Maple 2024 Questions and Posts

These are Posts and Questions associated with the product, Maple 2024

Whenever I have local proc inside a proc, and use local variables from the outer proc inside it, Mint tells me that the variables are not used.

This can't be right. Why does it say that? Here is MWE. I have this foo.mpl file

foo := proc()

local C1;
local y,x;

    proc()
        C1:= `tools/genglobal`(_C); 
        sol:=y(x)=  C1; 
    end proc();

end proc;

We see clearly that C1 is used, also x and y are used. There can be more code using these inside the inner proc. But this is what mint says

"C:\Program Files\Maple 2024\bin.X86_64_WINDOWS\mint.exe" foo.mpl

    |\^/|      Maple 2024 Diagnostic Program
._|\|   |/|_.  Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2024
 \  MINT   /   All rights reserved. Maple is a trademark of
 <____ ____>   Waterloo Maple Inc.
      |
Procedure foo() on lines 1 to 11
  These local variables were never used:  C1, x, y

Any idea why it says these are not used?

Also, I noticed it did not warn me that variable sol is global inside the proc. i.e. I was expecting something like this 

          These names were used as global names but were not declared: sol

Which is typical message mint gives when using a name inside a proc which was not declared,

Maple 2024.2 on Windows

I have a square matrix of data points. Each point is between 0 to 0.2. I wish to plot it and set the axes to values from 0 to 1. I want the 3D plot to be plotted with a constrained scaling. The two options I have are plots:-matrixplot and plots:-surfdata. 

* matrixplot can constrain the data, but it isn't obvious how to change the axes so that it shows from 0 to 1 in both directions. 

* In surfaceplot, it is easy to adjust the axes values, but scaling=constrained does nothing. 

(I assume someone else might also appreciate the answer. So, instead of me continuing to struggle, I post here and hope someone can answer without the use of many brain cells.) 

Example attached.

restart; N := 20; M := LinearAlgebra:-RandomMatrix(N, generator = rand(0 .. .2))

 

Scaling can be easily controlled, but labels are bad

plots:-matrixplot(N*M, labels = ["x", "y", "V"], scaling = constrained, axis = [tickmarks = [seq(0 .. 1, numelems = 10)]], size = [600, 600])

 

Axes are shown nicely, but scaling cannot be constrained.

plots:-surfdata(M, 0 .. 1, 0 .. 1, labels = ["x", "y", "V"], scaling = constrained, size = [600, 600])

 
 

NULL

Download Scaled_matrix_plot_with_axes.mw

If I understand right, in the following calling an exception should be raised since the return value of the matching coercion procedure is of course not of type “set”: 

restart;
foo := (x::coerce(set, (y::rtable) -> convert(y, list))) -> x:
foo(<0>);
 = 
                              [0]

Did I miss something?

I want to remove the Lambert function (LambertW) from my equation, but I don't know how. I tried using the explicit option, but it didn't work. How can I express the equation without LambertW?

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

declare(u(x, y, z, t))

u(x, y, z, t)*`will now be displayed as`*u

(2)

declare(f(x, y, z, t))

f(x, y, z, t)*`will now be displayed as`*f

(3)

pde := diff(diff(u(x, y, z, t), t)+6*u(x, y, z, t)*(diff(u(x, y, z, t), x))+diff(u(x, y, z, t), `$`(x, 3)), x)-lambda*(diff(u(x, y, z, t), `$`(y, 2)))+diff(alpha*(diff(u(x, y, z, t), x))+beta*(diff(u(x, y, z, t), y))+gamma*(diff(u(x, y, z, t), z)), x)

diff(diff(u(x, y, z, t), t), x)+6*(diff(u(x, y, z, t), x))^2+6*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x))+diff(diff(diff(diff(u(x, y, z, t), x), x), x), x)-lambda*(diff(diff(u(x, y, z, t), y), y))+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+gamma*(diff(diff(u(x, y, z, t), x), z))

(4)

pde_nonlinear, pde_linear := selectremove(proc (term) options operator, arrow; not has((eval(term, u(x, y, t) = a*u(x, y, t)))/a, a) end proc, expand(pde))

0, diff(diff(u(x, y, z, t), t), x)+6*(diff(u(x, y, z, t), x))^2+6*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x))+diff(diff(diff(diff(u(x, y, z, t), x), x), x), x)-lambda*(diff(diff(u(x, y, z, t), y), y))+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+gamma*(diff(diff(u(x, y, z, t), x), z))

(5)

thetai := t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i]; eval(pde_linear, u(x, y, z, t) = exp(thetai)); eq15 := isolate(%, w[i])

t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i]

 

w[i]*k[i]*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])+12*k[i]^2*(exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i]))^2+k[i]^4*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])-lambda*l[i]^2*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])+alpha*k[i]^2*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])+beta*k[i]*l[i]*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])+gamma*k[i]*r[i]*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])

 

w[i] = -(t*k[i]^4+gamma*t*k[i]*r[i]+alpha*t*k[i]^2+beta*t*k[i]*l[i]-lambda*t*l[i]^2+LambertW(12*t*k[i]*exp(-(t*k[i]^4+alpha*t*k[i]^2+beta*t*k[i]*l[i]+gamma*t*k[i]*r[i]-lambda*t*l[i]^2-x*k[i]^2-y*k[i]*l[i]-z*k[i]*r[i]-eta[i]*k[i])/k[i]))*k[i])/(t*k[i])

(6)

sol := solve(eq15, w[i], explicit)

-(t*k[i]^4+gamma*t*k[i]*r[i]+alpha*t*k[i]^2+beta*t*k[i]*l[i]-lambda*t*l[i]^2+LambertW(12*t*k[i]*exp(-(t*k[i]^4+alpha*t*k[i]^2+beta*t*k[i]*l[i]+gamma*t*k[i]*r[i]-lambda*t*l[i]^2-x*k[i]^2-y*k[i]*l[i]-z*k[i]*r[i]-eta[i]*k[i])/k[i]))*k[i])/(t*k[i])

(7)
 

NULL

Download remove.mw

How i can add lebel inside graph  like this picture for some graph , in somecoding i have but i can't how it work i want add to  my code but i can't do the same as paper did

label.mw

Hi! A basic issue.

Why view=[-2 ..1, -2 ..5]  is not useful here? According to the output, only the green line meets the view settings. I want to extend the left side of these three lines appropriately (show the intersection)

with(plots)

l := 2*x+y+1 = 0; l1 := 4*x+2*y+2 = 0; l2 := 4*x+2*y-2 = 0; l3 := 4*x-2*y+6 = 0

2*x+y+1 = 0

 

4*x+2*y+2 = 0

 

4*x+2*y-2 = 0

 

4*x-2*y+6 = 0

(1)

 

display({implicitplot(l, color = black, legend = l, thickness = 5, view = [-2 .. 1, -2 .. 5])}, {implicitplot(l1, color = red, legend = l1, view = [-2 .. 1, -2 .. 5])}, {implicitplot(l2, color = blue, legend = l2, view = [-2 .. 1, -2 .. 5])}, {implicitplot(l3, color = green, legend = l3, view = [-2 .. 1, -2 .. 5])})

 
 

NULL

Download The_intersection_parallelism_and_coincidence_of_two_straight_lines.mw

Hi,

I'm trying to use the Explore command to examine the effect of two parameters (mu and sigma) on the density function curve. The visualization isn't very optimal, especially with the mu parameter, and it's difficult to add options (range, color, gridlines, etc.). Any suggestions to optimize this idea? Thanks for your insights!

Q_Explore.mw

when we have ode equation we say what is type of equation then  i want solve by this method say the name of method and if possible i want to solve this equation by the method step by step too, maple can do that? also can we plot the solution or any geometricall presentation , also i have error in writing exact form of equation

restart

"with(Student[ODEs]): "

with(DETools)

ode1 := diff(y(x), x)+2*x*y(x) = x

diff(y(x), x)+2*x*y(x) = x

(1)

Type(ode1)

{linear, separable}

(2)

W := dsolve(ode1)

y(x) = 1/2+exp(-x^2)*c__1

(3)

odetest(W, ode1)

0

(4)

ODESteps(ode1)

"[[,,"Let's solve"],[,,(&DifferentialD;)/(&DifferentialD;x) y(x)+2 x y(x)=x],["&bullet;",,"Highest derivative means the order of the ODE is" 1],[,,(&DifferentialD;)/(&DifferentialD;x) y(x)],["&bullet;",,"Separate variables"],[,,((&DifferentialD;)/(&DifferentialD;x) y(x))/(2 y(x)-1)=-x],["&bullet;",,"Integrate both sides with respect to" x],[,,&int;((&DifferentialD;)/(&DifferentialD;x) y(x))/(2 y(x)-1) &DifferentialD;x=&int;-x &DifferentialD;x+`c__1`],["&bullet;",,"Evaluate integral"],[,,(ln(2 y(x)-1))/2=-(x^2)/2+`c__1`],["&bullet;",,"Solve for" y(x)],[,,y(x)=((e)^(-x^2+2 `c__1`))/2+1/2]]"

(5)

ode2 := (sin(x)*tan(x)+1)*dx-cos(x)*sec(y(x))^2*dy = 0

(sin(x)*tan(x)+1)*dx-cos(x)*sec(y(x))^2*dy = 0

(6)

Type(ode2)

Error, (in Student:-ODEs:-Type) could not determine the solving variable. Please specify it as an extra argument in the form: y(x)

 
 

NULL

Download ode-example.mw

i want try all number to my parameter for check the shape of plot there is any way for doing that?

restart

with(plots)

M := 4*b^2*beta*((a*y-2*alpha*t+x)*b^2+a*(-2*beta*t+a*(a*y-2*alpha*t+x)))/(-b^6*beta*y^2+(-4*t*y*beta^2+(-2*a^2*y^2+(4*(alpha*t-(1/2)*x))*y*a-4*(alpha*t-(1/2)*x)^2)*beta+3*a)*b^4+(-4*t^2*beta^3+4*a*t*(a*y-2*alpha*t+x)*beta^2-a^2*(a*y-2*alpha*t+x)^2*beta+6*a^3)*b^2+3*a^5)

alpha = 1; beta := 1; a := -1; b := -2; t := 0

alpha = 1

 

1

 

-1

 

-2

 

0

(1)

plots:-contourplot(M, x = -100 .. 100, y = -100 .. 100, title = contour, grid = [100, 100], colorbar = false)

 
 

NULL

Download control-trajectory.mw

THis IC for Abel ode is not valid and should result in no solution. But instead of returning NULL, dsolve throws internal error called Error, (in dsolve) invalid limiting point

restart;

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1844 and is the same as the version installed in this computer, created 2025, January 25, 22:5 hours Pacific Time.`

ode:=diff(y(x),x)-x^a*y(x)^3+3*y(x)^2-x^(-a)*y(x)-x^(-2*a)+a*x^(-a-1) = 0;

diff(y(x), x)-x^a*y(x)^3+3*y(x)^2-x^(-a)*y(x)-x^(-2*a)+a*x^(-a-1) = 0

DEtools:-odeadvisor(ode);
sol:=dsolve([ode,y(1)=1])

[_Abel]

Error, (in dsolve) invalid limiting point

tracelast;

 dsolve called with arguments: [diff(y(x), x)-x^a*y(x)^3+3*y(x)^2-x^(-a)*y(x)-x^(-2*a)+a*x^(-a-1) = 0, y(1) = 1], arbitraryconstants = subscripted, atomizenames = true, build = false, numeric = false, type = none
 #(dsolve,80): error

 \`dsolve/IC\` called with arguments: [diff(y(x), x)-x^a*y(x)^3+3*y(x)^2-x^(-a)*y(x)-x^(-2*a)+a*x^(-a-1) = 0, y(1) = 1], {y(x)}, skipimplicit = false, skippparticularsolforlinearODEs = true, solution = {}, usesolutions = particular and general
 #(\`dsolve/IC\`,64): draft := procname(_passed,':-usesolutions = "general"');

 \`dsolve/IC\` called with arguments: [diff(y(x), x)-x^a*y(x)^3+3*y(x)^2-x^(-a)*y(x)-x^(-2*a)+a*x^(-a-1) = 0, y(1) = 1], {y(x)}, skipimplicit = false, skippparticularsolforlinearODEs = true, solution = {}, usesolutions = general
 #(\`dsolve/IC\`,277): zz := map(op,{\`dsolve/IC/_C\`({ANS[i]},funcs,x,ics)});

 \`dsolve/IC/_C\` called with arguments: {y(x) = -exp(2*x^(-a+1)/(a-1))/(_C[1]-2*2^(2*(a+1)/(a-1))*(1/(-a+1))^((a+1)/(a-1))*(2^(-(5*a-3)/(a-1))*(1/(-a+1))^(-(a+1)/(a-1))*x^(2*a)*(-a+1)^2*(x^(-a+1)/(-a+1))^(1/(a-1))*(-4*x^(-a+1)*a^2/(-a+1)+8*a*x^(-a+1)/(-a+1)-4*x^(-a+1)/(-a+1)+2*a-2)*WhittakerM(-(a+1)/(a-1)+1/(a-1), -1/(a-1)+1/2, 4*x^(-a+1)/(-a+1))*exp(-2*x^(-a+1)/(-a+1))/((a+1)*(-3+a))-2^(-(3*a-1)/(a-1))*(1/(-a+1))^(-(a+1)/(a-1))*x^(2*a)*WhittakerM(-(a+1)/(a-1)+1/(a-1)+1, -1/(a-1)+1/2, 4*x^(-a+1)/(-a+1))*(-a+1)^2*(x^(-a+1)/(-a+1))^(1/(a-1))*exp(-2*x^(-a+1)/(-a+1))/((a+1)*(-3+a)))/(-a+1))^(1/2)+x^(-a)}, {y(x)}, x, [y(1) = 1]
 #(\`dsolve/IC/_C\`,1): ans := \`dsolve/IC/_C/do\`(solns,depvars,t,inits,'evaluated_ans', "default",':-giveup = giveup');

 \`dsolve/IC/_C/do\` called with arguments: {y(x) = -exp(2*x^(-a+1)/(a-1))/(_C[1]-2*2^(2*(a+1)/(a-1))*(1/(-a+1))^((a+1)/(a-1))*(2^(-(5*a-3)/(a-1))*(1/(-a+1))^(-(a+1)/(a-1))*x^(2*a)*(-a+1)^2*(x^(-a+1)/(-a+1))^(1/(a-1))*(-4*x^(-a+1)*a^2/(-a+1)+8*a*x^(-a+1)/(-a+1)-4*x^(-a+1)/(-a+1)+2*a-2)*WhittakerM(-(a+1)/(a-1)+1/(a-1), -1/(a-1)+1/2, 4*x^(-a+1)/(-a+1))*exp(-2*x^(-a+1)/(-a+1))/((a+1)*(-3+a))-2^(-(3*a-1)/(a-1))*(1/(-a+1))^(-(a+1)/(a-1))*x^(2*a)*WhittakerM(-(a+1)/(a-1)+1/(a-1)+1, -1/(a-1)+1/2, 4*x^(-a+1)/(-a+1))*(-a+1)^2*(x^(-a+1)/(-a+1))^(1/(a-1))*exp(-2*x^(-a+1)/(-a+1))/((a+1)*(-3+a)))/(-a+1))^(1/2)+x^(-a)}, {y(x)}, x, [y(1) = 1], evaluated_ans, default, giveup = giveup, usecansolve = false
 #(\`dsolve/IC/_C/do\`,133): Solns := map((u, S) -> map(limit,S,op(u)),csol,Solns);

 limit called with arguments: y(x) = -exp(2*x^(-a+1)/(a-1))/(_C[1]-2*2^(2*(a+1)/(a-1))*(1/(-a+1))^((a+1)/(a-1))*(2^(-(5*a-3)/(a-1))*(1/(-a+1))^(-(a+1)/(a-1))*x^(2*a)*(-a+1)^2*(x^(-a+1)/(-a+1))^(1/(a-1))*(-4*x^(-a+1)*a^2/(-a+1)+8*a*x^(-a+1)/(-a+1)-4*x^(-a+1)/(-a+1)+2*a-2)*WhittakerM(-(a+1)/(a-1)+1/(a-1), -1/(a-1)+1/2, 4*x^(-a+1)/(-a+1))*exp(-2*x^(-a+1)/(-a+1))/((a+1)*(-3+a))-2^(-(3*a-1)/(a-1))*(1/(-a+1))^(-(a+1)/(a-1))*x^(2*a)*WhittakerM(-(a+1)/(a-1)+1/(a-1)+1, -1/(a-1)+1/2, 4*x^(-a+1)/(-a+1))*(-a+1)^2*(x^(-a+1)/(-a+1))^(1/(a-1))*exp(-2*x^(-a+1)/(-a+1))/((a+1)*(-3+a)))/(-a+1))^(1/2)+x^(-a), _C[1] = exp((4*I)*Im(1/(a-1)))*infinity, parametric = false
 #(limit,2): return map(thisproc,_passed)

 limit called with arguments: y(x), _C[1] = exp((4*I)*Im(1/(a-1)))*infinity, parametric = false
 #(limit,33): error "invalid limiting point"

Error, (in dsolve) invalid limiting point

 locals defined as: ddir = ddir, dexpr = y(x), fexpr = fexpr, r = r, x = _C[1], fL = fL, L = exp((4*I)*Im(1/(a-1)))*infinity, efloat = efloat, lfloat = lfloat, ind_dexpr = ind_dexpr, ind_L = ind_L, lexpr = lexpr, t = t, limr = limr, liml = liml, pt = (_C[1] = exp((4*I)*Im(1/(a-1)))*infinity), inertfunctions = {}, limitX = limitX, parameters = parameters, Y = Y, limc = limc, cexpr = cexpr, texpr = texpr, bexpr = bexpr, limt = limt, limb = limb, param = param, c = c, N = N, Z = Z, P = P, o = o, e = e, uneval = uneval, i = i, A = A, cond = cond, ll = ll, rr = rr

 


 

Download internal_error_instead_of_no_solution.mw

Is there an equivalent of currentdir() which instead of returning current working directory, returns the directory of the file being read. So assume I have an ".mm" or ".mpl" file saved in some location and there is another file with a location fixed relative to this file, but not fixed in absolute location on the computer and not fixed relative with current working directory. One natural thing is to have a line in the first file that takes its current location (not current working location of the user!) and then use the fixed relative path info, and then gives the location of the second file to the user. Using currendir won't help here because current working directory is not necessarily the same as the location of the file you are reading, the first file. One may say the user is reading the first file so he knows already its location, right? Well, if the user is also the writer of the file, sure, not a problem, he can manually edit the lines of the file and put that location inside the file instead of using currentdir etc. However, if the user is not the writer and also does not know how to edit or whatever else reason, then the file should be able to inform Maple of its own location, so that's why something like currentdir() but not for the working directory, instead for currently being read file's directory is helpful. I checked FileTools package quickly and couldn't notice anything like what I want. Anyone have any clue on name of such command if exists or any other trick that does what I want (except expecting the user to do something ^_^ so all from the writer's side please ^_^).

i try find some part of solution of this kind of pde but i can't get results my openion is maybe this pde is wronge when i defined 

pde.mw

my solution is a little bit long which when i click on pdetest command i wait at least more than a hour but still is runing and i don't get any result and not give me error , which i don't know my result is true or not so How i can find that my pde by this solution it will be zero or not ?

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

declare(u(x, y, t))

u(x, y, t)*`will now be displayed as`*u

(2)

declare(f(x, y, t))

f(x, y, t)*`will now be displayed as`*f

(3)

pde := diff(u(x, y, t), t)-(diff(diff(u(x, y, t), `$`(x, 4))+5*u(x, y, t)*(diff(u(x, y, t), `$`(x, 2)))+(5/3)*u(x, y, t)^3+5*(diff(u(x, y, t), x, y)), x))-5*u(x, y, t)*(diff(u(x, y, t), y))+5*(int(diff(u(x, y, t), `$`(y, 2)), x))-5*(diff(u(x, y, t), x))*(int(diff(u(x, y, t), y), x))

diff(u(x, y, t), t)-(diff(diff(diff(diff(diff(u(x, y, t), x), x), x), x), x))-5*(diff(u(x, y, t), x))*(diff(diff(u(x, y, t), x), x))-5*u(x, y, t)*(diff(diff(diff(u(x, y, t), x), x), x))-5*u(x, y, t)^2*(diff(u(x, y, t), x))-5*(diff(diff(diff(u(x, y, t), x), x), y))-5*u(x, y, t)*(diff(u(x, y, t), y))+5*(int(diff(diff(u(x, y, t), y), y), x))-5*(diff(u(x, y, t), x))*(int(diff(u(x, y, t), y), x))

(4)

pde_nonlinear, pde_linear := selectremove(proc (term) options operator, arrow; has((eval(term, u(x, y, t) = a*u(x, y, t)))/a, a) end proc, pde)

-5*(diff(u(x, y, t), x))*(diff(diff(u(x, y, t), x), x))-5*u(x, y, t)*(diff(diff(diff(u(x, y, t), x), x), x))-5*u(x, y, t)^2*(diff(u(x, y, t), x))-5*u(x, y, t)*(diff(u(x, y, t), y))-5*(diff(u(x, y, t), x))*(int(diff(u(x, y, t), y), x)), diff(u(x, y, t), t)-(diff(diff(diff(diff(diff(u(x, y, t), x), x), x), x), x))-5*(diff(diff(diff(u(x, y, t), x), x), y))+5*(int(diff(diff(u(x, y, t), y), y), x))

(5)

thetai := t*w[i]+y*p[i]+x

t*w[i]+y*p[i]+x

(6)

eqw := w[i] = -5*p[i]^2

w[i] = -5*p[i]^2

(7)

Bij := proc (i, j) options operator, arrow; (-6*p[i]-6*p[j])/(p[i]-p[j])^2 end proc

proc (i, j) options operator, arrow; (-6*p[i]-6*p[j])/(p[i]-p[j])^2 end proc

(8)

NULL

theta1 := normal(eval(eval(thetai, eqw), i = 1)); theta2 := normal(eval(eval(thetai, eqw), i = 2))

-5*t*p[1]^2+y*p[1]+x

 

-5*t*p[2]^2+y*p[2]+x

(9)

eqf := f(x, y, t) = (-5*t*p[1]^2+y*p[1]+x)*(-5*t*p[2]^2+y*p[2]+x)-(6*(p[1]+p[2]))/(p[1]-p[2])^2

f(x, y, t) = (-5*t*p[1]^2+y*p[1]+x)*(-5*t*p[2]^2+y*p[2]+x)-6*(p[1]+p[2])/(p[1]-p[2])^2

(10)

eq17 := u(x, y, t) = 6*(diff(diff(f(x, y, t), x), x))/f(x, y, t)-6*(diff(f(x, y, t), x))^2/f(x, y, t)^2

u(x, y, t) = 6*(diff(diff(f(x, y, t), x), x))/f(x, y, t)-6*(diff(f(x, y, t), x))^2/f(x, y, t)^2

(11)

eqt := eval(eq17, eqf)

u(x, y, t) = 12/((-5*t*p[1]^2+y*p[1]+x)*(-5*t*p[2]^2+y*p[2]+x)-6*(p[1]+p[2])/(p[1]-p[2])^2)-6*(-5*t*p[1]^2-5*t*p[2]^2+y*p[1]+y*p[2]+2*x)^2/((-5*t*p[1]^2+y*p[1]+x)*(-5*t*p[2]^2+y*p[2]+x)-6*(p[1]+p[2])/(p[1]-p[2])^2)^2

(12)

``

pdetest(eqt, pde)

NULL

Download test.mw

Consider the following:

MyTableElement1 := proc(L::list(nonnegint))
  ## L will have only two elements
  local M, x, y;
  M:=L;
  x:=convert(M[1],string);
  y:=convert(M[2],string);

  return cat("\\begin{tabular}{c} ",x," \\\\ ",y," \\end{tabular}")

end;

MyTableElement1([2,3]);

will output

"\begin{tabular}{c} 2 \\ 3 \end{tabular}"

as desired. However, if one inserts an \hline into the table,

MyTableElement2 := proc(L::list(nonnegint))
  ## L will have only two elements
  local M, x, y;
  M:=L;
  x:=convert(M[1],string);
  y:=convert(M[2],string);

  return cat("\\begin{tabular}{c} ",x," \\\\ \\hline ",y," \\end{tabular}")

end;

will output

"\begin{tabular}{c} 2 \\ \hline 3 \end{tabular}"

again as desired. However, if I copy and paste this int a document, I get

"\begin{tabular}{c} 2 \\ hline 3 \end{tabular}".

Note that \hline is now just hline. Putting "\\\\" in front of the hline outputs

"\begin{tabular}{c} 2 \\ \\hline 3 \end{tabular}",

but this does not compile properly. How can I get a proper \hline command to appear in the table? Thank uou for your consideration.

 Can I solve the Tolman-Oppenheimer-Volkoff equation with Maple ?  I'm having trouble with Einstein's equation with the energy tensor as the second member

First 11 12 13 14 15 16 17 Last Page 13 of 46