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why area2 has rootof?...

Asked by: LeeHoYeung 535
polynomial codegeneration curvefitting
September 03 2016
0  1

updated:

with(CurveFitting);
f := PolynomialInterpolation([[0, x0],[1, x1],[2, x2],[3, x3],[4, x4]], x);
f2 := solve(f=y,x);
area1 := int(f, x=0..1);
with(student):
area2 := trapezoid(f2[1], x = 0..1);
with(CurveFitting);
f := PolynomialInterpolation([[0, x0],[1, x1],[2, x2],[3, x3]], x);
f2 := solve(f=y,x);
area1 := int(f, x=0..1);
with(student):
area2 := trapezoid(f2[1], x = 0..1);

 

i use 5 points trapezoid got RootOf  in result,

only 4 points is acceptable

 

when i try 5 points, there is no problem, but when more points such as

30 points, got RootOf for c sharp code

 

moreover, i got a problem when i copy the area1 result into 

visual studio c# code, it has error Integral Constant is too large

 

with(CurveFitting);
f := PolynomialInterpolation([[0, x0],[1, x1],[2, x2],[3, x3],[4, x4],[5, x5],[6, x6],[7, x7],[8, x8],[9, x9],[10, x10],[11, x11],[12, x12],[13, x13],[14, x14],[15, x15],[16, x16],[17, x17],[18, x18],[19, x19],[20, x20],[21, x21],[22, x22],[23, x23],[24, x24],[25, x25],[26, x26],[27, x27],[28, x28],[29, x29]], x);
f2 := solve(f=y,x);
area1 := int(f, y=0..1);
with(student):
area2 := trapezoid(f2[1], x = 0..1);
with(CodeGeneration):
CSharp(area1, resultname = "area1");
CSharp(area2, resultname = "area2");

i find area2 has

Warning, the function names {RootOf, Sum} are not recognized in the target language
Warning, precedence for Range unspecified
Warning, cannot translate range
area2 = RootOf((System.Double) (19276689540529530246975515949293568 * x3 - 2626509155780373903082144116707328 * x2 + 239680950855919251544490932629504 * x1 -

solving homogeneous algebraic equations for non-tr...

Asked by: sunit 105
solve
September 03 2016
0  3

Hi,

I am trying to solve a set of homogeneous equations for the non-trivial solutions. Mathematically it is possible to get it. But is there any way to get it in Maple. Please find the attached maple sheet for the question. Please help me regarding this.

Regards

Sunit

> 

restart
> 

with(plots):
> 

with(LinearAlgebra):
> 

eq[1] := diff(x[1](t), t)-x[2](t)

diff(x[1](t), t)-x[2](t)

 (1)
> 

eq[2] := diff(x[2](t), t)+2*zeta*beta*x[2](t)+beta^2*x[1](t)+n*psi*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

diff(x[2](t), t)+2*zeta*beta*x[2](t)+beta^2*x[1](t)+n*psi*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

 (2)
> 

eq[3] := diff(phi[1](t), t)-phi[2](t)

diff(phi[1](t), t)-phi[2](t)

 (3)
> 

eq[4] := diff(phi[2](t), t)+2*kappa*phi[2](t)+phi[1](t)+n*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

diff(phi[2](t), t)+2*kappa*phi[2](t)+phi[1](t)+n*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

 (4)
> 

for k to 4 do eqn[k] := simplify(coeff(map(expand, eval(eq[k], [x[1] = (proc (t) options operator, arrow; x[1]*exp(lambda*t) end proc), x[2] = (proc (t) options operator, arrow; x[2]*exp(lambda*t) end proc), phi[1] = (proc (t) options operator, arrow; phi[1]*exp(lambda*t) end proc), phi[2] = (proc (t) options operator, arrow; phi[2]*exp(lambda*t) end proc)])), exp(lambda*t))) end do

x[1]*lambda-x[2]

  

x[2]*lambda+2*zeta*beta*x[2]+beta^2*x[1]-n*psi*v*phi[1]+n*psi*v*phi[1]*exp(-2*lambda*Pi/(n*omega0))+n*psi*x[1]-n*psi*x[1]*exp(-2*lambda*Pi/(n*omega0))

  

phi[1]*lambda-phi[2]

  

phi[2]*lambda+2*kappa*phi[2]+phi[1]-n*v*phi[1]+n*v*phi[1]*exp(-2*lambda*Pi/(n*omega0))+n*x[1]-n*x[1]*exp(-2*lambda*Pi/(n*omega0))

 (5)
> 

A, b := GenerateMatrix([seq(eqn[k], k = 1 .. 4)], [x[1], x[2], phi[1], phi[2]])

A, b := Matrix(4, 4, {(1, 1) = lambda, (1, 2) = -1, (1, 3) = 0, (1, 4) = 0, (2, 1) = beta^2+n*psi-n*psi*exp(-2*lambda*Pi/(n*omega0)), (2, 2) = 2*Zeta*beta+lambda, (2, 3) = n*psi*v*exp(-2*lambda*Pi/(n*omega0))-n*psi*v, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = lambda, (3, 4) = -1, (4, 1) = n-n*exp(-2*lambda*Pi/(n*omega0)), (4, 2) = 0, (4, 3) = -n*v+1+n*v*exp(-2*lambda*Pi/(n*omega0)), (4, 4) = 2*kappa+lambda}), Vector(4, {(1) = 0, (2) = 0, (3) = 0, (4) = 0})

 (6)
> 

> 

right_vector := Matrix(4, 1, [r[1], r[2], r[3], r[4]])

right_vector := Matrix(4, 1, {(1, 1) = r[1], (2, 1) = r[2], (3, 1) = r[3], (4, 1) = r[4]})

 (7)
> 

junk := MatrixVectorMultiply(subs(lambda = I*omega, A), right_vector)

junk := Matrix(4, 1, {(1, 1) = I*omega*r[1]-r[2], (2, 1) = (beta^2+n*psi-n*psi*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(2*Zeta*beta+I*omega)*r[2]+(n*psi*v*exp(-(2*I)*omega*Pi/(n*omega0))-n*psi*v)*r[3], (3, 1) = I*omega*r[3]-r[4], (4, 1) = (n-n*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(-n*v+1+n*v*exp(-(2*I)*omega*Pi/(n*omega0)))*r[3]+(2*kappa+I*omega)*r[4]})

 (8)
> 

junk(1)

I*omega*r[1]-r[2]

 (9)
> 

for k to 4 do eqnn[k] := junk(k) end do

I*omega*r[1]-r[2]

  

(beta^2+n*psi-n*psi*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(2*zeta*beta+I*omega)*r[2]+(n*psi*v*exp(-(2*I)*omega*Pi/(n*omega0))-n*psi*v)*r[3]

  

I*omega*r[3]-r[4]

  

(n-n*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(1-n*v+n*v*exp(-(2*I)*omega*Pi/(n*omega0)))*r[3]+(2*kappa+I*omega)*r[4]

 (10)
> 

solve({seq(eqnn[k], k = 1 .. 4)}, {seq(r[k], k = 1 .. 4)})

{r[1] = 0, r[2] = 0, r[3] = 0, r[4] = 0}

 (11)
> 

``
> 

``
> 

``

 

Download question4.mw

Adomian Decomposition Method...

Asked by: noah2gud 25
solve ode syntax
September 02 2016
0  0

pls help review this code, its doesnt return a solution

 

 

restart;
Digits := 16;
M := .5; lambda := .5; Pr := .72; beta := 1; L[w] := 0; m := 1; R := 1; Ec := 1;
N := 7;
for j from 0 to N do J[j] := sum(f[k](t)*(diff(f[j-k](t), `$`(t, 2))), k = 0 .. j) end do;
for i from 0 to N do K[i] := sum((diff(f[k](t), t))*(diff(f[i-k](t), t)), k = 0 .. i) end do;
for j from 0 to N do G[j] := sum(f[k](t)*(diff(theta[j-k](t), t)), k = 0 .. j) end do;
for j from 0 to N do H[j] := sum((diff(f[k](t), t))*theta[j-k](t), k = 0 .. j) end do;
for i from 0 to N do P[i] := sum((diff(f[k](t), t, t))*(diff(f[i-k](t), t)), k = 0 .. i) end do;
epsilon := 1; delta := 0;
f[0] := proc (t) options operator, arrow; L[w]+epsilon+delta*A*t+(1/2)*A*t^2 end proc;
1 2
t -> L[w] + epsilon + delta A t + - A t
2
theta[0] := proc (t) options operator, arrow; 1+B*t end proc;
t -> 1 + B t
NULL;
;
NULL;
NULL;
NULL;
NULL;
for i to N do f[i] := simplify(-((m+1)*(1/2))*(int(int(int(J[i-1], t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))+m*(int(int(int(1-K[i-1], t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))-M*(int(int(int(diff(f[i-1](t), t)-1, t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))-lambda*(int(int(int(theta[i-1](t), t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))); f[i] := unapply(f[i], eta); theta[i] := simplify(-3*Pr*R*(((m+1)*(1/2))*(int(int(G[i-1], t = 0 .. eta), t = 0 .. eta))-(2*m-1)*(int(int(H[i-1], t = 0 .. eta), t = 0 .. eta))+Ec*(int(int(P[i-1], t = 0 .. eta), t = 0 .. eta)))/(4+3*R)); theta[i] := unapply(theta[i], eta) end do;
NULL;
F(eta):=collect((∑)f[z](eta),eta):
Theta(eta):=collect((∑)theta[z](eta),eta):
with(numapprox);
for k from 2 to 5 do W[k] := pade(diff(F(eta), eta), eta, [k, k]); Q[k] := pade(Theta(eta), eta, [k, k]); SOLL1[k] := expand(coeff(numer(W[k]), eta^k)) = 1; SOLL2[k] := expand(coeff(numer(Q[k]), eta^k)) = 0; SOL[k] := solve({SOLL1[k], SOLL2[k]}, {A, B}); print([k] = SOL[k]) end do;
Warning, computation interrupted

 

 

 

 

 

 

im just getting a generic recursive assignment plu...

Asked by: Adam Ledger 360
September 01 2016
0  2

im just getting a generic recursive assignment plus first unused arg error

thats what the maple engine says im doing wrong ill get the number of recursives counted but i guess it just makes me the most angry because its like the same type of error for me every ******* time

Navier-Stokes hand calculations...

Asked by: Samuel Hollis 100
fluid-dynamics
August 31 2016
0  1

Hi all,

I was wondering how to go about validating some airfoil designs for my Formula SAE team's CFD results.  I know this is more common with simplier calculations but I'm hoping using Maple and maybe the new algebraic manipulation of non-comunitive differential operators, I could achive what I am after.   The two calculations of interest are the drag force and downforce.  Can someone shed some light? Thanks

Workbook issues...

Asked by: erik10 786
assign matrix
August 29 2016
2  7

Dear Maple users

I have done some experiments with the new Workbook feature in Maple 2016. It is a very welcome addition, indeed. Earlier I have created Maple files in which data from an external Excel file was imported and being used for certain calculations. In order to make recalculations work properly, one need to let the Excel file follow the Maple file. That's where a Workbook come in handy! I tried placing those two files in a Workbook. It didn't work completely as advertised, I think. I moved the Workbook to another location on the harddrive to make sure it wouldn't interfere with the original files outside the Workbook. Then I recalculated the Maple document inside the Workbook. The good thing: The data from the Excel file was still present. The bad thing: If I changed some data in the Excel file inside the Workbook, it didn't register in the Maple file when updating it!

Maybe I should explain that I did import data from the Excel file into Maple via the menu: Tools > Assistants > Import Data... The data was retrieved as a matrix within the Maple file and assigned to a variable and used for plots ...

Why doesn't the above procedure work properly? I hope one don't need to use the Workbook URI to reference files within the workbook. It is not that userfriendly!

 

Regards,

Erik

To find a variable with subscript...

Asked by: taro 505
subscript
August 29 2016
1  8

Hello people in mapleprimes,

I think that I found a bug.

Using the screen opened with command + f, I tried to find a v__1211 in the file I appended here.

But, when the cursor is trapped on an output part, which is a blue part, maple wouldn't continue to find the next

v__1211 anymore even if I clicked the Find Next on the screen.

If I move the cursol one line below with a hand, the Find Next butttons works again, but it is intricate.

Isn't there any good way to avoid this trouble other than not using double _, that is __.?

I hope you will give me some hint.

taro

v_1211.mw

P.S. I clicked the above link and opened that file with maple. Then, the notification telling that this is read-only file and

you cannot save this file after some modification, appeared. I don't know whether there is any problem. 

Does appending a maple file on a post on this mapleprimes always done in such a way? 

Maple gets stuck...

Asked by: John Fredsted 2253
August 29 2016
0  9

The keyboard shortcut sequence for executing an entire worksheet is Alt+e+e+w. Occasionally, I hit Alt+e+w+w by accidence. In that case, Maple sometimes, not always!?, gets completely stuck and can only be shut down through the job list window (Windows Ctrl+Alt+Del). Can anybody else replicate that? And if so, has this erratically odd behaviour been fixed in later versions of Maple?

need to procedure for calculating......

Asked by: torabi 90
linear-algebra coeff determinant
August 25 2016
0  0

hi....how i can extract Coefficients  (i.e. {f1[2],f2[2],f2[3],f3[2],.....f3[6]}) from every algebric equations and create matrix A ,in form AX=0, (X are f1[2],f2[2],f2[3],f3[2],.....f3[6] ) then the determinant of the matrix of coefficients (A) set to zero for obtaining unknown parameter omega.?

Note that  if m=3 then 6 equations is appeare and if m=4 then 9 equations is appeare.thus i need a procedure that works for every arbitary value of ''m''.

in attached file below m=4 thus we have 9 equations, i.e. 3 for eq1[k_] and 3 for eq2[k_] and so on...

also we should use boundary conditions for some amount of fi[j] (i=1,2,3 and j=2,3,...,7)

be extacting above Coefficients for example from first equation ,

''**:= (1/128)*f1[2]*omega^2-(1/4)*f2[2]-(1/2)*f2[3]+(1/4)*f2[4]+(1/4)*f3[2]-(1/2)*f3[3]+(1/4)*f3[4]+140*f1[2]-80*f1[3]+20*f1[4]'''

must compute

coeff(**, f1[2]); coeff(**, f2[2]) and so on...

 

 

 

 

 

fdm-maple.mw

 

 ############################Define some parameters

 

 
restart; Digits := 15; A1 := 10; A2 := 10; A3 := 10; A4 := 1; A5 := 1; A6 := 1; A7 := 1; A8 := 1; A9 := 1; A10 := 1; A11 := 1; B1 := 10; B2 := 10; B3 := 10; B4 := 1; B5 := 1; B6 := 1; B7 := 1; B8 := 1; B9 := 1; B10 := 1; B11 := 1; C1 := 10; C2 := 10; C3 := 10; C4 := 1; C5 := 1; C6 := 1; C7 := 1; C8 := 1; C9 := 1; C10 := 1; C11 := 1; C12 := 1; C13 := 1; C14 := 1; C15 := 1; C16 := 1; A12 := 1; B12 := 1; C18 := 1; C17 := 1; C19 := 1; n := 1; U := proc (x, theta) options operator, arrow; f1(x)*cos(n*theta) end proc; V := proc (x, theta) options operator, arrow; f2(x)*sin(n*theta) end proc; W := proc (x, theta) options operator, arrow; f3(x)*cos(n*theta) end proc; n := 1; m := 4; len := 1; h := len/m; nn := m+1
 ############################Define some equation

eq1[k_] := -2*f1[k]*(-A11*n^4+A10*n^2+A12*omega^2)*h^4+(A6*(f2[k-1]-f2[k+1])*n^3+A9*(f3[k-1]-f3[k+1])*n^2-A5*(f2[k-1]-f2[k+1])*n-A8*(f3[k-1]-f3[k+1]))*h^3+(4*(f1[k]-(1/2)*f1[k-1]-(1/2)*f1[k+1]))*(A3*n^2-A2)*h^2+(-A4*(f2[k-2]-2*f2[k-1]+2*f2[k+1]-f2[k+2])*n-A7*(f3[k-2]-2*f3[k-1]+2*f3[k+1]-f3[k+2]))*h+12*A1*(f1[k]+(1/6)*f1[k-2]-(2/3)*f1[k-1]-(2/3)*f1[k+1]+(1/6)*f1[k+2]):
  ``

 

 

 

 

                                     ######################################  APPLY BOUNDARY CONDITIONS

f1[nn+1] := f1[m]:
 

for k from 2 to m do eq1[k_]; eq2[k_]; eq3[k_] end do

-(1/64)*f2[4]+(1/128)*f2[3]+(1/64)*(f3[4]-(1/2)*f3[3])*(omega^2-1)-(1/64)*f1[2]+(1/32)*f1[3]+(1/64)*f1[4]-280*f3[4]-120*f3[2]+300*f3[3]+20*f3[7]

 (1)

``



Download fdm-maple.mw

 

How can I install Maple on another pc?...

Asked by: laura_patierno 20
August 25 2016
3  2

Good morning, I'm a student and I installed Maple 18 on my PC, as a "Single User Profile". Unfortunately, I had to buy another computer, so now I'm trying to install the program on my new one. Even if I enter my Purchase Code and my details, Maple says that no more activations are left in my account, even if the expiration date is on March 2020. Is it possible to activate again the program? 

Thank you,

Laura

Achieve iterative relationship...

Asked by: lijiwei 25
pde iteration
August 24 2016
0  2

Please help me.I don't know how to achieve the following iteration relation by maple code.iterative relationship

 

 

Where is the help text for this environment variab...

Asked by: Earl 985
dsolve numeric warning
August 23 2016
1  0

In a Maple Primes reply by Joel Riel on Sept. 14, 2011 he included the following command referring to warnings issued from a dsolve, numeric command having events containing a halt action:

_Env_in_maplet := true:  # incantation to suppress integrator warnings

Where can if find explanatory help for his command and any others of a similar nature?

how to use genus function without knowing genus?...

Asked by: LeeHoYeung 535
August 23 2016
0  0

m that i guess is genus,

but if i do not know genus number, how can i calculate with genus function

genus(y^m-(x...., x, y);

when i change m only the genus number is also changing

is my function wrong?

can i use this as a verification?

if m i set is 3 and then genus(...) result is 3

if result is equal to input 3, then it is correct function?

is hilbert series only for genus 0?...

Asked by: LeeHoYeung 535
hilbertseries
August 23 2016
0  0

is hilbert series only for genus 0 only?

i got error

Error, (in Groebner:-Basis) the generators are not polynomials with respect to, {a, b, c, d}

animation plot of two GIFs...

Asked by: mehdi jafari 774
animation
August 22 2016
0  2

how can i do this GIFs with maple ?

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