Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

display([plottools[arc]([op(coordinates(Omega))], r, t .. t + Pi/2, color = red, t4), plottools[arc]([op(coordinates(Omega))], r, t + Pi .. t + (3*Pi)/2, color = coral, t4), plottools[arc]([op(coordinates(Omega))], r, t - Pi/2 .. t, color = cyan, t4), plottools[arc]([op(coordinates(Omega))], r, t + Pi/2 .. t + Pi, color = green, t4)],
draw([Cir(color = blue, t4), cir(color = grey, t4), sT(color = black, t4), XXp(color = black, l3), YYp(color = black, l3), L1(color = black, l3), L2(color = black, l3), N1(color = blue, symbol = solidcircle, symbolsize = 15), N2(color = blue, symbol = solidcircle, symbolsize = 15), N3(color = blue, symbol = solidcircle, symbolsize = 15), M1(color = blue, symbol = solidcircle, symbolsize = 15)]), axes = none, view = [-30 .. 10, -10 .. 10], size = [800, 800])::
plots:-animate(Proc, [t], t = 0 .. 2*Pi, frames = 30).;

why the instruction concerning the arcs is not resected ? Thank you.

I liked the recent question from user goebeld and especially the answer from Rouben Rostamian.
I admit, I didn’t even realize that Maple had VariationalCalculus procedures.
But what if the red and green  points are on the surface x1^4 + x2^4 + x3^4 -1 = 0
Points coordinates (-0.759835685700000, -0.759835685700000, 0.759835685700000) and
 (0.759835685700000, 0.759835685700000, -0.759835685700000).

Where will the shortest distance between these points on a given surface be? Taking into account symmetry, of course.

I have a thirder order ODE with non polynomial coefficients and I naively thought to try dsolve for fun to see what happens and Maple returned DESol with a second order differential equation and an arbitrary coefficient. I know Maple outputs DESol when it cannot find a solution similar to RootOf but the arbitrary constant is what is throwing me off. 

I am unsure how to interpret this, if a particular solution is found I could reduce the order and see how I could get with the second order ODE but maple doesn't produce a particular solution when I run that command. 

DESol_Question.mw

What is the problem with the integral below when I use a variable n?

with(Units:-Simple)

V__1 := Unit('m'^3) = Units:-Unit(m^3)NULL

V__2 := 2*Unit('m'^3) = 2*Units:-Unit(m^3)NULL

int(1/V, V = V__1 .. V__2)

ln(2)

(1)

`assuming`([int(n/V, V = n*Unit('m'^3) .. m*Unit('m'^3))], [n > 0, m > 0])

-ln(n)*n+ln(m)*n

(2)

NULL

Download Units_Int.mw

Dear all, is there a maple call to calculate the space curve connecting two points of a 3d plane?

e.g. the plane is defined by: f(x,y) = -x^2/9 + y^2/4

The two points are: P = (1,2,0), Q=(1,-1,0)

Searched: space curve laying on 3d plane connecting the two points.

Thanks

restart

with(PDEtools)

undeclare(prime)

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

(1)

with(DEtools)

NULL

with(DifferentialAlgebra)

"with(Student[ODEs][Solve]): "

with(IntegrationTools)

with(inttrans)

with(PDEtools)

with(Physics)

with(PolynomialTools)

with(RootFinding)

with(SolveTools)

with(LinearAlgebra)

with(sumtools)

pde := I*(diff(psi(x, t), t))+alpha*(diff(psi(x, t), `$`(x, 2)))+(beta[3]*abs(psi(x, t))+beta[4]*abs(psi(x, t))^2)*psi(x, t)+gamma*(diff(abs(psi(x, t))^2, `$`(x, 2)))*psi(x, t)/abs(psi(x, t)) = 0

case1 := {k = k, lambda = sqrt(-1/(18*alpha*beta[4]+18*gamma*beta[4]))*beta[3], w = -(9*alpha*k^2*beta[4]+2*beta[3]^2)/(9*beta[4]), A[0] = -beta[3]/(3*beta[4]), A[1] = beta[3]/(3*beta[4]), B[1] = 0}

" psi(x,t):=U(xi)*exp(I*(-k*x+w*t+theta))"

proc (x, t) options operator, arrow, function_assign; U(xi)*exp(I*(-k*x+w*t+theta)) end proc

(2)

" U(xi):=-(beta[3] (cosh(xi)-sinh(xi)))/(3 beta[4] cosh(xi))"

proc (xi) options operator, arrow, function_assign; -(1/3)*beta[3]*(cosh(xi)-sinh(xi))/(beta[4]*cosh(xi)) end proc

(3)

convert(U(xi), trig)

-(1/3)*beta[3]*(cosh(xi)-sinh(xi))/(beta[4]*cosh(xi))

(4)

xi := sqrt(-1/(18*alpha*beta[4]+18*gamma*beta[4]))*beta[3]*(2*alpha*kt+x)

(-1/(18*alpha*beta[4]+18*gamma*beta[4]))^(1/2)*beta[3]*(2*alpha*kt+x)

(5)

S := psi(x, t)

-(1/3)*beta[3]*(cosh((-1/(18*alpha*beta[4]+18*gamma*beta[4]))^(1/2)*beta[3]*(2*alpha*kt+x))-sinh((-1/(18*alpha*beta[4]+18*gamma*beta[4]))^(1/2)*beta[3]*(2*alpha*kt+x)))*exp(I*(-k*x+t*w+theta))/(beta[4]*cosh((-1/(18*alpha*beta[4]+18*gamma*beta[4]))^(1/2)*beta[3]*(2*alpha*kt+x)))

(6)

solution := subs(case1, S)

-(1/3)*beta[3]*(cosh((-1/(18*alpha*beta[4]+18*gamma*beta[4]))^(1/2)*beta[3]*(2*alpha*kt+x))-sinh((-1/(18*alpha*beta[4]+18*gamma*beta[4]))^(1/2)*beta[3]*(2*alpha*kt+x)))*exp(I*(-k*x-(1/9)*(9*alpha*k^2*beta[4]+2*beta[3]^2)*t/beta[4]+theta))/(beta[4]*cosh((-1/(18*alpha*beta[4]+18*gamma*beta[4]))^(1/2)*beta[3]*(2*alpha*kt+x)))

(7)

pdetest(psi(x, t) = -beta[3]*(cosh(sqrt(-1/(18*alpha*beta[4]+18*gamma*beta[4]))*beta[3]*(2*alpha*k+x))-sinh(sqrt(-1/(18*alpha*beta[4]+18*gamma*beta[4]))*beta[3]*(2*alpha*k+x)))*exp(I*(-k*x-(9*alpha*k^2*beta[4]+2*beta[3]^2)*t/(9*beta[4])+theta))/(3*beta[4]*cosh(sqrt(-1/(18*alpha*beta[4]+18*gamma*beta[4]))*beta[3]*(2*alpha*k+x)))*exp(I*(-k*x-(9*alpha*k^2*beta[4]+2*beta[3]^2)*t/(9*beta[4])+theta)), pde)

Error, (in pdetest) unable to determine the indeterminate function

 

NULL

 

 

 

 

Download pde-solve.mw

Dear all, in the example below I create a matrix(3x2) and each element contains a vector. How can I avoid the double brackets of the matrix elements or eliminate the double brackets?

Thanks for help

restart;
with(PolynomialTools);
with(RootFinding);
with(SolveTools);
with(LinearAlgebra);
NULL;
NULL;
E1 := (-alpha*k^2*A[1] - alpha*k^2*B[1] + 3*A[0]^2*A[1]*beta[4] + 3*A[0]^2*B[1]*beta[4] + A[1]^3*beta[4] + 3*A[1]^2*B[1]*beta[4] + 3*A[1]*B[1]^2*beta[4] + B[1]^3*beta[4] + 2*A[0]*A[1]*beta[3] + 2*A[0]*B[1]*beta[3] - w*A[1] - w*B[1])*cosh(xi)^6 + (-alpha*k^2*A[0] + A[0]^3*beta[4] + 3*A[0]*A[1]^2*beta[4] + 6*A[0]*A[1]*B[1]*beta[4] + 3*A[0]*B[1]^2*beta[4] + A[0]^2*beta[3] + A[1]^2*beta[3] + 2*A[1]*B[1]*beta[3] + B[1]^2*beta[3] - w*A[0])*sinh(xi)*cosh(xi)^5 + (2*alpha*k^2*A[1] + alpha*k^2*B[1] - 2*alpha*lambda^2*A[1] + 2*alpha*lambda^2*B[1] - 2*gamma*lambda^2*A[1] + 2*gamma*lambda^2*B[1] - 6*A[0]^2*A[1]*beta[4] - 3*A[0]^2*B[1]*beta[4] - 3*A[1]^3*beta[4] - 6*A[1]^2*B[1]*beta[4] - 3*A[1]*B[1]^2*beta[4] - 4*A[0]*A[1]*beta[3] - 2*A[0]*B[1]*beta[3] + 2*w*A[1] + w*B[1])*cosh(xi)^4 + (alpha*k^2*A[0] - A[0]^3*beta[4] - 6*A[0]*A[1]^2*beta[4] - 6*A[0]*A[1]*B[1]*beta[4] - A[0]^2*beta[3] - 2*A[1]^2*beta[3] - 2*A[1]*B[1]*beta[3] + w*A[0])*sinh(xi)*cosh(xi)^3 + (-alpha*k^2*A[1] + 4*alpha*lambda^2*A[1] + 4*gamma*lambda^2*A[1] + 3*A[0]^2*A[1]*beta[4] + 3*A[1]^3*beta[4] + 3*A[1]^2*B[1]*beta[4] + 2*A[0]*A[1]*beta[3] - w*A[1])*cosh(xi)^2 + (3*A[0]*A[1]^2*beta[4] + A[1]^2*beta[3])*sinh(xi)*cosh(xi) - 2*alpha*lambda^2*A[1] - 2*gamma*lambda^2*A[1] - A[1]^3*beta[4] = 0;
N := 6;
for i from 0 to N do
    equ[1][i] := coeff(E1, {cosh(xi)^i, sinh(xi)^i}, i) = 0;
end do;
             //        2               2     
equ[1][0] := \\-alpha k  A[1] - alpha k  B[1]

           2                      2                    3        
   + 3 A[0]  A[1] beta[4] + 3 A[0]  B[1] beta[4] + A[1]  beta[4]

           2                           2               3        
   + 3 A[1]  B[1] beta[4] + 3 A[1] B[1]  beta[4] + B[1]  beta[4]

                                                                \ 
   + 2 A[0] A[1] beta[3] + 2 A[0] B[1] beta[3] - w A[1] - w B[1]/ 

          6   /        2            3        
  cosh(xi)  + \-alpha k  A[0] + A[0]  beta[4]

                2                                   
   + 3 A[0] A[1]  beta[4] + 6 A[0] A[1] B[1] beta[4]

                2               2               2        
   + 3 A[0] B[1]  beta[4] + A[0]  beta[3] + A[1]  beta[3]

                               2                 \          
   + 2 A[1] B[1] beta[3] + B[1]  beta[3] - w A[0]/ sinh(xi) 

          5   /         2               2     
  cosh(xi)  + \2 alpha k  A[1] + alpha k  B[1]

                   2                      2     
   - 2 alpha lambda  A[1] + 2 alpha lambda  B[1]

                   2                      2     
   - 2 gamma lambda  A[1] + 2 gamma lambda  B[1]

           2                      2             
   - 6 A[0]  A[1] beta[4] - 3 A[0]  B[1] beta[4]

           3                 2             
   - 3 A[1]  beta[4] - 6 A[1]  B[1] beta[4]

                2                              
   - 3 A[1] B[1]  beta[4] - 4 A[0] A[1] beta[3]

                                            \         4   /      
   - 2 A[0] B[1] beta[3] + 2 w A[1] + w B[1]/ cosh(xi)  + \alpha 

   2            3                      2        
  k  A[0] - A[0]  beta[4] - 6 A[0] A[1]  beta[4]

                                    2                 2        
   - 6 A[0] A[1] B[1] beta[4] - A[0]  beta[3] - 2 A[1]  beta[3]

                                 \                  3   /
   - 2 A[1] B[1] beta[3] + w A[0]/ sinh(xi) cosh(xi)  + \
        2                      2                      2     
-alpha k  A[1] + 4 alpha lambda  A[1] + 4 gamma lambda  A[1]

           2                      3        
   + 3 A[0]  A[1] beta[4] + 3 A[1]  beta[4]

           2                                            \ 
   + 3 A[1]  B[1] beta[4] + 2 A[0] A[1] beta[3] - w A[1]/ 

          2
  cosh(xi) 

     /           2               2        \                  
   + \3 A[0] A[1]  beta[4] + A[1]  beta[3]/ sinh(xi) cosh(xi)

                   2                      2            3           
   - 2 alpha lambda  A[1] - 2 gamma lambda  A[1] - A[1]  beta[4] = 

   \    
  0/ = 0


                       equ[1][1] := 0 = 0

                       equ[1][2] := 0 = 0

                       equ[1][3] := 0 = 0

                       equ[1][4] := 0 = 0

                       equ[1][5] := 0 = 0

                       equ[1][6] := 0 = 0

NULL;
NULL;

Download loop_for_coeficent.mw

Is the a print or plot function that can generate from an expression an expression tree

and/or the corresponding expression DAG

 

Taken from ?ProgrammingGuide,Chapter02

I was just using Maple to do a simple calculation but the units came out all complicated. 

The expression in question is work done by a van der Waals gas. The units should come out to Joules per mol. 

When I do the calculation manually (second expression below) I do get that result, albeit in more basic units than Joules.

In the first expression, in which I am using subs to sub in values with units into the expression, the final expression is very complicated. Why?

with(Units:-Simple)

simplify(subs({R = 8.314*Unit('J'/('K'*'mol')), T = 298*Unit('K'), V__1 = Unit('L'/'mol'), V__2 = 50*Unit('L'/'mol'), a = 2.283*Unit('L'^2*'bar'/'mol'^2), b = 0.4278e-1*Unit('L'/'mol')}, -R*T*ln((V__2-b)/(V__1-b))+a*(1/V__1-1/V__2)))

(-9798.522418*Units:-Unit(J/(K*mol))*Units:-Unit(K)*Units:-Unit(L/mol)+2.23734*Units:-Unit(L^2*bar/mol^2))/Units:-Unit(L/mol)

(1)

How do we simplify the units above so they become the same as the units in the same (manual) calculation below?

-(8.314*Unit('J'/('K'*'mol'))*298)*Unit('K')*ln((50*Unit('L'/'mol')-0.4278e-1*Unit('L'/'mol'))/(Unit('L'/'mol')-0.4278e-1*Unit('L'/'mol')))+2.283*Unit('L'^2*'bar'/'mol'^2)/Unit('L'/'mol')

-9570.222418*Units:-Unit(m^2*kg/(s^2*mol))

(2)

NULL

Download Units_-_Subs.mw

restart;
Proc := proc(t) local t4, l3, R, r, eq, sol; _EnvHorizontalName := 'x'; _EnvVerticalName := 'y'; t4 := thickness = 4; l3 := linestyle = dot; R := 9; r := 1/2*R; geometry:-point(OO, 0, 0); geometry:-circle(Cir, [OO, R]); geometry:-point(K, R*cos(t), R*sin(t)); geometry:-point(Omega, r*cos(t), r*sin(t)); geometry:-circle(cir, [Omega, r]); eq := geometry:-Equation(cir); geometry:-line(XXp, y = 0); geometry:-line(YYp, x = 0); geometry:-line(L1, y = x); geometry:-line(L2, y = -x); geometry:-projection(M1, K, XXp); geometry:-coordinates(M1); geometry:-point(K2, geometry:-coordinates(M1)[1] - 2*R, 0); geometry:-coordinates(K2); geometry:-segment(sT, K2, M1); geometry:-point(N1, 0, R*sin(t)); subs(y = x, eq); sol := solve(%, x); geometry:-point(N2, sol[2], sol[2]); subs(y = -x, eq); sol := solve(%, x); geometry:-point(N3, sol[2], -sol[2]); plots:-display(geometry:-draw([Cir(color = blue, t4), cir(color = grey, t4), sT(color = black, t4), XXp(color = black, l3), YYp(color = black, l3), L1(color = black, l3), L2(color = black, l3), N1(color = blue, symbol = solidcircle, symbolsize = 15), N2(color = blue, symbol = solidcircle, symbolsize = 15), N3(color = blue, symbol = solidcircle, symbolsize = 15), M1(color = blue, symbol = solidcircle, symbolsize = 15)]), axes = none, view = [-30 .. 10, -10 .. 10], size = [800, 800]); end proc;
plots:-animate(Proc, [t], t = 0 .. 2*Pi, frames = 200);
NULL;
I am trying to program  this drawing, how to improve this code ? Thank you.

I know this question has been asked time and time again. Starting of with the expr . That is the end goal I want to achieve.  How would I reduce the expansion to get it into 1-f(x,y,z)/g(x,y,z) format?. I have tried all sorts of approaches.
 

restart

#

expr:=1 - (x__1*x__2 + y__1*y__2 - z__1*z__2)^2/((x__1^2 + y__1^2 - z__1^2)*(x__2^2 + y__2^2 - z__2^2))

1-(x__1*x__2+y__1*y__2-z__1*z__2)^2/((x__1^2+y__1^2-z__1^2)*(x__2^2+y__2^2-z__2^2))

(1)

normal( (1) );

(x__1^2*y__2^2-x__1^2*z__2^2-2*x__1*x__2*y__1*y__2+2*x__1*x__2*z__1*z__2+x__2^2*y__1^2-x__2^2*z__1^2-y__1^2*z__2^2+2*y__1*y__2*z__1*z__2-y__2^2*z__1^2)/((x__1^2+y__1^2-z__1^2)*(x__2^2+y__2^2-z__2^2))

(2)

simplify( (2) );

((y__2^2-z__2^2)*x__1^2-2*x__2*(y__1*y__2-z__1*z__2)*x__1+(y__1^2-z__1^2)*x__2^2-(y__1*z__2-y__2*z__1)^2)/((x__1^2+y__1^2-z__1^2)*(x__2^2+y__2^2-z__2^2))

(3)

radnormal(%)

(x__1^2*y__2^2-x__1^2*z__2^2-2*x__1*x__2*y__1*y__2+2*x__1*x__2*z__1*z__2+x__2^2*y__1^2-x__2^2*z__1^2-y__1^2*z__2^2+2*y__1*y__2*z__1*z__2-y__2^2*z__1^2)/((x__1^2+y__1^2-z__1^2)*(x__2^2+y__2^2-z__2^2))

(4)

Test:=combine(%)

(x__1^2*y__2^2-x__1^2*z__2^2-2*x__1*x__2*y__1*y__2+2*x__1*x__2*z__1*z__2+x__2^2*y__1^2-x__2^2*z__1^2-y__1^2*z__2^2+2*y__1*y__2*z__1*z__2-y__2^2*z__1^2)/((x__1^2+y__1^2-z__1^2)*(x__2^2+y__2^2-z__2^2))

(5)

 

n:={op(numer(Test))}

{x__1^2*y__2^2, x__2^2*y__1^2, -x__1^2*z__2^2, -x__2^2*z__1^2, -y__1^2*z__2^2, -y__2^2*z__1^2, -2*x__1*x__2*y__1*y__2, 2*x__1*x__2*z__1*z__2, 2*y__1*y__2*z__1*z__2}

(6)

d:={op(expand(denom(Test)))}

{x__1^2*x__2^2, x__1^2*y__2^2, x__2^2*y__1^2, y__1^2*y__2^2, z__1^2*z__2^2, -x__1^2*z__2^2, -x__2^2*z__1^2, -y__1^2*z__2^2, -y__2^2*z__1^2}

(7)

d subset n

false

(8)

d intersect n

{x__1^2*y__2^2, x__2^2*y__1^2, -x__1^2*z__2^2, -x__2^2*z__1^2, -y__1^2*z__2^2, -y__2^2*z__1^2}

(9)

add(%[i],i=1..nops(%))

x__1^2*y__2^2-x__1^2*z__2^2+x__2^2*y__1^2-x__2^2*z__1^2-y__1^2*z__2^2-y__2^2*z__1^2

(10)

factor( (10) );

x__1^2*y__2^2-x__1^2*z__2^2+x__2^2*y__1^2-x__2^2*z__1^2-y__1^2*z__2^2-y__2^2*z__1^2

(11)

n minus d

{-2*x__1*x__2*y__1*y__2, 2*x__1*x__2*z__1*z__2, 2*y__1*y__2*z__1*z__2}

(12)

 


 

Download 2024-07-20_Q_Simplify_Reformat.mw

We are pleased to announce that the registration for the Maple Conference 2024 is now open.

Like the last few years, this year’s conference will be a free virtual event. Please visit the conference page for more information on how to register.

This year we are offering a number of new sessions, including more product training options and an Audience Choice session.
You can find an overview of the program on the Sessions page. Those who register before September 10th, 2024 will have a chance to vote for the topics they want to learn more about during the Audience Choice session.

We hope to see you there!

Good afternoon, please I have the following question to see if someone can help me.

I am calculating an integral with a root and when Maple gives me the result it does so in power. I want the result to be given in square root, both this integral and others that I am going to solve.

Whenever I call RandomGraph(20,200), Maple crashes both on the laptop and on the PC: any suggestion?

with(GraphTheory); with(RandomGraphs)

interface(version)

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

(1)

G := RandomGraph(20, 200)


Download crash.mw

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