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

Asked by: Teep 200
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 55
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
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
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 55
solve simplification
October 02 2023
2  3

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

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