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Bug in the solve command...

Asked by: Kitonum 20736
solve
January 28 2024
1  7

If we solve the equation  x^x=1/sqrt(2)  in Maple 2018.2, then Maple returns only one solution  x=1/2 , although this equation has 2 solutions  x=1/2  or  x=1/4 . This can be seen if you plot graphs or , for example, solve by the  Student:-Calculus1:-Roots  command. In this case, the root  x=1/4   is returned only as a numerical approximation. I wonder if this bug has been fixed in the latest versions of Maple?

restart;
solve(x^x=1/sqrt(2));
Student:-Calculus1:-Roots(x^x=1/sqrt(2));

plot error in 3d plots ...

Asked by: KIRAN SAJJAN 40
ode syntax homework
December 19 2023
0  5

sachi_stream_error_3d.mw  3d_sachin_p1.mw

Dear sir, there is something missing why it is not able to evaluate?

By reference of some posts I have implemented to my ODE but not getting the graph.

what is the mistake in both files?

Ode equations solution ...

Asked by: SHIVAS 35
ode homework numeric
December 15 2023
0  4

How to solve this type of ode in maple

need the value of S, Q, E

How can I express a time series forecast as a tabl...

Asked by: Teep 195
December 09 2023
0  2

Good day.

I am working on a time series problem that uses 107 data sets (historic) and I wish to obtain a forecast for the next successive 12 events. I have obtained the time series plot for the predicted values and the associated dates separately (see attached), however - I am looking to get the solution in a more user-friendly format and was hoping someone could help me out.

Can someone tell me how to 

1. Express the data values only as whole number values (decimal-free)

2. Construct a table of data values and dates for the average forecast as well as the 2nd and 98th percentile forecasts?

Thanks for reading!

MaplePrimes_TS_Example.mw

Using Maple to measure maps, etc....

Asked by: Traruh Synred 55
image line
December 05 2023
2  13

I'd like to use Maple to make measurements on a map (Dealey Plaza). I can load an image in Sketcher and draw lines on it, but can't figure out how to access the lengths of those lines.

> 

restart``
> 

estart; with(Physics); with(LinearAlgebra); with(VectorCalculus); with(Optimization); with(Statistics); with(ArrayTools); with(plottools); with(plots); with(Threads); with(MmaTranslator[Mma]), with(StringTools); with(CodeGeneration); VectorCalculus:-`*`(Setup(mathematicalnotation = true), Setup(coordinatesystems = cartesian))

estart

  

[annulus, arc, arrow, circle, cone, cuboid, curve, cutin, cutout, cylinder, disk, dodecahedron, ellipse, ellipticArc, exportplot, extrude, getdata, hemisphere, hexahedron, homothety, hyperbola, icosahedron, importplot, line, octahedron, parallelepiped, pieslice, point, polygon, prism, project, rectangle, reflect, rotate, scale, sector, semitorus, sphere, stellate, tetrahedron, torus, transform, translate]

  

`Default differentiation variables for d_, D_ and dAlembertian are:`*{X = (x, y, z, t)}

  

`Systems of spacetime Coordinates are:`*{X = (x, y, z, t)}

 (1)
> 

``
> 

``
> 

NULL

 

> 

``
> 

``

Download DealeyPlazaToo.mw

How to find the location of extreme points?...

Asked by: raj2018 50
optimization calculus plotting
December 05 2023
1  18

Hi,
I have a function (see attached file).  How can I find by Maple 
those values of beta and f for which W will have 
three consecutive local extrema between the
phi=0 and phi_0 where W=dW/dphi=0 at phi=0 and W=0 at phi_0 and W<0 for 0<abs(phi)<phi_0?
Thanks,
plot.mw

How to diplay lots of curves...

Asked by: Traruh Synred 55
vector plotting display
December 01 2023
1  1

Using Maple-18 on Window 11...

I have a set of curves in a Maple 'vector.' I want to plot them all on the same figure, but if call 'display' with the vector it makes separate plots for each one. I have to all it with each plot individual to get them on the same plot:

lc is a 'vector' of curves (I use 'vector' because I want to append and that doesn't work for 'list')

display(lc) -- plots a separate plot for each element of lc

display(lc[1], lc[2], lc[3],...) puts them all on one plot as needed, but as there will be a large numbe of curvesr it's extremely tedious.

It is a Huygens principle based simulation of diffraction.

> 

restart
> 

estart; with(Physics); with(LinearAlgebra); with(VectorCalculus); with(Optimization); with(Statistics); with(ArrayTools); with(plots); with(plottools); with(Threads); with(MmaTranslator[Mma]), with(StringTools); with(CodeGeneration); with(ImageTools); with(ImageTools:-Draw); VectorCalculus:-`*`(Setup(mathematicalnotation = true), Setup(coordinatesystems = cartesian))

estart

  

[annulus, arc, arrow, circle, cone, cuboid, curve, cutin, cutout, cylinder, disk, dodecahedron, ellipse, ellipticArc, exportplot, extrude, getdata, hemisphere, hexahedron, homothety, hyperbola, icosahedron, importplot, line, octahedron, parallelepiped, pieslice, point, polygon, prism, project, rectangle, reflect, rotate, scale, sector, semitorus, sphere, stellate, tetrahedron, torus, transform, translate]

  

`Default differentiation variables for d_, D_ and dAlembertian are:`*{X = (x, y, z, t)}

  

`Systems of spacetime Coordinates are:`*{X = (x, y, z, t)}

 (1)
> 

NULL
> 

NULL

 

> 

radius := 1.0

1.0

 (2)
> 

> 

NULL
> 

> 

NULL
> 

``
> 

NULL
> 

alpha := sin((1/4)*Pi)

(1/2)*2^(1/2)

 (3)
> 

step := .2

.2

 (4)
> 

radius := 100.0

100.0

 (5)
> 

l1 := line([0, 0], [100, 100])

CURVES([[0., 0.], [100., 100.]])

 (6)
> 

loAng := 0.

0.

 (7)
> 

hiAng := (1/2)*Pi

(1/2)*Pi

 (8)
> 

c1 := arc([0, 0.], radius, loAng .. Pi, color = "red")
> 

c2 := arc([step, 0.], -alpha*step+radius, loAng .. hiAng, color = "blue")
> 

c3 := arc([2*step, 0.], -2*alpha*step+radius, loAng .. Pi, color = "purple")
> 

c4 := arc([3*step, 0.], -3*alpha*step+radius, loAng .. Pi, color = "black")
> 

plots[display](l1, c1, c2, c3, c4, view = [0. .. radius, 0 .. radius])

 
> 

`cir&Assign;arc`([x, 0.], radius-step, loAng .. hiAng, i, color = "red")

`cir&Assign;arc`([x, 0.], 99.8, 0. .. (1/2)*Pi, i, color = "red")

 (9)
> 

``
> 

xLimitWall := 500.0; nScatter := 20; step := xLimitWall/(nScatter+1); x := 0.; for i from 0 to nScatter do x := x+step; cir := arc([x, 0.], radius-step, 0 .. Pi, color = "red"); if i = 0 then lc := Vector([cir]) else i; cir; Append(lc, cir) end if end do; lc

xLimitWall := 500.0

  

nScatter := 20

  

step := 23.80952381

  

x := 0.

  

x := 23.80952381

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 47.61904762

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 71.42857143

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 95.23809524

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 119.0476190

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 142.8571428

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 166.6666666

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 190.4761904

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 214.2857142

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 238.0952380

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 261.9047618

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 285.7142856

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 309.5238094

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 333.3333332

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 357.1428570

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 380.9523808

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 404.7619046

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 428.5714284

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 452.3809522

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 476.1904760

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 499.9999998

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

Vector[column](%id = 4400555778)

 (10)
> 

lc[1]

CURVES(Matrix(%id = 4400554242), COLOUR(RGB, 1.00000000, 0., 0.))

 (11)
> 

lc(2)
> 

``
> 

lc
> 

lc[1]
> 

``

Download JFKWEdgeDifractionDirection.mwJFKWEdgeDifractionDirection.mwen.

Maple into LaTeX...

Asked by: petit loup 40
export latex
November 26 2023
0  2
Hello, I would like to integrate a Maple sheet into a LaTeX sheet. How to do ? Thanks in advance.

'local' dellarations inside if statements, don't ...

Asked by: Traruh Synred 55
syntax procedure 2dmath
November 24 2023
0  7

I find that if if declare a variable in a procedure inside a if  statement it Maple things something is wrong with the if statement:

tSound=proc(xMic,yMic,zMic,xGun,yGun,zGun,mode)  

global vSound;  

local locMic:=Vector([xMic,yMix,zMix]);  

local locGun:=Vector([xGun,yGun,zGun]);   l

ocal delGunToMix;   if mode=1 then #`direct  `    

local x=0.0;    <==remove this sand fine

delGunToMix:=locMic-locGun;    

return vSound*Norm(delGunToMix);  

elif  mode=2 then #`reflect off wall at z=0`        

end if;   return 0.0;  end proc:


Error, invalid 'if' statement
==>I can delclare the variable 'local' outside the if. Why? It doesn't make much sense, though not that hard to avoid.

first order pde...

Asked by: Suryakanth 5
homework pde numeric
November 12 2023
1  5

how to solve tis type of pdefirst_order_pde.mw

error in calculating table values for time depend...

Asked by: KIRAN SAJJAN 40
homework pde numeric
October 27 2023
0  3
> 

restart
> 

with(PDEtools); with(plots)
> 

inf := 6
> 

Gr := 3; beta := 2; sigma1 := .2; alpha0 := .1; Pr := 7.1; E1 := .5; S := .7; Gm := 3; Kp := .2; Lat := .5; Lac := .5; Sc := .5; a1 := .5; Rd := 3
> 

OdeSys := {diff(Phid(eta, t), t)-Lac*(Phi(eta, t)-Phid(eta, t)) = 0, diff(Thetad(eta, t), t)-Lat*(Theta(eta, t)-Thetad(eta, t)) = 0, diff(Phi(eta, t), eta, eta)-Sc*(diff(Phi(eta, t), t))-Sc*a1*R*(Phi(eta, t)-Phid(eta, t)) = 0, diff(Theta(eta, t), eta, eta)-Pr*(diff(Theta(eta, t), t))-Rd*Theta(eta, t)-(2/3)*R*(Theta(eta, t)-Thetad(eta, t)) = 0, (1+1/beta)*(diff(U(eta, t), eta, eta))-(diff(U(eta, t), t))-Kp*U(eta, t)-R*(U(eta, t)-Ud(eta, t))+Gr*Theta(eta, t)+Gm*Phi(eta, t)+E1*exp(-S*eta) = 0, sigma1*(diff(Ud(eta, t), t))-U(eta, t)+Ud(eta, t) = 0}
> 

Cond := {Phi(0, t) = 1, Phi(eta, 0) = 0, Phi(inf, t) = 0, Phid(eta, 0) = 0, Theta(eta, 0) = 0, Theta(inf, t) = 0, Thetad(eta, 0) = 0, U(0, t) = t, U(eta, 0) = 0, U(inf, t) = 0, Ud(eta, 0) = 0, (D[1](Theta))(0, t) = -alpha0*(-1+Theta(0, t))}
> 

OdeSys1 := {diff(Phid1(eta, t), t)-Lac*(Phi1(eta, t)-Phid1(eta, t)) = 0, diff(Thetad1(eta, t), t)-Lat*(Theta1(eta, t)-Thetad1(eta, t)) = 0, diff(Phi1(eta, t), eta, eta)-Sc*(diff(Phi1(eta, t), t))-Sc*a1*R*(Phi1(eta, t)-Phid1(eta, t)) = 0, diff(Theta1(eta, t), eta, eta)-Pr*(diff(Theta1(eta, t), t))-Rd*Theta1(eta, t)-(2/3)*R*(Theta1(eta, t)-Thetad1(eta, t)) = 0, (1+1/beta)*(diff(U1(eta, t), eta, eta))-(diff(U1(eta, t), t))-Kp*U1(eta, t)-R*(U1(eta, t)-Ud1(eta, t))+Gr*Theta1(eta, t)+Gm*Phi1(eta, t)+E1*exp(-S*eta) = 0, sigma1*(diff(Ud1(eta, t), t))-U1(eta, t)+Ud1(eta, t) = 0}
> 

Cond1 := {Phi1(0, t) = 1, Phi1(eta, 0) = 0, Phi1(inf, t) = 0, Phid1(eta, 0) = 0, Theta1(eta, 0) = 0, Theta1(inf, t) = 0, Thetad1(eta, 0) = 0, U1(0, t) = 1, U1(eta, 0) = 0, U1(inf, t) = 0, Ud1(eta, 0) = 0, (D[1](Theta1))(0, t) = -alpha0*(-1+Theta1(0, t))}
> 

``
> 

NULL
> 

NULL
> 

colour := [red, green, blue, black]
> 

RVals := [1, 5, 10, 20]
> 

NULL
> 

for j to numelems(RVals) do Ans := pdsolve((eval([OdeSys, Cond], R = RVals[j]))[], numeric, time = t, spacestep = 0.25e-1, timestep = 1); Ans1 := pdsolve((eval([OdeSys1, Cond1], R = RVals[j]))[], numeric, time = t, spacestep = 0.25e-1, timestep = 1) end do
> 

interface(rtablesize = 100); interface(displayprecision = 5); Matrix([[eta, `&Nu;u1`, `&Nu;ud1`, Shr1, Shrd1, `&Nu;u2`, `&Nu;ud2`, Shr2, Shrd2, `&Nu;u3`, `&Nu;ud3`, Shr3, Shrd3, `&Nu;u4`, `&Nu;ud4`, Shr4, Shrd4], seq([seq([(eval(diff(Theta(.5, eta), eta), Ans[k]))(0), (eval(diff(Phi(.5, eta), eta), Ans[k]))(0), (eval(Thetad(.5, eta), Ans[k]))(0), (eval(Phid(.5, eta), Ans[k]))(0)][], k = 1 .. numelems(RVals))])]); interface(rtablesize = 10); interface(displayprecision = -1)

Error, index must evaluate to a name when indexing a module

  
> 

interface(rtablesize = 100); interface(displayprecision = 5); Matrix([[eta, `&Nu;u1`, `&Nu;ud1`, Shr1, Shrd1, `&Nu;u2`, `&Nu;ud2`, Shr2, Shrd2, `&Nu;u3`, `&Nu;ud3`, Shr3, Shrd3, `&Nu;u4`, `&Nu;ud4`, Shr4, Shrd4], seq([seq([(eval(diff(Theta1(1.1, eta), eta), Ans1[k]))(0), (eval(diff(Phi1(1.1, eta), eta), Ans1[k]))(0), (eval(Thetad1(1.1, eta), Ans1[k]))(0), (eval(Phid1(1.1, eta), Ans1[k]))(0)][], k = 1 .. numelems(RVals))])]); interface(rtablesize = 10); interface(displayprecision = -1)

Error, index must evaluate to a name when indexing a module

  
> 

NULL

Download error_in_table_value.mw

first and second order derivative plot of pdes...

Asked by: KIRAN SAJJAN 40
homework pde numeric
October 17 2023
0  10

How to plot the second order derivative and first oder derivatives plot in time dependent pde and vector plot of  theta(y,t), u(y,t) at y=0..10 and t=0..1

nowhere i found a vector plot of time-dependent pde 

how to plot give me suggestions.

in vector plots, flow patterns should show with arrow marks

> 

  restart;
  inf:=10:
  pdes:= diff(u(y,t),t)-xi*diff(u(y,t),y)=diff(u(y,t),y$2)/(1+lambda__t)+Gr*theta(y,t)+Gc*C(y,t)-M*u(y,t)-K*u(y,t),
         diff(theta(y,t),t)-xi*diff(theta(y,t),y)=1/Pr*diff(theta(y,t),y$2)+phi*theta(y,t),
         diff(C(y,t),t)-xi*diff(C(y,t),y)=1/Sc*diff(C(y,t),y$2)-delta*C(y,t)+nu*theta(y,t):
  conds:= u(y,0)=0, theta(y,0)=0, C(y,0)=0,
          u(0,t)=0, D[1](theta)(0,t)=-1, D[1](C)(0,t)=-1,
          u(inf,t)=0, theta(inf,t)=0, C(inf,t)=0:
  pars:= { Gr=1, Gc=1, M=1, nu=1, lambda__t=0.5,
           Sc=0.78, delta=0.1, phi=0.5, K=0.5, xi=0.5
         }        

{Gc = 1, Gr = 1, K = .5, M = 1, Sc = .78, delta = .1, nu = 1, phi = .5, xi = .5, lambda__t = .5}

 (1)
> 

  PrVals:=[0.71, 1.00, 3.00, 7.00]:
  colors:=[red, green, blue, black]:
  for j from 1 to numelems(PrVals) do
      pars1:=`union`( pars, {Pr=PrVals[j]}):
      pdSol:= pdsolve( eval([pdes], pars1),
                       eval([conds], pars1),
                       numeric
                     );
      plt[j]:=pdSol:-plot( diff(u(y,t),y), y=0, t=0..2, numpoints=200, color=colors[j]);
  od:
  plots:-display( [seq(plt[j], j=1..numelems(PrVals))]);

 
> 

PrVals := [.71, 1.00, 3.00, 7.00]; colors := [red, green, blue, black]; for j to numelems(PrVals) do pars1 := `union`(pars, {Pr = PrVals[j]}); pdSol := pdsolve(eval([pdes], pars1), eval([conds], pars1), numeric); plt[j] := pdSol:-plot(diff(u(y, t), y, y), y = 0, t = 0 .. 2, numpoints = 200, color = colors[j]) end do; plots:-display([seq(plt[j], j = 1 .. numelems(PrVals))])

 
 

 

Download badPDE.mw

ScatterPlot range?...

Asked by: Traruh Synred 55
axis plotting scatterplot
October 13 2023
0  2

How do I set the axis range in a Maple scatter plot. It's not evident to me from the Help.

how to solve Pde using LaPlace Transformation ...

Asked by: SHIVAS 35
syntax homework pde
October 13 2023
1  21

Please help me how to impliment to solve this problem 

Download dust_practice_code.mw

dust_paper.pdf

Read and writing histogram or list to files?...

Asked by: Traruh Synred 55
vector export incomplete-question
October 12 2023
0  10

As my jobs are still crashing with memory leak, I'd like to write results out to files and read them back to add them together.

I see something called 'Export' and something called 'Import'. It didn't work for me. Does the file have to already exist? An example would be nic

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