Maple 2015 Questions and Posts

These are Posts and Questions associated with the product, Maple 2015

Hi everibody 

I work with Maple 2015 under OS-X El Capitan.

Using more than one matrix vector product (either M.V  or MatrixVectorMultiply(M,V)  ; M is a n by p matrix and V a column vector of size p) within the same block of commands generates an error.

Do other people have the same problem ?
Thanks for your feedback.

SomethingGoesWrong.mw


PS : I know I can do this   X . <<1, 1, -1> | <-1, 2, 0>> but this doesn't explain the error I get

 

what are the dynamical system which act on invariant manifold?

Hi,

This sequence of commands works perfectly well

     plotsetup(jpeg, plotoutput=SomeJpegFile);
     plot(x, x=0..1);
     plotsetup(default);


Why this one doesn't create the file SomeJpegFile ?

f := proc()
     plotsetup(jpeg, plotoutput=SomeJpegFile);
     plot(x, x=0..1);
     plotsetup(default);
end proc;

f();


Thanks in advance

is it a complete set of all combinations of elementary operations?

i search all and solve, but result are not all integers

updated 1A

with(LinearAlgebra):
with(combinat):
b1 := Matrix([[a1,a2,a3],[a4,a5,a6],[a7,a8,a9]]);
b2 := Matrix([[a1,a4,a7],[a2,a5,a8],[a3,a6,a9]]);
list8 := choose([1,2,3],2);
#[op([1]),2]
result := []:
result := [op(result),b1]:
for i from 1 to nops(list8) do
 temp := Matrix([[a1,a2,a3],[a4,a5,a6],[a7,a8,a9]]);
 print("b1",temp);
 temp[list8[i][2]] := temp[list8[i][1]]+temp[list8[i][2]]:
 print(temp);
 result := [op(result),temp]
od:
for i from 1 to nops(list8) do
 temp := Matrix([[a1,a4,a7],[a2,a5,a8],[a3,a6,a9]]);
 print("b1",temp);
 temp[list8[i][2]] := temp[list8[i][1]]+temp[list8[i][2]]:
 print(temp);
 result := [op(result),temp]
od:
for i from 1 to nops(result) do
 result := [op(result),Transpose(result[i])]:
od:
final := choose(result, 10):
for i from 1 to nops(final) do
 om := map(Determinant,final[i]):
 syss := []:
 for kk from 1 to nops(om) do
  for k from 1 to nops(om) do
   if k <> kk then
    syss := [op(syss),om[k]=om[kk]]:
   end if:
  od:
 od:
 sys := choose(syss, 9):
 for ij from 1 to nops(sys) do
  sol := solve(sys[ij], [a1,a2,a3,a4,a5,a6,a7,a8,a9]);
  if nops(sol) > 1 then
   for j from 1 to nops(sol) do
    if type(rhs(sol[j][1]))=integer and type(rhs(sol[j][2]))=integer and type(rhs(sol[j][3]))=integer and type(rhs(sol[j][4]))=integer and type(rhs(sol[j][5]))=integer and type(rhs(sol[j][6]))=integer and type(rhs(sol[j][7]))=integer and type(rhs(sol[j][8]))=integer and type(rhs(sol[j][9]))=integer then
     print(i,sol,sys,nops(sys)):
    end if:
   od:
  end if:
  if nops(sol) = 1 then
   if type(rhs(sol[1][1]))=integer and type(rhs(sol[1][2]))=integer and type(rhs(sol[1][3]))=integer and type(rhs(sol[1][4]))=integer and type(rhs(sol[1][5]))=integer and type(rhs(sol[1][6]))=integer and type(rhs(sol[1][7]))=integer and type(rhs(sol[1][8]))=integer and type(rhs(sol[1][9]))=integer then
    print(i,sol,sys,nops(sys)):
   end if:
  end if:
 od:
od:

Dear 

Hope everyone is good. I am face to attaine the converges solution of the attached problem. Please have a look and fix my problem. I am waiting your response

diverges.mw


 

لا شيء

-------------------------------------------------- -------------------------------------------------- -------------------------------------------------- -------------------------

إعادة بدء

مع (LinearAlgebra)

مع (orthopoly)

مع (طالب)

لا شيء

لا شيء

لا شيء

لا شيء

سيل (ألفا): = 2؛  سيل (بيتا): = 1؛  ألفا: = 1.5؛  بيتا: = .5

2

 

1

 

1.5

 

0.5

(1)

n: = 8؛  m: = 8

8

 

8

(2)

 

لا شيء

x [3]: = .611423302089630؛  x [4]: ​​= 1.09446605083631؛  x [5]: = 1.99636816302962؛  x [6]: = 3.38757178455234؛  x [7]: = 5.41873370919121؛  x [8]: = 8.49143699030089

،611423302089630

 

+1.09446605083631

 

1.99636816302962

 

3.38757178455234

 

5.41873370919121

 

8.49143699030089

(3)

# 1 / حساب مصفوفة (A). (طريقة الجمع)

A := array(1 .. n, 1 .. m); for j to m do A[1, j] := evalf(subs(x = 0, L(j-1, 2*x-1))) end do; for j to m do A[2, j] := evalf(subs(x = 0, diff(L(j-1, 2*x-1), x))) end do; for i from 3 to n do for j to m do A[i, j] := evalf(subs(x = x[i], fracdiff(L(j-1, 2*x-1), x, alpha, method = direct))+subs(x = x[i], fracdiff(L(j-1, 2*x-1), x, beta, method = direct))+subs(x = x[i], diff(L(j-1, 2*x-1), x))+subs(x = x[i], L(j-1, 2*x-1))) end do end do

print(`A=`, A)

`A=`, A

(4)

A := convert(A, Matrix)

A := Matrix(8, 8, {(1, 1) = 1., (1, 2) = 2., (1, 3) = 3.500000000, (1, 4) = 5.666666667, (1, 5) = 8.708333333, (1, 6) = 12.88333333, (1, 7) = 18.50972222, (1, 8) = 25.97658730, (2, 1) = 0., (2, 2) = -2., (2, 3) = -6., (2, 4) = -13., (2, 5) = -24.33333333, (2, 6) = -41.75000000, (2, 7) = -67.51666667, (2, 8) = -104.5361111, (3, 1) = 1., (3, 2) = -2.987486314, (3, 3) = -3.301220288, (3, 4) = .5119939327, (3, 5) = 9.171314221, (3, 6) = 23.72035697, (3, 7) = 45.59773916, (3, 8) = 76.72165628, (4, 1) = 1., (4, 2) = -4.549878909, (4, 3) = -1.208865530, (4, 4) = 6.408882482, (4, 5) = 16.03540544, (4, 6) = 27.10075251, (4, 7) = 40.26736031, (4, 8) = 57.11215315, (5, 1) = 1., (5, 2) = -7.181375466, (5, 3) = 6.777193107, (5, 4) = 12.19170970, (5, 5) = 9.600555508, (5, 6) = 7.084730200, (5, 7) = 11.13249218, (5, 8) = 24.60731420, (6, 1) = 1., (6, 2) = -10.92878792, (6, 3) = 28.28352183, (6, 4) = -10.19173665, (6, 5) = -20.04576479, (6, 6) = 9.17677094, (6, 7) = 39.97816692, (6, 8) = 49.07345342, (7, 1) = 1., (7, 2) = -16.09078867, (7, 3) = 78.08969329, (7, 4) = -166.5158779, (7, 5) = 129.0586058, (7, 6) = 104.8307190, (7, 7) = -104.838425, (7, 8) = -111.0119440, (8, 1) = 1., (8, 2) = -23.55908364, (8, 3) = 192.6052140, (8, 4) = -856.8131732, (8, 5) = 2255.610395, (8, 6) = -3256.154493, (8, 7) = 1577.05254, (8, 8) = 2063.443568})

(5)

NULL

# ------------------------------------------------- --------------------------
# 2 / حساب مصفوفة (ب) من قبل أدومين بوليس لمصطلح غير الخطية.

"G(y):=(e)^(y)"

proc (y) options operator, arrow; exp(y) end proc

(6)

"g(x):=evalf(((4*sqrt(x))/(sqrt(Pi)))+(8/(3))*((x^(3/(2)))/(sqrt(Pi)))+2*x+x^(2)+(e)^(x^(2)))"

proc (x) options operator, arrow; evalf(4*sqrt(x)/sqrt(Pi)+(8/3)*x^(3/2)/sqrt(Pi)+2*x+x^2+exp(x^2)) end proc

(7)

#Find أدومين بولي:

for k from 0 to n-1 do AP[k] := evalf(subs(lambda = 0, (diff(G(sum(y[t]*lambda^t, t = 0 .. k)), [`$`(lambda, k)]))/factorial(k))) end do

exp(y[0])

 

y[1]*exp(y[0])

 

y[2]*exp(y[0])+.5000000000*y[1]^2*exp(y[0])

 

y[3]*exp(y[0])+y[2]*y[1]*exp(y[0])+.1666666667*y[1]^3*exp(y[0])

 

y[4]*exp(y[0])+y[3]*y[1]*exp(y[0])+.5000000000*y[2]^2*exp(y[0])+.5000000000*y[2]*y[1]^2*exp(y[0])+0.4166666667e-1*y[1]^4*exp(y[0])

 

y[5]*exp(y[0])+y[4]*y[1]*exp(y[0])+y[3]*y[2]*exp(y[0])+.5000000000*y[3]*y[1]^2*exp(y[0])+.5000000000*y[2]^2*y[1]*exp(y[0])+.1666666667*y[2]*y[1]^3*exp(y[0])+0.8333333333e-2*y[1]^5*exp(y[0])

 

y[6]*exp(y[0])+y[5]*y[1]*exp(y[0])+y[4]*y[2]*exp(y[0])+.5000000000*y[4]*y[1]^2*exp(y[0])+.5000000000*y[3]^2*exp(y[0])+y[3]*y[2]*y[1]*exp(y[0])+.1666666667*y[3]*y[1]^3*exp(y[0])+.1666666667*y[2]^3*exp(y[0])+.2500000000*y[2]^2*y[1]^2*exp(y[0])+0.4166666667e-1*y[2]*y[1]^4*exp(y[0])+0.1388888889e-2*y[1]^6*exp(y[0])

 

y[7]*exp(y[0])+.5000000000*y[3]*y[2]*y[1]^2*exp(y[0])+.5000000000*y[5]*y[1]^2*exp(y[0])+y[5]*y[2]*exp(y[0])+y[6]*y[1]*exp(y[0])+y[4]*y[3]*exp(y[0])+.5000000000*y[3]^2*y[1]*exp(y[0])+.1666666667*y[2]^3*y[1]*exp(y[0])+0.1984126984e-3*y[1]^7*exp(y[0])+y[4]*y[2]*y[1]*exp(y[0])+0.8333333333e-2*y[2]*y[1]^5*exp(y[0])+0.8333333333e-1*y[2]^2*y[1]^3*exp(y[0])+0.4166666667e-1*y[3]*y[1]^4*exp(y[0])+.5000000000*y[3]*y[2]^2*exp(y[0])+.1666666667*y[4]*y[1]^3*exp(y[0])

(8)

NULL

#Find a ماتريسز b ^ (k) و C ^ (k): = A ^ (- 1) * b ^ (k)، ثم ايجاد حل تقريبي Y [k]: = سوم (C ^ (k) [i ] * L [i]، i = 1 .. n ):

# 1) البحث ب (0)

b0 := array(1 .. n, 1 .. m-7); for i to 2 do b0[i, 1] := 0 end do; for i from 3 to n do b0[i, 1] := evalf(subs(x = x[i], g(x[i]))) end do

print(`b0=`, b0)

`b0=`, b0

(9)

b0 := convert(b0, Matrix)

b0 := Matrix(8, 1, {(1, 1) = 0, (2, 1) = 0, (3, 1) = 5.533921684, (4, 1) = 10.78339161, (5, 1) = 69.22208674, (6, 1) = 96372.14332, (7, 1) = 0.5649990671e13, (8, 1) = 0.2063418920e32})

(10)

# 2) البحث عن ج (0)

C0 := LinearSolve(A, b0)

C0 := Matrix(8, 1, {(1, 1) = -0.11474558283495975e27, (2, 1) = -0.6041534517526968e26, (3, 1) = 0.28431046341368933e27, (4, 1) = -0.1109483456679843e28, (5, 1) = 0.2601411410469915e28, (6, 1) = -0.34736953613415415e28, (7, 1) = 0.23829217145639085e28, (8, 1) = -0.634449734180237e27}, datatype = float[8])

(11)

for i to n do k0[i] := C0[i, 1] end do

HFloat(-1.1474558283495975e26)

 

HFloat(-6.041534517526968e25)

 

HFloat(2.8431046341368933e26)

 

HFloat(-1.109483456679843e27)

 

HFloat(2.601411410469915e27)

 

HFloat(-3.4736953613415415e27)

 

HFloat(2.3829217145639085e27)

 

HFloat(-6.34449734180237e26)

(12)

# 3) البحث عن y (0)

y[0] := sum(k0[s]*L(s-1, 2*x-1), s = 1 .. 8)

-HFloat (5.083969685801073e25) -HFloat (1.4661238981264424e26) * س + HFloat (1.2387812172594187e26) * (2 * س 1) ^ 2-HFloat (1.9836944590452831e24) * (2 * س 1) ^ 3 HFloat (5.120751558697758 E25) * (2 * س 1) ^ 4 + HFloat (2.0830079097858884e25) * (2 * س 1) ^ 5 HFloat (2.8586478120802086e24) * (2 * س 1) ^ 6 + HFloat (1.2588288376592004e23) * (2 * س 1) ^ 7

(13)

# -------------------------

#Find b (1)

لا شيء

لا شيء

لا شيء

b1: = أري (1 .. n، 1 .. m-7)؛  ل i تو 2 دو b1 [i، 1]: = 0 إند دو؛  من i إلى n n b1 [i، 1]: = سوبس (x = x [i]، أب [0]) إند دو

برينت (`b1 =`، b1)

`b1 =`، b1

(14)

b1: = كونفيرت (b1، ماتريكس)

b1: = مصفوفة (8، 1، {(1، 1) = 0، (2، 1) = 0، (3، 1) = إكس (هفلوات (-1.3446720400287247e26))، (4، 1) = إكس هفلوت (-1.000132892371102e26))، (5، 1) = إكس (هفلوت (-1.7743764624635952e26))، (6، 1) = إكس (هفلوت (9.701444095568667e26))، (7، 1) = إكس 1.9741498268709318e28))، (8، 1) = إكس (هفلوات (4.2920269682087554e30))})

(15)

لا شيء

# 2) البحث ج (1)

لينيرزولف (A، b1)

المصفوفة ([هفلوات (هفلوات (وندفيند))]، [هفلوت (هفلوات (وندفيند))]، [هفلوات (هفلوات (وندفيند))]، [هفلوات (هفلوات (وندفيند))]، [هفلوات (هفلوات (وندفيند) )، [هفلوات (هفلوات (وندفيند))]، [هفلوات (هفلوات (وندفيند))]، [هفلوات (هفلوات (وندفيند))]])

(16)

لا شيء


 

تحميل jam.mw

Hi everybody,

I want to solve numerically an ode and I get this error (undocumented on the maplesoft web site https://www.maplesoft.com/support/help/errors/....)

Error, (in sol) maximum number of event iterations reached (100) at t=2.6610663

I understand where this error can come from but the help pages don't say anything to fix this.
There is some stuff about round-off that could help but I don't understand how to use it.

I would be grateful if you provide me some help.
Thanks in advance


Download ErrorWithDsolve.mw

 

 

Dear 

Hope everyone is fine. In attached file I solved system of equations. But the solution like this 

Sol[1]:={{...},{...}}

But I want the solution like

Sol[1]:={...}

Please see the attachment and fix my problem

Problem.mw

Dear

I am facing to eliminate diff(p(x, y), y, x) from Eq1 and Eq2. My procedure is given below:

Eq1 := 2*rho[nf]*a^2*x*(diff(f(eta), eta, eta))*(diff(f(eta), eta))/h+rho[nf]*sqrt(nu[f])*(diff(f(eta), eta))*a*x*(diff(f(eta), eta, eta))/h^2+rho[nf]*sqrt(nu[f])*f(eta)*a*x*(diff(f(eta), eta, eta, eta))/h^2+2*rho[nf]*omega[0]*a*x*(diff(g(eta), eta))/h = -(diff(p(x, y), y, x))+mu[nf]*a*x*(diff(f(eta), eta, eta, eta, eta))/h^3-sigma[nf]*B[0]^2*a*x*(diff(f(eta), eta, eta))/h;

Eq2 := 0 = -(diff(p(x, y), y, x));

eliminate({Eq1, Eq2}, diff(p(x, y), y, x));

Dear 

I want to graw following points (u[i,j], i=0..M,j=0..N) obtained in Sol[i] in 3D where i takes along x-axes, j y-axis and u along z axes. I also want the style of point plot as surface. Same do for v and w. I am waiting your response, Thanks

3D_plots.mw

Dear

I want to draw the graphs of the attached system of PDEs for different values of M in 3D please fix my problem. I am waiting your positive response.

graphs_for_pde.mw

Dearz 

I want to ask how to run multiple program at a time in maple? I am waiting your positive response. 

Dearz

I draw multiple graphs in singal coordinate with same line style. I don't know how to change the line style and color for g[1], g[2] and g[3] becuase of loop. Please some fix my problem to give them different style and color.

graph.mw

Dear all!

I am facing problem to find the solution of system of linear equations as attached for different values of alpha, please the see the attachment and fix my problem

Equations.mw

Thanks in advance

Anybody know how to compute coding for eigenvalues for basic reproduction number using the next generation matrix?

I dont know how to compute coding for eigenvalues. 

Coding_Basic_Reproduction_Number.mw

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