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Inacio Aprendanet

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Procedures, procedures 2...

Inacio Aprendanet 65 Maple
textplot
August 06 2018
1 1

Hello again, folks!!!

 

Can you help me in this matter?

 


 

``

> 

restart; with(plots)
> 

arcsinplot := proc (asin) local A, B, C, E, F, G, H, J, theta, c1, c2, c3; theta := arcsin(asin); c1 := COLOR(RGB, 1, .75, .2); c2 := COLOR(RGB, .7, .4, .1); c3 := COLOR(RGB, 1, .2, .1); A := plot(sin(x), x = -Pi .. Pi, color = c3, tickmarks = [1, 1]); B := plot(sin(x), x = -(1/2)*Pi .. (1/2)*Pi, color = c2, thickness = 4); C := polygonplot([[-(1/2)*Pi, -1], [(1/2)*Pi, -1], [(1/2)*Pi, 1], [-(1/2)*Pi, 1], [-(1/2)*Pi, -1]], color = c1, style = patchnogrid); E := plot([[-(1/2)*Pi, -1], [(1/2)*Pi, -1], [(1/2)*Pi, 1], [-(1/2)*Pi, 1], [-(1/2)*Pi, -1]], color = orange, linestyle = 3); F := plottools[arrow]([0, asin], [theta, asin], 0.5e-1, .10, .15, color = red); G := plottools[arrow]([theta, asin], [theta, 0], .10, .20, .10, color = red); H := textplot([theta, -.15, evalf(theta, 3)], 'align' = {'above', 'center'}); J := textplot([-.2, asin, evalf(asin, 3)], 'align' = {'above', 'left'}); display([F, G, A, B, C, E, H, J]) end proc
> 

arccosplot := proc (acos) local A, B, C, E, F, G, H, J, theta, c1, c2, c3; theta := arccos(acos); c1 := COLOR(RGB, .6, .6, .85); c2 := COLOR(RGB, .3, .4, .87); c3 := COLOR(RGB, .1, .2, .6); A := plot(cos(x), x = -(1/2)*Pi .. (3/2)*Pi, color = c3, tickmarks = [0, 0]); B := plot(cos(x), x = 0 .. Pi, color = c2, thickness = 4); C := polygonplot([[0, -1], [Pi, -1], [Pi, 1], [0, 1], [0, -1]], color = c1, style = patchnogrid); E := plot([[0, -1], [Pi, -1], [Pi, 1], [0, 1], [0, -1]], color = navy, linestyle = 3); F := plottools[arrow]([0, acos], [theta, acos], 0.5e-1, .10, .15, color = navy); G := plottools[arrow]([theta, acos], [theta, 0], .10, .20, .18, color = navy); H := textplot([theta, -.15, evalf(theta, 3)], 'align' = {'above', 'center'}); J := textplot([-.2, acos, evalf(acos, 3)], 'align' = {'above', 'left'}); display([A, B, E, F, G, C, H, J]) end proc
> 

arctanplot := proc (a) local A, B, C, E, F, G, H, J, theta, c1, c2, c3, L, R, m; theta := arctan(a); L := -(1/2)*Pi+0.1e-1; R := (1/2)*Pi-0.1e-1; m := 12; c1 := COLOR(RGB, .75, 95, .75); c2 := COLOR(RGB, .4, .9, .4); c3 := COLOR(RGB, .2, .5, .2); A := plot(tan(x), x = -Pi .. Pi, y = -m .. m, color = c3, tickmarks = [1, 1], discont = true); B := plot(tan(x), x = L .. R, y = -m .. m, color = c2, thickness = 4); C := polygonplot([[L, -m], [R, -m], [R, m], [L, m], [L, -m]], color = c1, style = patchnogrid); E := plot([[L, -m], [R, -m], [R, m], [L, m], [L, -m]], color = green, linestyle = 3); F := plottools[arrow]([0, a], [theta, a], .4, .6, .15, color = c3); G := plottools[arrow]([theta, a], [theta, 0], 0.8e-1, .15, .15, color = c3); H := textplot([theta, -.8, evalf(theta, 3)], 'align' = {'above', 'center'}); J := textplot([-.2, a, evalf(a, 3)], 'align' = {'above', 'left'}); display([F, G, A, B, C, E, H, J]) end proc
> 

arcsinplot(.9)

Error, (in plots:-textplot) unexpected value for align option:, center

  
> 

arccosplot(.9)

Error, (in plots:-textplot) unexpected value for align option:, center

  
> 

arctanplot(.9)

Error, (in plots:-textplot) unexpected value for align option:, center

  
> 

``

``


 

Download Duvida2.mw

Procedures, procedures...

Inacio Aprendanet 65 Maple 2018
August 01 2018
1 1

Hello to everyone!

 

I was trying to implement the following proc:
 

``

> 

restart; with(plots); with(plottools)
> 

"AngleSpectrum := proc( theta ) local A, B, C, a1,a2,col,k,n; n := floor(2*Pi/theta): for k from 1 to n do a1 := theta*(k-1); a2 := theta*(k); if( k mod 2 = 0) then col := COLOR(RGB,.8,.3,.5); else col := COLOR(RGB,.4,.3,.5) ; fi; A[k] := plottools[pieslice]([0,0], 1, a1..a2, color = col ): C[k] := textplot( [ evalf(1.2*cos(a2)), evalf(1.2*sin(a2)), convert(a2, string)]): od: display( seq( {A[k], C[k]}, k = 1..n), scaling=constrained); end proc:"

Error, unterminated loop

"AngleSpectrum := proc( theta ) local A, B, C, a1,a2,col,k,n; n := floor(2*Pi/theta): for k from 1 to n do a1 := theta*(k-1); a2 := theta*(k); if( k mod 2 = 0) then col := COLOR(RGB,.8,.3,.5); else col := COLOR(RGB,.4,.3,.5) ; fi; A[k] := plottools[pieslice]([0,0], 1, a1..a2, color = col ): C[k] := textplot( [ evalf(1.2*cos(a2)), evalf(1.2*sin(a2)), convert(a2, string)]): od: display( seq( {A[k], C[k]}, k = 1..n), scaling=constrained); end proc:"

  
> 

``


Can anyone help me to figure out my mistake?

Download proc.mw

Maxwell Equations in Potential Fields...

Inacio Aprendanet 65 Maple
physics
May 02 2017
1 5

I wish to express the Maxwell equations in potential fields deriving from a Lagrangian in cartesian coordinates, but expressed in vectorial form; But I am receiving an message error that I do not understand.

Field_A-MaplePrimes.mw
 

 

Initial Definitions:

 

``

I wish in this work to express the Maxwell equations deriving from the Lagrangian in the fields phiand "A,"

phi

(1.1)

but expressed in vectorial form;

 

> 

restart; clear; with(Physics); with(Physics[Vectors]); with(Library)interface(imaginaryunit = I)

clear

 

I

(1.2)
> 

Physics:-Coordinates(X = [t, x, y, z])

`Detected \`t\`, the time variable, in position 1. Changing the signature of the spacetime metric accordingly, to: + - - - `

  

`Default differentiation variables for d_, D_ and dAlembertian are: `*{X = (t, x, y, z)}

 

`Systems of spacetime Coordinates are: `*{X = (t, x, y, z)}

 

{X}

(1.3)
> 

Physics:-Vectors:-Setup(math = true, Physics:-Vectors:-diff = X)

`* Partial match of 'math' against keyword 'mathematicalnotation'`

 

`* Partial match of 'Physics:-Vectors:-diff' against keyword 'differentiationvariables'`

 

`Default differentiation variables for d_, D_ and dAlembertian are: `*{X = (t, x, y, z)}

 

[differentiationvariables = [X], mathematicalnotation = true]

(1.4)
> 

``

Some definitions

 

 

Defining the Maxwell tensor

 

> 

Physics:-Define(F):``

`Defined objects with tensor properties`

(2.1)

 

Defining the field A with their components:

 

> 

A[mu] = Vector(4, [phi(X), A__1(X), A__2(X), A__3(X)]); Define(%)

A[mu] = Vector[column](%id = 18446744074366759750)

 

`Defined objects with tensor properties`

 

{F, A[mu], Physics:-Dgamma[mu], Physics:-Psigma[mu], Physics:-d_[mu], Physics:-g_[mu, nu], Physics:-KroneckerDelta[mu, nu], Physics:-LeviCivita[alpha, beta, mu, nu], Physics:-SpaceTimeVector[mu](X)}

(2.2)
> 

Physics:-CompactDisplay(phi(X), A__1(X), A__2(X), A__3(X))

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

 

A__1(t, x, y, z)*`will now be displayed as`*A__1

 

A__2(t, x, y, z)*`will now be displayed as`*A__2

 

A__3(t, x, y, z)*`will now be displayed as`*A__3

(2.3)

 

Applying:

 

 

> 

``

> 

F[alpha, beta] := Physics:-Vectors:-`+`(Physics:-d_[beta](A[alpha]), -Physics:-d_[alpha](A[beta]));

Physics:-d_[beta](A[alpha], [X])-Physics:-d_[alpha](A[beta], [X])

(3.1)
> 

``

 

NULL

NULL

Term 1:

 

 

> 

eq1 := Physics:-d_[alpha](F[alpha, beta])

Physics:-d_[alpha](Physics:-d_[beta](A[`~alpha`], [X]), [X])-Physics:-dAlembertian(A[beta], [X])

(4.1)
> 

Physics:-SumOverRepeatedIndices(Physics:-d_[alpha](Physics:-d_[beta](A[`~alpha`], [X]), [X])-Physics:-dAlembertian(A[beta], [X]))

Physics:-d_[beta](diff(phi(X), t), [X])-Physics:-d_[beta](diff(A__1(X), x), [X])-Physics:-d_[beta](diff(A__2(X), y), [X])-Physics:-d_[beta](diff(A__3(X), z), [X])-Physics:-dAlembertian(A[beta], [X])

(4.2)
> 

Physics:-SubstituteTensorIndices(beta = 4, Physics:-d_[beta](diff(phi(X), t), [X])-Physics:-d_[beta](diff(A__1(X), x), [X])-Physics:-d_[beta](diff(A__2(X), y), [X])-Physics:-d_[beta](diff(A__3(X), z), [X])-Physics:-dAlembertian(A[beta], [X]))

diff(diff(phi(X), t), z)-(diff(diff(A__1(X), x), z))-(diff(diff(A__2(X), y), z))-(diff(diff(A__3(X), z), z))-Physics:-dAlembertian(A__3(X), [X])

(4.3)
> 

``

> 

Physics:-SubstituteTensorIndices(beta = 1, Physics:-d_[beta](diff(phi(X), t), [X])-Physics:-d_[beta](diff(A__1(X), x), [X])-Physics:-d_[beta](diff(A__2(X), y), [X])-Physics:-d_[beta](diff(A__3(X), z), [X])-Physics:-dAlembertian(A[beta], [X]))

diff(diff(phi(X), t), t)-(diff(diff(A__1(X), t), x))-(diff(diff(A__2(X), t), y))-(diff(diff(A__3(X), t), z))-Physics:-dAlembertian(phi(X), [X])

(4.4)
> 

SubstituteTensorIndices(beta = 2, Physics[d_][beta](diff(phi(X), t), [X])-Physics[d_][beta](diff(A__1(X), x), [X])-Physics[d_][beta](diff(A__2(X), y), [X])-Physics[d_][beta](diff(A__3(X), z), [X])-Physics[dAlembertian](A[beta], [X]))

Error, (in dchange/info) the number of new and old independent variables must be the same. Found {x, y} as new, while {} as old

 
> 

SubstituteTensorIndices(beta = 3, Physics[d_][beta](diff(phi(X), t), [X])-Physics[d_][beta](diff(A__1(X), x), [X])-Physics[d_][beta](diff(A__2(X), y), [X])-Physics[d_][beta](diff(A__3(X), z), [X])-Physics[dAlembertian](A[beta], [X]))

Error, (in dchange/info) the number of new and old independent variables must be the same. Found {x, y} as new, while {} as old

 
> 

Physics:-SubstituteTensorIndices(beta = 4, Physics:-d_[beta](diff(phi(X), t), [X])-Physics:-d_[beta](diff(A__1(X), x), [X])-Physics:-d_[beta](diff(A__2(X), y), [X])-Physics:-d_[beta](diff(A__3(X), z), [X])-Physics:-dAlembertian(A[beta], [X]))

diff(diff(phi(X), t), z)-(diff(diff(A__1(X), x), z))-(diff(diff(A__2(X), y), z))-(diff(diff(A__3(X), z), z))-Physics:-dAlembertian(A__3(X), [X])

(4.5)

``

What is the origin of the two error messages above? I did some wrong definition? Why this works in t and z but not in x and y?

 

NULL


 

Download Field_A-MaplePrimes.mw

 

 

 

Solving an ODE ...

Inacio Aprendanet 65 Maple
ode
November 23 2015
0 9

Hello,

 I am trying to solve an differential equation in Maple, but I have no response from Maple.Can someone give a look for me? The coefficients a and b cannot be zero.

 Thanks a lot.

 

Download edo_solução_A_U.mw

Tensor To Vector Form...

Inacio Aprendanet 65 Maple
June 10 2015
0 0

Hello;

 

I wish to express a tensorial equation or expression a simplified vector form.

 

In the worksheet attached, I was trying to express Maxwell Equations in the familiar vector form from the tensorial form, using the F[mu,nu] tensor.

 

But I cannot achieve the familiar tensor form. If someone can give a hand, it would help me a lot.

 

HowtoExpressCompactForm.mw

 

 

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