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These are replies submitted by tsunamiBTP


I renamed the file that I uploaded coeffs_of_homogen_soln_discrepancy'.mw instead of coeffs_of_homogen_soln_discrepancy.mw.  The prime symbol, ', for some reason did not allow the file to be uploaded.  Removing the prime symbol allowed me to upload the file.


Did you ever resolve this issue of uploading files?  I am having a problem with my WINDOWS 7 machine & running MAPLE 12.  I assume the version of MAPLE is irrelevant since I can put the .mw file on a flash drive & use another machine that does not have MAPLE installed.  The browser on this other machine is Chrome (Version 54.0.2840.99 m).  I then go to the MAPLEPrimes website & attempt to upload & still cannot get the file to upload

So what can I do?


I did all of your suggestions with NO success.  I successfully uploaded .mw files only weeks ago.  Now I cannot since the new website formatting.  Can someone address this?  I resorted to posting a link to a remote server for someone to access my .mw file.  I still cannot upload anything via the directions listed above.

Can this convolution operation be done symbollically with arbitrary constants for the elements of v1 & v2?  If so how?  See attached:


I determined what was incorrect in the previous MAPLE worksheet, but now I am encountering another FALSE return.  I have stared at this for hours & cannot understand the result I am now getting.

Can anyone CLUE me in?

Q[1] := (exp(-n*T*s)-exp(-(n+1)*T*s)+(-exp(-Z[1]*n*T)*(s-Z[1])*exp(-n*T*(s-Z[1]))+exp(-Z[2]*n*T)*(s-Z[2])*exp(-n*T*(s-Z[2])))/(Z[1]-Z[2])+2*exp(-n*T*s)*(-1+Heaviside(-n*T)))/c+Z[1]*Z[2]*exp(-n*T*(s-Z[1]))/((s-Z[1])*exp(Z[1]*n*T)*(Z[1]-Z[2])*c)-Z[2]*Z[1]*exp(-n*T*(s-Z[2]))/((s-Z[2])*exp(Z[2]*n*T)*(Z[1]-Z[2])*c); 1; Q[2] := ((s-Z[1])*exp(-n*T*(s-Z[1]))*exp(-Z[1]*n*T)/(Z[2]-Z[1])+exp(-n*T*s)*(-1+Heaviside(-n*T)))/c+Z[1]*Z[2]*exp(-n*T*(s-Z[1]))/((s-Z[1])*exp(Z[1]*n*T)*(Z[1]-Z[2])*c)+(exp(-Z[2]*n*T)*(s-Z[2])*exp(-n*T*(s-Z[2]))/(Z[1]-Z[2])+exp(-n*T*s)*(-1+Heaviside(-n*T)))/c-Z[2]*Z[1]*exp(-n*T*(s-Z[2]))/((s-Z[2])*exp(Z[2]*n*T)*(Z[1]-Z[2])*c)+(exp(-n*T*s)-exp(-(n+1)*T*s))/c



Q[1] = Q[2]"(->)"true

(-exp(-Z[1]*n*T)*(s-Z[1])*exp(-n*T*(s-Z[1]))+exp(-Z[2]*n*T)*(s-Z[2])*exp(-n*T*(s-Z[2])))/((Z[1]-Z[2])*c)+2*exp(-n*T*s)*(-1+Heaviside(-n*T))/c+Z[1]*Z[2]*exp(-n*T*(s-Z[1]))/((s-Z[1])*exp(Z[1]*n*T)*(Z[1]-Z[2])*c)-Z[2]*Z[1]*exp(-n*T*(s-Z[2]))/((s-Z[2])*exp(Z[2]*n*T)*(Z[1]-Z[2])*c)+(1-exp(-T*s))*exp(-n*T*s)/c = (-exp(-Z[1]*n*T)*(s-Z[1])*exp(-n*T*(s-Z[1]))+exp(-Z[2]*n*T)*(s-Z[2])*exp(-n*T*(s-Z[2])))/((Z[1]-Z[2])*c)+2*exp(-n*T*s)*(-1+Heaviside(-n*T))/c+Z[1]*Z[2]*exp(-n*T*s)/((s-Z[1])*(Z[1]-Z[2])*c)-Z[2]*Z[1]*exp(-n*T*s)/((s-Z[2])*(Z[1]-Z[2])*c)+(1-exp(-T*s))*exp(-n*T*s)/c

Q[2] = (-exp(-Z[1]*n*T)*(s-Z[1])*exp(-n*T*(s-Z[1]))+exp(-Z[2]*n*T)*(s-Z[2])*exp(-n*T*(s-Z[2])))/((Z[1]-Z[2])*c)+2*exp(-n*T*s)*(-1+Heaviside(-n*T))/c+Z[1]*Z[2]*exp(-n*T*s)/((s-Z[1])*(Z[1]-Z[2])*c)-Z[2]*Z[1]*exp(-n*T*s)/((s-Z[2])*(Z[1]-Z[2])*c)+(1-exp(-T*s))*exp(-n*T*s)/c


Download inexplicable.mw


Apparently I did not recognize all of the exponential terms were entered correctly so that MAPLE would correctly recognize those terms.

I do not know, but maybe I need to chalk it up to fatigue.  I am getting something of use now.

I do not know, but maybe I need to chalk it up to fatigue.  I am getting something of use now.

I derived this polynomial in an attempt to resolve modal dynamics of a physical system.  My guess someone has done this before & can refer me to some literature that can expand my knowledge on the subject.

I am attempting to resolve both magnitude & phase of complex #'s generated via the Fourier transform of my data set.



Not sure why my browser is screwing up the images?

This document is an evolution of the MAPLE docs "resolving the fundamental oscillator.mw" & "quadric form & conic sections.mw".  In the 1st document resolution of the modal paramenters, M, beta, & Omega are accomplished via analysis of 2 adjacent complex #'s @ 2 test freq's, omega[1]& omega[2].  The process was successful, but took a number of iterations resolve the parameters.  During that process it became apparent that a more direct approach utilizing 3 adjacent data points instead of 2 probably would yield better results & do it more efficiently in terms of computation power.

For a complex # Z[n] = A[n]+I*B[n]:

M[1] := sqrt(A[1]^2+B[1]^2); M[2] := sqrt(A[2]^2+B[2]^2); M[3] := sqrt(A[3]^2+B[3]^2); Phi[1] := exp(I*phi[1]); Phi[2] := exp(I*phi[2]); Phi[3] := exp(I*phi[3]); R := M[2]*Phi[2]/(M[1]*Phi[1]*M[3]*Phi[3])



R^2 = (A[2]^2+B[2]^2)*exp((I*2)*(phi[2]-phi[1]-phi[3]))/((A[1]^2+B[1]^2)*(A[3]^2+B[3]^2))(->)true(->)true

phi[1] := arctan(B[1]/A[1]); K[1] := tan(phi[1]); phi[2] := arctan(B[2]/A[2]); K[2] := tan(phi[2]); phi[3] := arctan(B[3]/A[3]); K[3] := tan(phi[3]); K[2]-K[1]-K[3]




x := B[1]/A[1]; y := B[2]/A[2]; z := B[3]/A[3]; kappa := y-x-z; chi := (A[2]^2+B[2]^2)/((A[1]^2+B[1]^2)*(A[3]^2+B[3]^2))



exp((I*2)*(phi[2]-phi[1]-phi[3])) = exp((2*I)*(arctan(y)-arctan(x)-arctan(z)))(->)true

chi = (1+y^2)*A[2]^2/(A[1]^2*A[3]^2*(1+x^2)*(1+z^2))(->)true

A[1]^2*A[3]^2*chi/A[2]^2 = (1+y^2)/((1+x^2)*(1+z^2))(->)true

A[1]^2*A[3]^2*chi/A[2]^2 = (1+y^2)/((1+x^2)*(1+(y-x-kappa)^2))(->)true

The function higlighted in yellow is the ratio of the magnitudes of 3 adjacent complex #'s @ freq's, omega[1], omega[2], & omega[3].  If the data point for omega[2] is a peak & the other 2 are lower in magnitude then the function in yellow should be maximized relative to x, y, & z while the parameters χ & κ are obtained from the magnitude & phase info from the data.  A[1]^(2), A[2]^(2), & A[3]^(2) are the Re components of the Fourier transform of the 3 data points.

M = (1+y^2)/((1+x^2)*(1+z^2))(->)(1+z^2)*(x^2+1)*M-1 = y^2

NOTE the parameters x, y, & z can be interchanged by simply reassigning their definitions.  Let z represent z^2:

z := M*(1+x^2)*(1+y^2)-1



plots[animate]('plots[implicitplot3d]', [z = R, x = -2 .. 2, y = -2 .. 2, M = -2 .. 2, style = PATCHCONTOUR, glossiness = 1.0, axes = frame, scaling = constrained, grid = [25, 25, 25], labels = [x, z, y]], R = -5 .. 5)



plots[animate]('plots[implicitplot3d]', [sqrt(z) = R, x = -2 .. 2, y = -2 .. 2, M = -2 .. 2, style = PATCHCONTOUR, glossiness = 1.0, axes = frame, scaling = constrained, grid = [25, 25, 25], labels = [x, z, y]], R = 0 .. 5)



Recasting the equation such that:

z^2 = M*(1+x^2)*(1+y^2)-1(->)M/(z^2+1) = 1/((1+x^2)*(1+y^2))

The left side of the equation will come from the data & can be any Re value:

plots[implicitplot3d](1/((1+x^2)*(1+y^2)) = R, x = -2 .. 2, y = -2 .. 2, R = -2 .. 2, style = PATCHCONTOUR, glossiness = 1.0, shading = Z, axes = frame, scaling = constrained, grid = [25, 25, 25], labels = [x, y, R])



plots[animate]('plots[implicitplot]', [1/((1+x^2)*(1+y^2)) = R, y = -5 .. 5, x = -5 .. 5, scaling = constrained, grid = [100, 100], labels = [y, x]], R = 0 .. 1)




Download scratchpad.mw

I tested this relation several times & MAPLE conflicts itself on multiple occasions.  My guess when +- is encountered by MAPLE it attempts to translate the problem into a complex # & depending on the order of interpretation it might give I^2 vs I^4?  This is a guess on my part, but I have no definitive confirmation.

`&+-`(2*sqrt(tan(FAZE)^2)) = `&+-`(sqrt(4*tan(FAZE)^2))(->)true

`&+-`(2)*sqrt(tan(FAZE)^2) = `&+-`(sqrt(4*tan(FAZE)^2))(->)false``


Download quadratic_formula_fa.mw

See below, the terms in RED are presumably identical & MAPLE seems to indicate this, but the 3rd line cannot confirm this?  What is MAPLE not recognizing?

sum(exp(-I*omega*n*T)/(I*omega)-exp(-I*omega*n*T)*(1/(I*omega-I*omega[i]*sqrt(1-beta^2)+omega[i]*alpha)+1/(I*omega+I*omega[i]*sqrt(1-beta^2)+omega[i]*alpha))/(2*sqrt(1-beta^2))-exp(-I*omega*(n+1)*T)/(I*omega), n = 0 .. m) = sum((1/(I*omega)-(I*omega+omega[i]*alpha)*(omega[i]^2*(1-beta^2+alpha^2)-omega^2-(2*I)*omega*omega[i]*alpha)/(sqrt(1-beta^2)*((omega[i]^2*(1-beta^2+alpha^2)-omega^2)^2+(2*omega*omega[i]*alpha)^2)))*exp(-I*omega*n*T)-exp(-I*omega*(n+1)*T)/(I*omega), n = 0 .. m)

sum(-exp(-I*omega*(n+1)*T)/(I*omega), n = 0 .. m) = sum(-exp(-I*omega*n*T)*exp(-I*omega*T)/(I*omega), n = 0 .. m)(->)true(->)true

sum(exp(-I*omega*n*T)/(I*omega)-exp(-I*omega*n*T)*(1/(I*omega-I*omega[i]*sqrt(1-beta^2)+omega[i]*alpha)+1/(I*omega+I*omega[i]*sqrt(1-beta^2)+omega[i]*alpha))/(2*sqrt(1-beta^2))-exp(-I*omega*(n+1)*T)/(I*omega), n = 0 .. m) = sum((1/(I*omega)-(I*omega+omega[i]*alpha)*(omega[i]^2*(1-beta^2+alpha^2)-omega^2-(2*I)*omega*omega[i]*alpha)/(sqrt(1-beta^2)*((omega[i]^2*(1-beta^2+alpha^2)-omega^2)^2+(2*omega*omega[i]*alpha)^2)))*exp(-I*omega*n*T)-exp(-I*omega*n*T)*exp(-I*omega*T)/(I*omega), n = 0 .. m)

Download puzzling.mw


In symbolic equation mode it is difficult to realize which terms fall within the juridiction of the summation series.  Editing in TEXT mode it is apparent that not all of the terms are being summed from 0 to m.

If I still continue to experience contradictions on this issue I will post further replies, but it appears I found the problem.


Robert thanks, I am just getting back to this problem & I think what you replied might help

Robert thanks, I am just getting back to this problem & I think what you replied might help

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