## parametric degree...

Hi,

How we can find the degree of the equation in which its powers are parametric?

For example, let

H := x^k+x^(2*k);

where k is a positive number.

Now, the degree must be 2*k, but when I use "frontend" I receive "one" !!!!

See:

assume(k>0);

frontend(degree,[H,x^k],[{+, *,^}]);

1

## Maple Freezes When Doing Multivariate Integral...

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

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
r(u,v,w) = parametrisering af voluminet i rummet
jv = jacobi for voluminet
v(u0,u1,v0,v1,w0,w1) = voluminet af figuren
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?

## matrices as arguments to a function...

Hi,

I'd like to pass a matrix/row as an argument to a function (as in the example below) but I cannot find any documentation on it. Is it possible? If so, how could it be done?

a:=Array(1,5,frandom(0..20))

b:=sin(a)

best regards.

## mass on vertical spring and dry friction...

I need 4400 N of friction and not 2200N, so in wich direction operate it?Whit 2200N i I have mauch oscillation.fall_elevator_on_spring.msimfall_elevator_on_spring.msimthanks

## please (i need code to calculate brownian motion ...

Hi professors,

i want code of  function in maple to calculate values  of B(t),

i have this matlab code

randn('state',100)
T = 1; N = 5; dt = T/N;

dW = sqrt(dt)*randn(1,N);
W = cumsum(dW)

but does not calculate B(0.25) and B(0.5)

Thanks,

## 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.
\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.

## Compute integral of piecewise function...

Dear all

I have a continuous piecewise function, but I can't evaluate its integral

Integral.mw

## How to show all permutions...

Hi

Say I have 3 players on 2 teams. The teams play each other and there are 9 single [[A[s], B[s]], [A[s], B[m]], [A[s], B[w]], [A[m], B[s]], [A[m], B[m]], [A[m], B[w]], [A[w], B[s]], [A[w], B[m]], [A[w], B[w]]]matchups.

A, B, C & X, Y, Z. are the players. A and X are the strongest players, C and Z are the weakest.

Here's one: [[A,X],[B,Y],[C,Z],[A,Y],[B,Z],[C,X],[A,Z],[B,X],[C,Y]]

So i'm looking for some code to display all such permutations.

Carl came up with some code a while back which 'kind of' does it

P:= [A,B]:  S:= [s,m,w]:
[seq(rtable((1..nops(S)) \$ nops(P), ()-> index~(P, S[[args]]), order= C_order))];
[[A[s], B[s]], [A[s], B[m]], [A[s], B[w]], [A[m], B[s]], [A[m], B[m]], [A[m], B[w]], [A[w], B[s]], [A[w], B[m]], [A[w], B[w]]]

## Problem with the use of GetConstant...

This is perhaps a stupid question, when I use the ScientificConstant package and call a constant e.g. R this works smoothly. But when I assign the value to a variable to use it in a calculation Maple complains about the units. However, if I assign the constant manually (without using GetConstant) Maple has no issues in solving. Is there a trick to use such a constant in a calculation? I have attached a worksheet to illustrate my question better. Thank you in advance for helping me out.GetConstantQuestion.mw

## Integration and complex values...

Hi guys,

I've got problem with integrating terms consisting complex values, I would like to use principle value (1/x+ie = P(1/x) -i pi \delta(x)) to make integration process easier but dont know how to do it with maple . without using that maple gives very long answer.

ex.mw

Best

## 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!

## How to plot absolute advantage of option A over op...

Dear community,

this is a related questio to "Determine zeros, indifference curve of two levels, numerical approximation".

I am  trying to model the advantage of corporate taxation (final asset value: V_TEV) over partnership taxation (final asset value: V_P).
I would like to plot the absolute advantage of corporate taxation (VT=V_TEV-V_P) as a function of income (E) and retention period (T). Here x=E, Y=T. I alread plotted the VT. However, Id like to have the graph differently:
I would like to construct the graph in such a way that the absolute wealth advantage VT can be read from the ordinate. Can someone please help me with that?

Here are the formulars, the study is based on:

E := 'E'
h := 4
m := 0.035
g:= h*m
k := 0.15
a := 0.25;
F_ANR := 4*m;
r:= 0.1;
T := 'T';
ESt := piecewise
(E < 9984, 0,
E < 14926, (1008.7*(E - 9984)/10000 + 1400)*(E - 9984)/10000,
E < 58596, (206.43*(E - 14926)/10000 + 2397)*(E - 14926)/10000 + 938.24,
E < 277826, 0.42*E - 9267.53,
0.45*E - 17602.28);

GewSt := piecewise(E < 24500, 0, (E - 24500)*g)

stev := EStk/K

K := 0.6*E*(1 - k - g)*(1 + r*(1 - k - g))^T

EStk := piecewise(K < 9984, 0,
K < 14926, (1008.7*(K - 9984)/10000 + 1400)*(K - 9984)/10000,
K < 58596, (206.43*(K - 14926)/10000 + 2397)*(K - 14926)/10000 + 938.24,
K < 277826, 0.42*K - 9267.53,
0.45*K - 17602.28)

V_TEV := E*(1 + (-k - g))*(1 + r*(1 - k - g))^T*(1 - 0.6*stev)

Er := E + (E - ESt)*r

EStr := piecewise(Er < 9984, 0,
Er < 14926, (1008.7*(Er - 9984)/10000 + 1400)*(Er - 9984)/10000,
Er < 58596, (206.43*(Er - 14926)/10000 + 2397)*(Er - 14926)/10000 + 938.24,
Er < 277826, 0.42*Er - 9267.53,
0.45*Er - 17602.28);

srp := EStr/E

r_p := r*(1 - srp)

V_P := (E - ESt + GewSt - min(ESt, GewSt, E*F_ANR))*(1 + r_p)^T

VT := V_TEV - V_P

plot3d(VT, E = 0 .. 500000, T = 1 .. 15, axes = boxed)

Thank you so much in advance!! Rebekka

## 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

 >