Maple 2016 Questions and Posts

These are Posts and Questions associated with the product, Maple 2016

I'm trying to solve a system of differential equations and encountered this error: Error, (in fsolve) {f1[0], f1[1], f1[2], f1[3], f2[0], f2[1], f2[2], f2[3]} are in the equation, and are not solved for. How can this error be rectified?

Hello everyone

I create a curved space ( with Physics) and create a metric tensor of 

a sphere . I see some Christoffel correcly . Is it possible to visualize all non zero Christoffel in one shot ?

Thank's a lot

Best Regards

restart; with(Physics)

Physics:-Setup(mathematicalnotation = true)

[mathematicalnotation = true]

(1)

Physics:-Setup(spacetimeindices, dimension = 2, signature = "++")

[dimension = 2, signature = `+ +`, spacetimeindices = greek]

(2)

Physics:-Coordinates(X)

{X}

(3)

ds2 := Physics:-`^`(dx1, 2)+Physics:-`*`(Physics:-`^`(sin(x1), 2), Physics:-`^`(dx2, 2))

dx1^2+sin(x1)^2*dx2^2

(4)

NULL

Physics:-Setup(metric = ds2)

[metric = {(1, 1) = 1, (2, 2) = sin(x1)^2}]

(5)

NULL

NULL

g_[]

g[mu, nu] = (Matrix(2, 2, {(1, 1) = 1, (1, 2) = 0, (2, 2) = sin(x1)^2}, storage = triangular[upper], shape = [symmetric]))

(6)

Physics:-Christoffel[`~k`, i, j]

Physics:-Christoffel[`~k`, i, j]

(7)

Physics:-Christoffel[`~1`, 2, 2]

-sin(x1)*cos(x1)

(8)

Physics:-Christoffel[`~2`, 1, 2]

cos(x1)/sin(x1)

(9)

Physics:-Christoffel[`~1`, 1, 1]

0

(10)

Download Approfondimento_1_-_Calcolo_Sfera_2D.mw

Hello everybody

I would like to check, with Spacetime Tensors computation , if  a transfomation is a Lorentz transformation , i.e that leavs Minkosky metric invariant 

For esample a boost  or axis rotation transformation

Some could help me ? ( Maple 2016)

Thank's a lot

Any comment, idea or innovation to calculate this parametric integral?

Note M, II, JJ are arbitrary positive integers (0<M, II, JJ<11).

F must be a function of Pm at the final!

``

restart

M := 3:

JJ := 5

II := 5

with(ArrayTools):

W := RandomArray(II, JJ, M):

V := ArrayTools:-RandomArray(II, JJ, M):

w := add(add(add(W[i, j, m]*LegendreP(i-1, x)*LegendreP(j-1, y)*p[m], i = 1 .. II), j = 1 .. JJ), m = 1 .. M):

v := add(add(add(V[i, j, m]*LegendreP(i-1, x)*LegendreP(j-1, y)*p[m], i = 1 .. II), j = 1 .. JJ), m = 1 .. M):

L := add(add((LegendreP(i-1, x)*LegendreP(j-1, y))^2, i = 1 .. II), j = 1 .. JJ):

H := 1+tanh(w-v)

F := int(H*L, [y = -1 .. 1, x = -1 .. 1])

Warning,  computation interrupted

 

``

``

Download integralproblem.mw

Good day everyone,

I have been having problems with a system of PDE solution using `numeric`.

It's giving me the error code "Error, (in pdsolve/numeric/par_hyp) input system is too far from a 'standard' form (see ?pdsolve,numeric for more detail)" and I have checked to the best of my ability for the error but could not see anything.

The code is attached below.

Please, anyone with useful information should help. Thanks

Numeric.mw

How can these eight equations q[0]...q[7] be solved for the eight unknowns a1[0]...a1[7] and with the lowest CPU time

11.mw

Good day everyone,

I am trying to rotate the plots of pde solution using transplot, but it is giving me errors. Anyone with better suggestions should help. The code is attached below. Thanks

Transplot_not_working.mw

I want to use union, intersection and minus to find. Help me

What is the best and accurate way to export a large symbolic matrix (200*300) from Maple to Matlab? The Marix have a lot of variables, symbols and operators such as diiff, int, ....

Here is a simple example:

NULL

restart

NULL

A := Matrix(2, 6, {(1, 1) = x*y*z, (1, 2) = (1/2)*tau[2], (1, 3) = sin(x*y*z), (1, 4) = ln(x*y*z), (1, 5) = tau[1]*exp(x*y*z), (1, 6) = sin(x+y)+cos(x+y), (2, 1) = x^2+1, (2, 2) = x^2+1/sin(x*y*z), (2, 3) = 2*exp(y), (2, 4) = tau[1], (2, 5) = diff(f(x, y, z), x), (2, 6) = int(f(x, y, z), x)})

A := 1/sin(protected)

(1)

``

CodeGeneration[Matlab](codegen[makeproc](A, [x, y, tau[1], tau[2]]))

Error, (in codegen/makeproc) optional arguments must be equations [x, y, tau[1], tau[2]]

 

``

``

``

``

``

``

Download export.mw

Where is the problem within this procedure which I can not get the numerical values of V[1] , V[2], ...

restart

A := Matrix([[2*t, 2, 3], [4, 5*t, 6], [7, 8*t, 9]])

A := Matrix(3, 3, {(1, 1) = 2*t, (1, 2) = 2, (1, 3) = 3, (2, 1) = 4, (2, 2) = 5*t, (2, 3) = 6, (3, 1) = 7, (3, 2) = 8*t, (3, 3) = 9})

(1)

B := LinearAlgebra:-Transpose(Matrix([t, 2*t, 3*t]))

B := Matrix(3, 1, {(1, 1) = t, (2, 1) = 2*t, (3, 1) = 3*t})

(2)

``

test:=proc(n)
  local s,t,M,V;
  s:=1:
  for t from 1 to n do
    M:=A+A^(-1);
    V[s]:=(M.B):
    s:=s+1:
  end do;
  V;
end proc:

``

test(4)

V

(3)

V[1]

V[1]

(4)

``

``

Download ProcPropl.mw

In part of my program, I have a loop that the iterative calculations are performed there. During running the program when it comes to the loop the memory usage become full in a short period of time and I face the memory shortage. Since my program is so long and huge, I only can show the loop part of it here, you may look at where is the problem of high memory usage in loop and how to deal with it. Any comment will be appreciated.

I again note that, this segment can not be run independently since it is a part of big program. I put it just to see and mmake comment if any.

M := 3; Nm := 1

w0 := Matrix(M+Nm, 1)

wd0 := Matrix(M+Nm, 1)

taim := 1

F0 := convert([seq(Quadrature(Quadrature(simplify(add(add(W[i, j, 4, r]*LegendreP(i, 1)*LegendreP(j, 0), i = 0 .. II), j = 0 .. JJ)), `&zeta;__1` = -1 .. 1, method = romberg[3]), `&eta;__1` = -1 .. 1, method = romberg[3]), r = 1 .. M), seq(0, n = 1 .. Nm)], Matrix)

T := 1/(2*Pi*`&omega;__km`[M][2])

dt := (1/10)*T

0.1123479896110e-4

(1)

for i to M do tau[i](t) := tau[i] end do

for i to Nm do p[i](t) := p[i] end do

`&alpha;__N` := .5; `&beta;__N` := .25; a__0 := 1/(`&beta;__N`*dt^2); a__1 := `&alpha;__N`/(`&beta;__N`*dt); a__2 := 1/(`&beta;__N`*dt); a__3 := 1/(2*`&beta;__N`)-1; a__4 := `&alpha;__N`/`&beta;__N`-1; a__5 := dt*(`&alpha;__N`/(2*`&beta;__N`)-1); a__6 := dt*(1-`&alpha;__N`); a__7 := `&alpha;__N`*dt

q := Matrix(1 .. M+Nm, 1 .. floor(taim/dt)+1)

dq := Matrix(1 .. M+Nm, 1 .. floor(taim/dt)+1)

ddq := Matrix(1 .. M+Nm, 1 .. floor(taim/dt)+1)

q(1 .. M+Nm, 1) := w0

dq(1 .. M+Nm, 1) := wd0

for i to M do tau[i] := q(i, 1) end do

for i to Nm do p[i] := q(M+i, 1) end do

ddq(1 .. M+Nm, 1) := 1/ML.(diff((diff(sin(`&omega;__b`*t__0), t__0))*LinearAlgebra:-Transpose(F0), t__0)-CL.dq(1 .. M+Nm, 1 .. 1)-KL.q(1 .. M+Nm, 1 .. 1)-eqMNL)

t__0 := dt

V := LinearAlgebra:-Transpose(convert([seq(Tau[i], i = 1 .. M), seq(P[i], i = 1 .. Nm)], Matrix))

Qn__2 := LinearAlgebra:-Transpose(Matrix(1, M+Nm))

Qn__3 := LinearAlgebra:-Transpose(Matrix(1, M+Nm))

External force

 

`&omega;__b` := 25

``

F := diff((diff(sin(`&omega;__b`*t), t))*LinearAlgebra:-Transpose(convert(F0, Matrix)), t)

``

s := 1

k__d := 100000

with(Student[NumericalAnalysis]); dt

``

Loop

 

for t from t__0 by dt to taim do EQ := KL.V+a__0*ML.V+a__1*CL.V-ML.(a__0*q(1 .. M+Nm, s .. s)+a__2*dq(1 .. M+Nm, s .. s)+a__3*ddq(1 .. M+Nm, s .. s))-CL.(a__1*q(1 .. M+Nm, s .. s)+a__4*dq(1 .. M+Nm, s .. s)+a__5*ddq(1 .. M+Nm, s .. s))-F-Qn__2-Qn__3; G := Matrix(M+Nm, proc (i, j) options operator, arrow; (diff(EQ[i], V[j, 1]))[1] end proc); G1 := 1/G; if t = t__0 then X[1] := 1/(CL*a__1+ML*a__0+KL).(F+ML.(a__0*q(1 .. M+Nm, s .. s)+a__2*dq(1 .. M+Nm, s .. s)+a__3*ddq(1 .. M+Nm, s .. s))+CL.(a__1*q(1 .. M+Nm, s .. s)+a__4*dq(1 .. M+Nm, s .. s)+a__5*ddq(1 .. M+Nm, s .. s))) else X[1] := q(1 .. M+Nm, s .. s) end if; for k to 11 do X[k+1] := eval(V-G1.EQ, Equate(V, X[k])) end do; q(1 .. M+Nm, s+1 .. s+1) := X[k]; ddq(1 .. M+Nm, s+1 .. s+1) := a__0*(q(1 .. M+Nm, s+1 .. s+1)-q(1 .. M+Nm, s .. s))-a__2*dq(1 .. M+Nm, s .. s)-a__3*ddq(1 .. M+Nm, s .. s); dq(1 .. M+Nm, s+1 .. s+1) := dq(1 .. M+Nm, s .. s)+a__6*ddq(1 .. M+Nm, s .. s)+a__7*ddq(1 .. M+Nm, s+1 .. s+1); Wxy2 := add(add(add(h*W[i, j, 2, o]*LegendreP(i, `&zeta;__2`)*LegendreP(j, `&eta;__2`)*q[o, s+1], i = 0 .. II), j = 0 .. JJ), o = 1 .. M); Wxy3 := add(add(add(h*W[i, j, 3, o]*LegendreP(i, `&zeta;__2`)*LegendreP(j, `&eta;__2`)*q[o, s+1], i = 0 .. II), j = 0 .. JJ), o = 1 .. M); Plt := plots:-implicitplot(Wxy2-Wxy3, `&zeta;__2` = -1 .. 1, `&eta;__2` = -1 .. 1, color = red, thickness = 2, gridrefine = 3); j := 111111; Hvs2 := 1; for i while i <= j do Pnt[i] := op([1, i], Plt); if Wxy2-Wxy3 = 0 then j := 0 elif convert(Pnt[i], string)[1] = "C" then j := 0 else a__e[i] := (1/2)*abs(max(Column(Pnt[i], 1))-min(Column(Pnt[i], 1))); if a__e[i] = 0 then a__e[i] = 0.1e-5 end if; b__e[i] := (1/2)*abs(max(Column(Pnt[i], 2))-min(Column(Pnt[i], 2))); if b__e[i] = 0 then b__e[i] = 0.1e-5 end if; xc[i] := (max(Column(Pnt[i], 1))+min(Column(Pnt[i], 1)))*(1/2); yc[i] := (max(Column(Pnt[i], 2))+min(Column(Pnt[i], 2)))*(1/2); Hv2[i] := ((`&zeta;__2`-xc[i])/a__e[i])^2+((`&eta;__2`-yc[i])/b__e[i])^2-1; Hvs2 := Hv2[i]*Hvs2 end if end do; Qn__2 := LinearAlgebra:-Transpose(convert([(1/2)*k__d*Grid:-Seq(Quadrature(Quadrature(Heaviside(-Hvs2)*abs(Wxy2-Wxy3)*add(add(W[i, j, 2, r]*LegendreP(i, `&zeta;__2`)*LegendreP(j, `&eta;__2`), i = 0 .. II), j = 0 .. JJ), `&zeta;__2` = -1 .. 1, method = romberg[5]), `&eta;__2` = -1 .. 1, method = romberg[5]), r = 1 .. M), seq(0, n = 1 .. Nm)], Matrix)); Qn__3 := -Qn__2; s := s+1 end do

``

Download HighMemUseProb.mw

Good day everyone, 

Can I plot the graph of the sheet attached below such that x will be on the vertical component and y will be on the horizontal component? Can this be done on Maple? Anyone with useful information should please help.

plot_graph.mw

I am trying to do the following computation. I  extracted n*1 matrix from n*n matrix which unbelievably gives vector?

How I can do the following multiplication without using convert command? Or how to extract n*1 matrix (not vector) from n*n matrix without using convert?

``

restart

``

``

A := Matrix(4, 4, {(1, 1) = m[1, 1], (1, 2) = m[1, 2], (1, 3) = m[1, 3], (1, 4) = m[1, 4], (2, 1) = m[2, 1], (2, 2) = m[2, 2], (2, 3) = m[2, 3], (2, 4) = m[2, 4], (3, 1) = m[3, 1], (3, 2) = m[3, 2], (3, 3) = m[3, 3], (3, 4) = m[3, 4], (4, 1) = m[4, 1], (4, 2) = m[4, 2], (4, 3) = m[4, 3], (4, 4) = m[4, 4]})

A := Matrix(4, 4, {(1, 1) = 0, (1, 2) = m[1, 2], (1, 3) = m[1, 3], (1, 4) = m[1, 4], (2, 1) = 0, (2, 2) = m[2, 2], (2, 3) = m[2, 3], (2, 4) = m[2, 4], (3, 1) = 0, (3, 2) = m[3, 2], (3, 3) = m[3, 3], (3, 4) = m[3, 4], (4, 1) = 0, (4, 2) = m[4, 2], (4, 3) = m[4, 3], (4, 4) = m[4, 4]})

(1)

A(1 .. 4, 1) := Matrix(4, 1):

A

Matrix([[0, m[1, 2], m[1, 3], m[1, 4]], [0, m[2, 2], m[2, 3], m[2, 4]], [0, m[3, 2], m[3, 3], m[3, 4]], [0, m[4, 2], m[4, 3], m[4, 4]]])

(2)

B := A(1 .. 4, 2)

B := Vector(4, {(1) = m[1, 2], (2) = m[2, 2], (3) = m[3, 2], (4) = m[4, 2]})

(3)

A.B

4

(4)

F := Matrix(4, 1, {(1, 1) = 0.4279668887e-7, (2, 1) = -0.3901148183e-7, (3, 1) = 0.3900685346e-7, (4, 1) = 0.})

Typesetting:-delayDotProduct(A, B)-F

Error, (in rtable/Sum) invalid input: dimensions do not match: Vector[column](1 .. 4) cannot be added to Matrix(1 .. 4, 1 .. 1)

 

A.convert(B, Matrix)-F

Matrix(4, 1, {(1, 1) = m[1, 2]*m[2, 2]+m[1, 3]*m[3, 2]+m[1, 4]*m[4, 2]-0.4279668887e-7, (2, 1) = m[2, 2]^2+m[2, 3]*m[3, 2]+m[2, 4]*m[4, 2]+0.3901148183e-7, (3, 1) = m[3, 2]*m[2, 2]+m[3, 3]*m[3, 2]+m[3, 4]*m[4, 2]-0.3900685346e-7, (4, 1) = m[2, 2]*m[4, 2]+m[3, 2]*m[4, 3]+m[4, 2]*m[4, 4]})

(5)

``

Download soalzarb.mw

If i have p := 8*T(x, 7)*T(x, 2)+4*T(x, 5)*T(x, 1)+6*T(x, 3)*T(x, 3)+7*T(x, 1)*T(x, 4)

 I want to convert the the multiplication functions like T(x, 7)*T(x, 2) into summation T(x, 7)+T(x, 2)

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