/2021/texmf-dist/tex/latex/base/bk12.clo))
(/usr/local/texlive/2021/texmf-dist/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the ?' option.
(/usr/local/texlive/2021/texmf-dist/tex/latex/amsmath/amstext.sty
(/usr/local/texlive/2021/texmf-dist/tex/latex/amsmath/amsgen.sty))
(/usr/local/texlive/2021/texmf-dist/tex/latex/amsmath/amsbsy.sty)
(/usr/local/texlive/2021/texmf-dist/tex/latex/amsmath/amsopn.sty))
(/usr/local/texlive/2021/texmf-dist/tex/latex/l3backend/l3backend-luatex.def)
(./foo.aux) (/usr/local/texlive/2021/texmf-dist/tex/latex/base/ts1cmr.fd)
! Missing # inserted in alignment preamble.
<to be read again>
\cr
l.6 \left[\begin{array}{}

?

Adding the c` fixes the Latex.

This came up with my code generated an empty  matrix from some computation.

May be this could be corrected for future version of Maple?

Thank you.

Maple 2021.2 on windows 10.

## Finding operands and operating on multiple operand...

Hello Maple gurus!

I have two questions related to working with operands:

Question 1

I often find myself in a situation where I have a non-trivial expression for instance containing double integrals with complex exponentials, and want to perform some operation on a heavily nested operand like the exponent to a specific exponential inside the double integral. Usually what I do is use a list argument with the op() or subsop() to operate on the nested operator by finding specific operand numbers.

However, the problem with this is that I am hard-coding the operand number(s) for the operator, and this expression can be located in the middle of a large worksheet. If something above these op() or subop() calls changes and the changes trickle down, the operands might change number and the commands are no longer valid.

Does Maple have any commands that will let me 'find' an operand like one does in by-hand calculations? For example, there might be an exponent nested in a double integral that has 'a*b' in it. What I want is to operate on the operand containing 'a*b' rather than specifying the actual operand number. Is there anything like this?

Question 2

Somewhat related to the above, I sometimes want to do a single function on multiple operands. I tried applyop but that seems to apply a function to each operand individually. What if, for example, I want to run combine() on 2 specific operands, assuming these operands are heavily nested, to combine just those two operands.

Thank you!

## Exception from Latex may be due to typesetting...

When I convert Maple expression to Latex, before calling Latex, I replace some math names by strings in order to keep them as is in the generated Latex instead of using Maple own shortened name when conversion to latex().

Later on, in the Latex file, I add \DeclareMathOperator on each long name. This way the long math names remain and it is more clear.

This has been working well for years. Same code. No problems. All my Latex was generated this way.

Except just now, I hit a case where Maple's latex() gives an error when the math has WeierstrassP in it. latex() generates exception.

I will email this also to Maplesoft. But thought to also post it here in case someone can see what the problem is.

 > interface(version); Physics:-Version();

 > restart;
 > #interface(warnlevel=4); #kernelopts('assertlevel'=2): interface(typesetting=standard); #to prevent bug. see https://www.mapleprimes.com/questions/232450-Why-Maple-Writes-The-Equation-Like-This

 > r:=11/("\\WeierstrassPPrime"(x,a,b)+"\\WeierstrassP"(x,a,b)^2)*"\\WeierstrassP"(x,a,b)*"\\WeierstrassPPrime"(x,a,b)-6/("\\WeierstrassPPrime"(x,a,b)+"\\WeierstrassP"(x,a,b)^2)*"\\WeierstrassP"(x,a,b)^2+1/2*a/("\\WeierstrassPPrime"(x,a,b)+"\\WeierstrassP"(x,a,b)^2)

 > latex(r)

Error, (in latex) unable to proceed; could you please report this problem at physics@maplesoft.com

 > interface(typesetting=extended);

 > latex(r)

Error, (in TypeTools/nc_var_local) invalid input: member received MathematicalFunctionsNames, which is not valid for its 2nd argument, s

 >