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

Asked by: BekkiRR 55
plotting duplicate-question
March 08 2022
0  2

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...

Asked by: nm 8552
latex
March 08 2022
3  1

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();

`Standard Worksheet Interface, Maple 2021.2, Windows 10, November 23 2021 Build ID 1576349`

`The "Physics Updates" version in the MapleCloud is 1165 and is the same as the version installed in this computer, created 2022, March 7, 23:42 hours Pacific Time.`

> 

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
 

extended

> 

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)

11*("\WeierstrassP")(x, a, b)*("\WeierstrassPPrime")(x, a, b)/(("\WeierstrassPPrime")(x, a, b)+("\WeierstrassP")(x, a, b)^2)-6*("\WeierstrassP")(x, a, b)^2/(("\WeierstrassPPrime")(x, a, b)+("\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);

standard

> 

latex(r)

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

> 

 

Download march_8_2021_latex.mw

How come maple not be able so evalb this simple fa...

Asked by: Magnus Berg 20
evalb
March 08 2022
1  3

Hi, this is a small problem in af greater one for me. I'm trying to test to bigger equations if they are the same, which i suspect, the thing is, that maple wont evalb it. When i try with this simple problem, it gives me false. Can someone explaine this to me? Thank you for you help.

exception using solve. How to catch when using ass...

Asked by: nm 8552
solve exception assertion
March 08 2022
2  6

I am getting an exception divide by zero using solve. The problem is that when using kernelopts('assertlevel'=2):  I am no longer able to catch the exception in a catch try.

Removing kernelopts('assertlevel'=2):  I can catch the exception.

But I need to use kernelopts('assertlevel'=2): in my program.   

Is there a way to keep kernelopts('assertlevel'=2): and still catch exception thrown by solve?

Is this a bug in solve? And why using kernelopts('assertlevel'=2): prevents catching the exception?

Using Maple 2021.2 on windows 10. Worksheet attached.

 exception generated

 

 

> 

restart;

> 

trial_solution_constants:=[A[1]];
eq:=-A[1]-exp(x^2)*exp(-x^2) = 0;
solve(identity(eq,x),trial_solution_constants)

[A[1]]

-A[1]-exp(x^2)*exp(-x^2) = 0

Error, (in unknown) numeric exception: division by zero

Using assertlevel, now unable to catch exception

 
> 

restart;

> 

interface(warnlevel=4);
kernelopts('assertlevel'=2):

3

> 

try
   trial_solution_constants:=[A[1]];
   eq:=-A[1]-exp(x^2)*exp(-x^2) = 0;
   solve(identity(eq,x),trial_solution_constants)
catch:
   print("error happend ",lastexception);
end try;
print(" I am here");

[A[1]]

-A[1]-exp(x^2)*exp(-x^2) = 0

Error, (in unknown) assertion failed

" I am here"

Not Using assertlevel now can catch exception

 
> 

restart;

> 

interface(warnlevel=4);

3

> 

try
   trial_solution_constants:=[A[1]];
   eq:=-A[1]-exp(x^2)*exp(-x^2) = 0;
   solve(identity(eq,x),trial_solution_constants)
catch:
   print("error happend ",lastexception);
end try;
print(" I am here");

[A[1]]

-A[1]-exp(x^2)*exp(-x^2) = 0

"error happend ", unknown, "numeric exception: division by zero"

" I am here"

> 

 

Download march_8_2021_solve.mw

 

Update Sept 7,2022

FYI, here is another internal exception generated by solve which shows only when kernelopts('assertlevel'=2): is set, and which can not be trapped using try/catch. May be this could be fixed in future version of Maple. 

Worksheet attached.


 

> 

interface(version);

`Standard Worksheet Interface, Maple 2022.1, Windows 10, May 26 2022 Build ID 1619613`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1314 and is the same as the version installed in this computer, created 2022, September 2, 15:54 hours Pacific Time.`

> 

restart;
> 

interface(warnlevel=4);
kernelopts('assertlevel'=2):

3

> 

eq:=1 = -X*(-(Y^2*exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)+2*exp(X*Y)*y0*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*Y+exp(X*Y)*y0^2*exp(X*y0)*exp(x0*Y)*exp(x0*y0))/(exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*X+exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*x0+2*Y+2*y0)+(exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*Y+exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*y0+1)/(exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*X+exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*x0+2*Y+2*y0)^2*(Y*exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*X+exp(X*Y)*y0*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*X+exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)+Y*exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*x0+exp(X*Y)*y0*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*x0))/Y/(-(Y*exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*X+exp(X*Y)*y0*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*X+exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)+Y*exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*x0+exp(X*Y)*y0*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*x0)/(exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*X+exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*x0+2*Y+2*y0)+(exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*Y+exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*y0+1)/(exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*X+exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)*x0+2*Y+2*y0)^2*(X^2*exp(X*Y)*exp(X*y0)*exp(x0*Y)*exp(x0*y0)+2*exp(X*Y)*exp(X*y0)*x0*exp(x0*Y)*exp(x0*y0)*X+exp(X*Y)*exp(X*y0)*x0^2*exp(x0*Y)*exp(x0*y0)+2)):
> 


try
     sol:=solve(identity(eq,X),[x0, y0]);
catch:
     print("exception");
end try;

Error, (in unknown) assertion failed

> 

 


 

Download solve_exception.mw

 

 

 

piecewise function and integral ...

Asked by: Zeineb 520
integration piecewise plotting
March 07 2022
1  5

Dear all 
I have a function defined over the closed interval [ x[k], x[k+2] ] and zero elsewhere 
I would like to plot this sequence of function and compute an integral. 

I need your help to finish the attahced code, something is wrong. I can't  use piecewise funciton in loop and plot all functions in the same graph

piecewise_funciton_and_integral.mw

thanks for your remaks and help

Simple isolate fails...

Asked by: opus64 110
isolate
March 07 2022
4  7

Hello, can someone explain why something like this fails? The help page for 'isolate' says the second argument can be 'any algebraic expression'. Thanks.

How do I solve systems of second order differentia...

Asked by: mmsV 25
ode dsolve differential-equations
March 07 2022
3  2

I have the following systems of ODE in hand and would like to solve them. It would be great if somebody could help me with it.

> 

dudx := -415; dudy := 3901; dudz := -3365; dvdx := 23; dvdy := -1270; dvdz := 994; dwdx := 57; dwdy := -1665; dwdz := 1683; taup := 0.5390603100674905e-5

-415

  

3901

  

-3365

  

23

  

-1270

  

994

  

57

  

-1665

  

1683

  

0.5390603100674905e-5

 (1)
> 

u := .387; v := -.205; w := -.286; x0 := -0.979849e-2; y0 := -0.14583e-2; z0 := 0.623749e-1

.387

  

-.205

  

-.286

  

-0.979849e-2

  

-0.14583e-2

  

0.623749e-1

 (2)
> 

a__1 := dudx/taup; a__2 := dudy/taup; a__3 := dudz/taup; a__4 := 1/taup; a__5 := u/taup; b__1 := dvdx/taup; b__2 := dvdy/taup; b__3 := dvdz/taup; b__4 := 1/taup; b__5 := v/taup; c__1 := dwdx/taup; c__2 := dwdy/taup; c__3 := dwdz/taup; c__4 := 1/taup; c__5 := w/taup

-76985820.00

  

723666708.0

  

-624234420.0

  

185508.0000

  

71791.59600

  

4266684.000

  

-235595160.0

  

184394952.0

  

185508.0000

  

-38029.14000

  

10573956.00

  

-308870820.0

  

312209964.0

  

185508.0000

  

-53055.28800

 (3)
> 

sys := diff(x(t), t, t) = a__1*x(t)+a__2*y(t)+a__3*z(t)-a__4*(diff(x(t), t))+a__5, diff(y(t), t, t) = b__1*x(t)+b__2*y(t)+b__3*z(t)-b__4*(diff(y(t), t))+b__5, diff(z(t), t, t) = c__1*x(t)+c__2*y(t)+c__3*z(t)-c__4*(diff(z(t), t))+c__5

diff(diff(x(t), t), t) = -76985820.00*x(t)+723666708.0*y(t)-624234420.0*z(t)-185508.0000*(diff(x(t), t))+71791.59600, diff(diff(y(t), t), t) = 4266684.000*x(t)-235595160.0*y(t)+184394952.0*z(t)-185508.0000*(diff(y(t), t))-38029.14000, diff(diff(z(t), t), t) = 10573956.00*x(t)-308870820.0*y(t)+312209964.0*z(t)-185508.0000*(diff(z(t), t))-53055.28800

 (4)
> 

ics := x(0) = x0, y(0) = y0, z(0) = z0, (D(x))(0) = 0, (D(y))(0) = 0, (D(z))(0) = 0

x(0) = -0.979849e-2, y(0) = -0.14583e-2, z(0) = 0.623749e-1, (D(x))(0) = 0, (D(y))(0) = 0, (D(z))(0) = 0

 (5)


Thank you very much!

Download m_solution.mw

How to solve this type of equations...

Asked by: Madhukesh J K 140
homework numeric differential-equations
March 07 2022
2  2

Hi 

Warm greetings.

Is it possible to solve the numerical scheme present in the below paper.

Anita Chaturvedi, Kokila Ramesh, and Vatsala G A. (2017). “A MATHEMATICAL APPROACH TO STUDY THE EFFECT OF POLLUTANTS/TOXICANTS IN AQUATIC ENVIRONMENT.” International Journal of Research - Granthaalayah, 5(4) RAST, 33-38.

https://doi.org/10.5281/zenodo.803418

Thank you.

Calculating Implicit Integral with Maple...

Asked by: bstuan 90
calculus integration homework
March 07 2022
1  6

Could please help me solving the following problem?
Thank you a lot.

Question disappeared...

Asked by: Axel Vogt 5821
March 06 2022
5  1

The question https://www.mapleprimes.com/questions/233780-Plot-Absolute-Advantage-Of-Option-A disappeared (I know since I answered today).

Why?

Simplify with Side Relations and then eval...

Asked by: Ronan 1022
eval simplify
March 06 2022
3  1

I simplified a vector column using side relations. Then I wanted to evaluate using

eval( equation,  [x1=3,  x2=5......})

But side relations uses the reverse order i.e. after evaluation

[3=x1, 5=x2......]

So then the internals of the list need to be swaped tto work with eval.That is easy. I am just wondering is there a neater way to achieve this?

restart

NULL

P1 := Vector(3, {(1) = -(y[1]-y[3])*(y[2]-y[3])*((x[2]^2-x[2]*x[3]+x[3]^2)*x[1]^2-x[2]*x[3]*(x[2]+x[3])*x[1]+x[2]^2*x[3]^2)*(y[1]-y[2]), (2) = -(x[1]-x[3])*(x[2]-x[3])*(x[1]-x[2])*((y[2]^2-y[2]*y[3]+y[3]^2)*y[1]^2-y[2]*y[3]*(y[2]+y[3])*y[1]+y[2]^2*y[3]^2), (3) = ((-y[1]^2*y[2]+(3*y[2]*y[3]-y[3]^2)*y[1]-y[2]^2*y[3])*x[2]+x[3]*(y[1]^2*y[3]+y[2]*(y[2]-3*y[3])*y[1]+y[2]*y[3]^2))*x[1]^2+((y[1]^2*y[3]+y[2]*(y[2]-3*y[3])*y[1]+y[2]*y[3]^2)*x[2]^2+3*x[3]*(y[2]-y[3])*(y[1]-y[3])*(y[1]-y[2])*x[2]-x[3]^2*(y[1]^2*y[2]+(-3*y[2]*y[3]+y[3]^2)*y[1]+y[2]^2*y[3]))*x[1]-x[3]*((y[1]^2*y[2]+(-3*y[2]*y[3]+y[3]^2)*y[1]+y[2]^2*y[3])*x[2]-x[3]*(y[1]^2*y[3]+y[2]*(y[2]-3*y[3])*y[1]+y[2]*y[3]^2))*x[2]})

eqns := {(x[1]-x[2])*(x[2]-x[3])*(x[3]-x[1]) = R, (y[1]-y[2])*(y[2]-y[3])*(y[3]-y[1]) = S, x[1]^2*x[2]^2-x[1]^2*x[2]*x[3]+x[1]^2*x[3]^2-x[1]*x[2]^2*x[3]-x[1]*x[2]*x[3]^2+x[2]^2*x[3]^2 = Y, y[1]^2*y[2]^2-y[1]^2*y[2]*y[3]+y[1]^2*y[3]^2-y[1]*y[2]^2*y[3]-y[1]*y[2]*y[3]^2+y[2]^2*y[3]^2 = X, x[1]^2*x[2]+x[1]^2*x[3]+x[1]*x[2]^2-6*x[1]*x[2]*x[3]+x[1]*x[3]^2+x[2]^2*x[3]+x[2]*x[3]^2 = Z, y[1]^2*y[2]+y[1]^2*y[3]+y[1]*y[2]^2-6*y[1]*y[2]*y[3]+y[1]*y[3]^2+y[2]^2*y[3]+y[2]*y[3]^2 = W}

P1new := simplify(P1, eqns)

Vector[column](%id = 36893490132854572084)

 (1)

values := {x[1] = 3, x[2] = 5, x[3] = 7, y[1] = 2, y[2] = -11, y[3] = 13}

{x[1] = 3, x[2] = 5, x[3] = 7, y[1] = 2, y[2] = -11, y[3] = 13}

 (2)

vals1 := eval(eqns, values)

{-3432 = S, 16 = R, 120 = Z, 316 = Y, 2018 = W, 22753 = X}

 (3)

eval(P1new, vals1)

Vector[column](%id = 36893490132854572084)

 (4)

vals1swap := [seq(rhs(vals1[i]) = lhs(vals1[i]), i = 1 .. nops(vals1))]

[S = -3432, R = 16, Z = 120, Y = 316, W = 2018, X = 22753]

 (5)

eval(P1new, vals1swap)

Vector[column](%id = 36893490132849052116)

 (6)

eval(P1, values)

Vector[column](%id = 36893490132871267020)

 (7)

``

NULL

``

Download Q_6-03-2022_side_rels_and_eval.mw

Need help on graph...

Asked by: AHSAN 150
plotting
March 06 2022
2  1

Need help to plot a graph along x-axis  in attached worksheet. 

help_graph.mw

Pythagorean Puzzle...

Asked by: Tokoro 115
graphtheory circuit
March 05 2022
1  8

NULL

> 

restart;
> 

with(plots):with(plottools):

Solve diagonal resistance of nodes (0,0,0)-(3,4,5), (Edge length = ohm).(156/47 ohm)

   

plots[display]([nodes, node2, plotlinesx], scaling = constrained, style = wireframe, axes = boxed, orientation = [-50, 70, 0])

  

Solve minimum diagonal surface distance of nodes (0,0,0)-(3,4,5).(sqrt(74))
NULL

NULL

Download Resistance-345.mw

Solve diagonal resistance of nodes (0,0,0)-(3,4,5),

Edge length = ohm, therefore, each edge has 3, 4 and 5 ohm, respectivery. (156/47 ohm)

Solve minimum diagonal surface distance of nodes (0,0,0)-(3,4,5). (sqrt(74))

Electric circuit study.

Tokoro.

Loading times(when saving and after pauses in writ...

Asked by: Kalledude 5
osx macosx incomplete-question
March 05 2022
1  1

A have som problems when i Will save a project. It Will take 2-5 Minutes where my other freinds never Experince this? Also i have some problems when i pauses writing, when i take notes in class, it Will give me the loading circle on mac( iam using a MacBook Air 2018) 

i hope you Can help:)

thx

How to optimize with a constraint ...

Asked by: Magnus Berg 20
optimization
March 05 2022
2  5

Hi, im trying to optimize a function with a constraint. 

I've tried the Optimize package but I can't seem to make it work. 

I've attached  an image to my question, witht the function and the constraint. I want to find the optimal "t_x"

Function: rho*ln((-beta*tau + rho)/(1 + t__x)) + sigma*ln(sigma/(1 + t__y)) + beta*tau + B - rho - sigma - beta*tau*ln((-beta*tau + rho)/(1 + t__x))

Constaint: -t__x*(-beta*tau + rho)/(1 + t__x) + t__y*sigma/(1 + t__y) = R

Hope you can help 

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