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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

Four-vectors in Maple...

Asked by: Traruh Synred 55
vector physics duplicate-question
October 05 2023
1  20

Is there a simple 4-vector package available for Maple? Yes, I know about using Tensors, but don't want to fool with metrics and raising and lowering operators.

I have written my  own, but it seems buggy. I generate some vectors in in CM that should add up to a massless neutrino, but some times when I boost them to the 'lab' and do the addition there the neutrion acquires a substantial mass. It's not a merely numerical issue. It's weird because most of the time the neutrion mass is 0 or close to it.

My homemade boost proc 'boostTo' is attached.

unable to plot 3d and 2d plots...

Asked by: KIRAN SAJJAN 40
ode numeric differential-equations
October 05 2023
0  3

  I am unable to draw both 3d plots sowing error please help me to solve

> 

restart:NULLNULL
> 

p1 := 0.1e-1; p2 := 0.2e-1; p3 := 0.1e-1; Px := p1+p2+p3
> 

rf := 1050; kf := .52; cpf := 3617; sigmaf := .8
> 

sigma1 := 25000; rs1 := 5200; ks1 := 6; cps1 := 670
> 

sigma2 := 59.7*10^6; rs2 := 8933; ks2 := 400; cps2 := 385
> 

sigma3 := 2380000; rs3 := 4250; ks3 := 8.9538; cps3 := 686.2
> 

NULL
> 

B1 := 1+2.5*Px+6.2*Px^2; B2 := 1+13.5*Px+904.4*Px^2; B3 := 1+37.1*Px+612.6*Px^2; B4 := (ks1+2*kf-2*Px*(kf-ks1))/(ks1+2*kf+Px*(kf-ks1)); B5 := (ks2+3.9*kf-3.9*Px*(kf-ks2))/(ks2+3.9*kf+Px*(kf-ks2)); B6 := (ks3+4.7*kf-4.7*Px*(kf-ks3))/(ks3+4.7*kf+Px*(kf-ks3))
> 

a2 := B1*p1+B2*p2+B3*p3
> 

a1 := 1-p1-p2-p3+p1*rs1/rf+p2*rs2/rf+p3*rs3/rf
> 

a3 := 1-p1-p2-p3+p1*rs1*cps1/(rf*cpf)+p2*rs2*cps2/(rf*cpf)+p3*rs3*cps3/(rf*cpf)
> 

a4 := B4*p1+B5*p2+B6*p3
> 

NULL
> 

a5 := 1+3*((p1*sigma1+p2*sigma2+p3*sigma3)/sigmaf-p1-p2-p3)/(2+(p1*sigma1+p2*sigma2+p3*sigma3)/((p1+p2+p3)*sigmaf)-((p1*sigma1+p2*sigma2+p3*sigma3)/sigmaf-p1-p2-p3))

``

``

> 



NULL
> 

ODE:=[(a2+K)*(diff(U0(eta), eta, eta))/a1-Ra*(diff(U0(eta), eta))+lambda0/a1-a5*M1^2*U0(eta)/a1+K*(diff(N0(eta), eta))/a1+la*Ra*Theta0(eta)*(1+Qc*Theta0(eta)), (a2+K)*(diff(U1(eta), eta, eta))/a1-H^2*l1*U1(eta)-Ra*(diff(U1(eta), eta))+lambda1/a1-a5*M1^2*U1(eta)/a1+K*(diff(N1(eta), eta))/a1+la*Ra*(Theta1(eta))(1+2*Qc*Theta0(eta)), diff(N0(eta), eta, eta)-Ra*a1*Pj*(diff(N0(eta), eta))-2*n1*N0(eta)-n1*(diff(U0(eta), eta)), diff(N1(eta), eta, eta)-Ra*a1*Pj*(diff(N1(eta), eta))-2*n1*N1(eta)-n1*(diff(U1(eta), eta))-H^2*a1*Pj*l1*N1(eta), (a4/(a3*Pr)-delta*Ra^2/H^2+4*Rd*(1+(Tp-1)^3*Theta0(eta)^3+3*(Tp-1)^2*Theta0(eta)^2+(3*(Tp-1))*Theta0(eta))/(3*a3*Pr))*(diff(Theta0(eta), eta, eta))-Ra*(diff(Theta0(eta), eta))+a5*Ec*M1^2*U0(eta)^2/a3+(a2+K)*Ec*(diff(U0(eta), eta))^2/a1+Q*Theta0(eta)/a3+4*(diff(Theta0(eta), eta))^2*Rd*(3*(Tp-1)+6*(Tp-1)^2*Theta0(eta)+3*(Tp-1)^3*Theta0(eta)^2)/(3*a3*Pr), (a4/(a3*Pr)-delta*Ra^2/H^2+4*Rd*(1+(Tp-1)^3*Theta0(eta)^3+3*(Tp-1)^2*Theta0(eta)^2+(3*(Tp-1))*Theta0(eta))/(3*a3*Pr))*(diff(Theta1(eta), eta, eta))-(H^2*l1+2*Ra*delta*l1+Ra)*(diff(Theta1(eta), eta))+(Q/a3-delta*H^2*l1^2)*Theta1(eta)+2*(a2+K)*Ec*(diff(U0(eta), eta))*(diff(U1(eta), eta))/a1+2*a5*Ec*M^2*U0(eta)*U1(eta)/a3+4*(diff(Theta0(eta), eta, eta))*Theta1(eta)*Rd*(3*(Tp-1)+6*(Tp-1)^2*Theta0(eta)+3*(Tp-1)^3*Theta0(eta)^2)/(3*a3*Pr)+4*Rd*(diff(Theta0(eta), eta))^2*(6*(Tp-1)^2*Theta1(eta)+6*(Tp-1)^3*Theta0(eta)*Theta1(eta))/(3*a3*Pr)+4*Rd*(diff(Theta1(eta), eta))*(diff(Theta0(eta), eta))*(6*(Tp-1)+6*(Tp-1)^3*Theta0(eta)^2+12*(Tp-1)^2*Theta0(eta))/(3*a3*Pr)]:
> 


(LB,UB):= (0,1):


BCs:= [
  
  U0(0) = 0, U1(0) = 0, N0(0) = 0, N1(0) = 0, Theta0(0) = 0, Theta1(0) = 0, U0(1) = 0, U1(1) = 0, N0(1) = 0, N1(1) = 0, Theta0(1) = 1, Theta1(1) = 0
]:
> 

NULL
> 


Params:= Record(
   
   M1=  1.2, Rd=0.8,la=0.8,n1=1.2,Q=0.2,Pj=0.001,Ra=0.8,Ec=1,    Pr= 21,   delta= 0.2,    t1= (1/4)*Pi, lambda0=2,lambda1=3,   Qc= 0.1,    l1= 1,K=0.4,H=3 ,deltat=0.05  ):
   
> 

NBVs:= [   
 
a1**D(U0)(0) = `C*__f` , # Skin friction coefficient
 (a4+(4*Rd*(1/3))*(1+(Tp-1)*(Theta0(0)+0.1e-2*exp(l1*t1)*Theta1(0)))^3)*((D(Theta0))(0)+0.1e-2*exp(l1*t1)*(D(Theta1))(0)) = `Nu*`    # Nusselt number     
]:
Nu:= `Nu*`:
Cf:= `C*__f`:

 
> 

Solve:= module()
local
   nbvs_rhs:= rhs~(:-NBVs), #just the names
   Sol, #numeric dsolve BVP solution of any 'output' form
   ModuleApply:= subs(
      _Sys= {:-ODEs[], :-BCs[], :-NBVs[]},
      proc({
          M1::realcons:=  Params:-M1,
         Pr::realcons:= Params:-Pr,
         Rd::realcons:= Params:-Rd,
         la::realcons:= Params:-la,
         Tp::realcons:= Params:-Tp,
         n1::realcons:= Params:-n1,
         Q::realcons:= Params:-Q,
         Pj::realcons:= Params:-Pj,
         Ra::realcons:= Params:-Ra,
         Ec::realcons:= Params:-Ec,
         t1::realcons:=  Params:-t1,
         delta::realcons:= Params:-delta,
         lambda0::realcons:= Params:-lambda0,
         lambda1::realcons:= Params:-lambda1,
         Qc::realcons:= Params:-Qc,
         K::realcons:= Params:-K,
         l1::realcons:= Params:-l1,
         H::realcons:= Params:-H
      })
         Sol:= dsolve(_Sys, _rest, numeric);
         AccumData(Sol, {_options});
         Sol
      end proc
   ),
   AccumData:= proc(
      Sol::{Matrix, procedure, list({name, function}= procedure)},
      params::set(name= realcons)
   )
   local n, nbvs;
      if Sol::Matrix then
         nbvs:= seq(n = Sol[2,1][1,Pos(n)], n= nbvs_rhs)
      else
         nbvs:= (nbvs_rhs =~ eval(nbvs_rhs, Sol(:-LB)))[]
      fi;
      SavedData[params]:= Record[packed](params[], nbvs)
   end proc,
   ModuleLoad:= eval(Init);
export
   SavedData, #table of Records
   Pos, #Matrix column indices of nbvs
   Init:= proc()
      Pos:= proc(n::name) option remember; local p; member(n, Sol[1,1], 'p'); p end proc;
      SavedData:= table();
      return
   end proc ;
   ModuleLoad()
end module:
 
> 


 
> 

 

> 

#procedure that generates 3-D plots (dropped-shadow contour + surface) of an expression


ParamPlot3d:= proc(
   Z::{procedure, `module`}, #procedure that extracts z-value from Solve's dsolve solution
   X::name= range(realcons), #x-axis-parameter range
   Y::name= range(realcons), #y-axis-parameter range
   FP::list(name= realcons), #fixed values of other parameters
   {
      #fraction of empty space above and below plot (larger "below"
      #value improves view of dropped-shadow contourplot):
      zmargin::[realcons,realcons]:= [.05,0.15],
      eta::realcons:= :-LB, #independent variable value
      dsolveopts::list({name, name= anything}):= [],
      contouropts::list({name, name= anything}):= [],
      surfaceopts::list({name, name= anything}):=[]    
   }
)
local
   LX:= lhs(X), RX:= rhs(X), LY:= lhs(Y), RY:= rhs(Y),
   Zremember:= proc(x,y)
   option remember; #Used because 'grid' should be the same for both plots.
      Z(
         Solve(
            LX= x, LY= y, FP[],
            #Default dsolve options can be changed by setting 'dsolveopts':
            'abserr'= 0.5e-7, 'interpolant'= false, 'output'= Array([eta]),  
            dsolveopts[]
         )
      )
   end proc,
   plotspec:= (Zremember, RX, RY),
   C:= plots:-contourplot(
      plotspec,
      #These default plot options can be changed by setting 'contouropts':
      'grid'= [25,25], 'contours'= 5, 'filled',
      'coloring'= ['yellow', 'orange'], 'color'= 'green',
      contouropts[]
   ),
   P:= plot3d(
      plotspec,
      #These default plot options can be changed by setting 'surfaceopts':
      'grid'= [25,25], 'style'= 'surfacecontour', 'contours'= 6,
      surfaceopts[]
   ),
   U, L #z-axis endpoints after margin adjustment
;
   #Stretch z-axis to include margins:
   (U,L):= ((Um,Lm,M,m)-> (M*(Lm-1)+m*Um, M*Lm+m*(Um-1)) /~ (Um+Lm-1))(
      zmargin[],
      (max,min)(op(3, indets(P, 'specfunc'('GRID'))[])) #actual z-axis range
   );
   plots:-display(
      [
         plots:-spacecurve(
            {
               [[lhs(RX),rhs(RY),U],[rhs(RX),rhs(RY),U],[rhs(RX),rhs(RY),L]], #yz backwall
               [[rhs(RX),rhs(RY),U],[rhs(RX),lhs(RY),U],[rhs(RX),lhs(RY),L]]  #xz backwall
            },
            'color'= 'grey', 'thickness'= 0
         ),
         plottools:-transform((x,y)-> [x,y,L])(C), #dropped-shadow contours
         P
      ],
      #These default plot options can be changed simply by putting the option in the
      #ParamPlot3d call:
      'view'= ['DEFAULT', 'DEFAULT', L..U], 'orientation'= [-135, 75], 'axes'= 'frame',
      'labels'= [lhs(X), lhs(Y), Z], 'labelfont'= ['TIMES', 'BOLDOBLIQUE', 16],
      'caption'= nprintf(cat("%a = %4.2f, "$nops(FP)-1, "%a = %4.2f"), (lhs,rhs)~(FP)[]),
      'captionfont'= ['TIMES', 14],
      'projection'= 2/3,   
      _rest
   )
end proc:

> 

NULL
> 

NULL
> 

GetNu := proc (Sol::Matrix) options operator, arrow; Sol[2, 1][1, Solve:-Pos(:-Nu)] end proc
> 

ParamPlot3d(
   GetNu,Q= 0..5, Rd= 0..5, [
   
   Pr= 21   ],
   labels= [Q, gamma, Nu]
);

Error, (in plot/iplot2d/levelcurve) could not evaluate expression

  

``

Download P6_3D_plots.mw

How to use simplify command?...

Asked by: raj2018 50
solve simplification
October 02 2023
2  3

HI,
I want to simplify an algebraic experssion. How do I do this with Maple?
A1.mw

MemoryInUse() slow and seemed weird....

Asked by: Traruh Synred 55
memory duplicate-question incomplete-question
October 01 2023
0  14

I have been using 'MemoryInUse()' to try to track down a memory leak that is crashing my Maple-based simulation. The problematic proc seems to be ProbDStarLNu which calculates the probablity of decay as a function of the angles of the decay product. It gets called a lot in acceptance rejection decay generation.

'MemoryInUse()' slows it down a lot. It also seemed to give weird results to me. I calculate the mem used on entry and then after the 4 trig functions have been called. The amount of mem 'in use' goes down after the trig functions are called. I was suspecting they were the source of the leak, but they seem almost an anti-leak.

This weird behavior caused me to write my own mem counting proc ('memUsed') based on summing over the results of 'mem:= kernelopts(memusage)'.

It is much faster. It gives nearly but not quite the same numbers. It still goes "backward" when the trig functions are called. Most of the mem growth comes from the algebra that follows the trig.

Why would that be?

I have included code for 'ProbDStarLNu'. It's pretty simple.

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