Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

i already use this method for a lot of equation but this time something not normal hapening what is problem?

``

restart

with(PDEtools)

with(LinearAlgebra)

with(Physics)

with(SolveTools)

``

eq0 := -4*alpha*k^2*m^2*n^2*A[0]^2+4*beta*k*m*n^2*A[0]^3-4*gamma*k*m*n^2*A[0]^3+4*delta^2*m*n^2*A[0]^2-4*n^2*sigma*A[0]^4-4*m*n^2*w*A[0]^2 = 0

eq1 := -8*alpha*k^2*m^2*n^2*A[0]*A[1]+12*beta*k*m*n^2*A[0]^2*A[1]-12*gamma*k*m*n^2*A[0]^2*A[1]+8*delta^2*m*n^2*A[0]*A[1]-16*n^2*sigma*A[0]^3*A[1]+2*a*alpha*m*n*A[0]*A[1]-8*m*n^2*w*A[0]*A[1] = 0

eq2 := -4*alpha*k^2*m^2*n^2*A[1]^2+12*beta*k*m*n^2*A[0]*A[1]^2-12*gamma*k*m*n^2*A[0]*A[1]^2+4*delta^2*m*n^2*A[1]^2-24*n^2*sigma*A[0]^2*A[1]^2+a*alpha*m^2*A[1]^2+3*alpha*b*m*n*A[0]*A[1]-4*m*n^2*w*A[1]^2 = 0

eq3 := 4*beta*k*m*n^2*A[1]^3-4*gamma*k*m*n^2*A[1]^3-16*n^2*sigma*A[0]*A[1]^3+alpha*b*m^2*A[1]^2+alpha*b*m*n*A[1]^2+4*alpha*c*m*n*A[0]*A[1] = 0

eq4 := -4*n^2*sigma*A[1]^4+alpha*c*m^2*A[1]^2+2*alpha*c*m*n*A[1]^2 = 0

C := solve({eq0, eq1, eq2, eq3, eq4}, {a, b, c, `__ `*A[0]})

Warning, solving for expressions other than names or functions is not recommended.

 

(1)
 

NULL

Download problem.mw

Can someone tell me how to calculate the Christoffel symbols in spherical coordinates in Euclidean three dimensional space?

Thank you very much in advance!

Hello 

I am working on my vector file and have another question:

1. How do I display any vectors in a matrix notation next to each other or above each other (like: [1;2;3]) 

Find attached the file:question_vector_.mw

I really appreciate any help you can provide.

At the end of this link - (2.14) and (2.15) - the problem and the solution have the same maple code, so I don't understand how to solve the problem.

https://www.maplesoft.com/support/help/Maple/view.aspx?path=isimplicitlydeclaredlocal

Is it possible to have a variable in a filename ?

as an example if I save a file by


save M, "Result(Variable).txt";

So If Variable is e.g. set to

Variable:=10;
then the filename saved should be
Result(10).txt

It is not that this a terribly difficult to work out, but I feel I am probably missing something. I need to check if a 3D point lies on a 3D line. What is a good approach here. I started of with the idea all alpha's are equal. but there are exceptions. See P3 and P4

restart

NULL

l := `<,>`(3+2*alpha, 1+6*alpha, 4-5*alpha)

Vector[column](%id = 36893489809910741940)

(1)

NULL

P := [9, 19, -11]

[9, 19, -11]

(2)

seq(solve({l[i] = P[i]}, alpha), i = 1 .. 3)

{alpha = 3}, {alpha = 3}, {alpha = 3}

(3)

l1 := `<,>`(3+2*alpha, 1+0*alpha, 4-5*alpha)

Vector[column](%id = 36893489809910721460)

(4)

P1 := [9, 1, -11]

[9, 1, -11]

(5)

seq(solve({l1[i] = P1[i]}, alpha), i = 1 .. 3)

{alpha = 3}, {alpha = alpha}, {alpha = 3}

(6)

l2 := `<,>`(3+2*alpha, 1+0*alpha, 4-0*alpha)

Vector[column](%id = 36893489809910705556)

(7)

P2 := [9, 1, 4]

[9, 1, 4]

(8)

seq(solve({l2[i] = P2[i]}, alpha), i = 1 .. 3)

{alpha = 3}, {alpha = alpha}, {alpha = alpha}

(9)

l3 := `<,>`(3+2*alpha, 0+0*alpha, 4-0*alpha)

Vector[column](%id = 36893489809963852012)

(10)

P3 := [9, 0, 4]

[9, 0, 4]

(11)

seq(solve({l3[i] = P3[i]}, alpha), i = 1 .. 3)

{alpha = 3}, {alpha = alpha}

(12)

P4 := [9, 0, -2]

[9, 0, -2]

(13)

seq(solve({l3[i] = P4[i]}, alpha), i = 1 .. 3)

{alpha = 3}, {alpha = alpha}

(14)

 

Download 2024-12-21_Q_3D_point_lies_on_3D_line.mw

I don't know what that line above the question is. Thanks in Advance.

NULLComplex Numbers

 

Key Skills 11-48

NULLc11 := 2-3*i+(6+8*i)"(=)"8+5*i

c12 := 4+5*i-8+2*i"(=)"-4+7*i

c13 := -3+2*i-4+4*i"(=)"-7+6*i

c14 := 3-4*i+(3+4*i) = 6NULL

c15 := 2-5*i-8-6*i"(=)"-6-11*i

c16 := -8+4*i-2+2*i"(=)"-10+6*i

c17 := 3*(2-6*i)"(=)"6-18*i

c18 := -4*(2+8*i)"(=)"-8-32*i

NULLc19 := 2*i(2-3*i) = 2*i(2-3*i)NULL

c20 := 3*i*(-3+4*i) = 3*i*(-3+4*i)

c21 := (3-4*i)*(2+i) = (3-4*i)*(2+i)NULL

c22 := (5+3*i)*(2-i) = (5+3*i)*(2-i)

``

``

Download 1.3-Complex_Numbers_bad.mw

I'm trying to get my problems in standard form  a + bi . Questions 19 - 22 are wrong.

How can I display the symbol (blue solid circle) and the line (blue line) together in the legend box (( from   to ))?

plot(sin(x), x = -3 .. 3, colour = [blue], style = pointline, symbol = [solidcircle], numpoints = 20, legend = ["sin(x)"])

 

 
 

``

Download Plot1.mw

As a Maple beginner, I am now interested in symbolic calculations in Maple. As before, I set a problem from a subject area that interests me in order to learn from professional answers.

Determine all regular square (n;n) matrices (determinant not equal to zero) that are commutable with every regular (n;n) matrix with respect to matrix multiplication.

(I know the solution from long ago.)

Example code

printlevel :=1     

for indx1 from 1 by 1 to  3  do  

f[indx1] :=indx1;  

 end do;

This prints
f1:=1
f2:=2
f3:=3

How do I use the "save" command to save exactly the loop's results above to a file so that I can read the file later and execute it in another  maple worksheet.

The maple manual https://www.maplesoft.com/support/help/Maple/view.aspx? 

for "save"   contains no examples, and definately not how to save results of a loop using the save command. e.g. how do you append  with a file using the "save" command ?

Note: I dont need any help with reading the results, from the saved file, my question is only about writing the results with "save" command. The "save" command gives me the best results for reading files back into a speadsheet, and text file save routines just gives me ascii garbage and not the exact results in executable maple format as "save" does, saving exacltly what you see on screen. Therefore text save routines are useless to me.

I have a file TEST.m. How can I make it so that every time I start Maple, all the subprograms in the TEST.m file will run first? Then I just need to type the function with(TEST): sumpro(2,3,4) to get the result 9. I copied the TEST.m file into Maple's lib directory, but it doesn't run after starting Maple.

I just need to type sumvip(2, 3, 4) to get the result, but Maple doesn't understand it.

Please help.

TEST := module () local sumpro; export sumvip; option package;  sumpro := proc (a, b, c) local sumex; sumex := a+b+c; printf("sum of %A , %A and %A is %A", a, b, c, sumex) end proc; sumvip := proc () sumpro(args) end proc end module:

save TEST, "TEST.m"

with(TEST)

[sumvip]

(1)

sumvip(2, 3, 4)

sum of 2 , 3 and 4 is 9

 

NULL

Download TEST.mw

2024-12-20_Q_simplification_Question.mw
Solve the general cubic. Apply values and simplify. 

Could someone show how Maple simplifies to the value of X=3? I tried doing it manually and I could not figure it out. 

Also is there a Help assistant to see the setps?

restart

 

 

X^3+a*X=b

X^3+X*a = b

(1)

 

 

sol:=solve(X^3+a*X=b,[X])

[[X = (1/6)*(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3)-2*a/(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3)], [X = -(1/12)*(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3)+a/(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3)+((1/2)*I)*3^(1/2)*((1/6)*(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3)+2*a/(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3))], [X = -(1/12)*(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3)+a/(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3)-((1/2)*I)*3^(1/2)*((1/6)*(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3)+2*a/(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3))]]

(2)

vals:=[a=6,b=45]

[a = 6, b = 45]

(3)

Nans:=(map(eval,sol,vals))

[[X = (1/6)*(4860+12*166617^(1/2))^(1/3)-12/(4860+12*166617^(1/2))^(1/3)], [X = -(1/12)*(4860+12*166617^(1/2))^(1/3)+6/(4860+12*166617^(1/2))^(1/3)+((1/2)*I)*3^(1/2)*((1/6)*(4860+12*166617^(1/2))^(1/3)+12/(4860+12*166617^(1/2))^(1/3))], [X = -(1/12)*(4860+12*166617^(1/2))^(1/3)+6/(4860+12*166617^(1/2))^(1/3)-((1/2)*I)*3^(1/2)*((1/6)*(4860+12*166617^(1/2))^(1/3)+12/(4860+12*166617^(1/2))^(1/3))]]

(4)

simplify(Nans)

[[X = 3], [X = (1/4)*(I*3^(1/2)*(180+44*17^(1/2))^(2/3)+(8*I)*3^(1/2)-(180+44*17^(1/2))^(2/3)+8)/(180+44*17^(1/2))^(1/3)], [X = -3/2-((1/2)*I)*51^(1/2)]]

(5)
 

 

Download 2024-12-20_Q_simplification_Question.mw

In the decimal system, we are looking for all natural numbers with at most six digits that only swap the order of the digits when multiplied by 2, 3, ..., 6.

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