Carl Love

Carl Love

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11 years, 190 days
Wayland, Massachusetts, United States
My name was formerly Carl Devore.

MaplePrimes Activity

These are replies submitted by Carl Love

@eithne I have the correct Build ID. Nonetheless it confusied me because it's dated Nov 24, 2023. I see now that's a later date than the announcement of Maple 2023.2, but that was not obvious at first.

@nm I think this is what happened: I installed my Maple (on a brand new computer) yesterday at about 1:30 PM (EST). As usual, I had it check for updates during the install. The Post at the head of this thread was made at 2:06 PM (EST), after I installed. But I guess the update was already available some short time before the Post, so I got it with my install.

Yes, this whole confusion could be avoided if Maple just said the complete version number.

@nm I tried the menu option Tools => Check for Update, but it said that I already had the latest version.

@mmcdara It's easy to make this mistake given the Question's title. I made it myself,.but I noticed it while posting my tentative Answer. The OP wants to know the values of beta and f for which there are three (or more?) extrema. I don't know what "consecutive" means in this context.

I downloaded the update, and tried to install it, but it refused, saying "You've already upgraded to Maple 2023.2".

This isn't your fault, but MaplePrimes doesn't correctly upload ".maple" workbooks. Would you please put the files together in a ".zip" file and upload that? Let me know if you don't know what a ".zip" file is (or a websearch will tell you and lead you to a free utility for making them).

Please put any followups to this Question in this thread. Below, I've copied your new Question here, and I'll delete the new Question itself. OP's writing from here on:

I am an ophthalmologist and a novice in programing. I am having a problem obtaining the x-y coordinate equations for each of the fitted Splines in Maple.  Attached is the raw data and the Maple Data2_12_5_2023.xlsx Spline_Fits_12_5_2023.maple worksheet for which I need the individual spline equations and to learn how to obtain them.  I will pay you for the service. Can you please obtain the x-y Cartesian equations , not parametric, for each of the fitted Splines, give me a step-wise method for obtaining them and how to plot the Spline fits on the raw data plot?  

Your assistance is most appreciated.


Ronald A Schachar, MD, PhD

Cell: (858) 784-1705


@delvin The Jacobi functions require two arguments. Your math-paper transcription shows the 2nd argument as a fancy-script L, which I've duplicated below. Also, the parameter of Xi is phi, not psi or Psi.


    12*Psi^3*rho__3^2*D[1,1](w)(phi) +
    (4*omega*rho__3^2 - 3*rho__2^2*Psi)*w(phi) +
    Psi*rho__3^2*(rho__1 + 2*rho__3)*w(phi)^3


w:= phi-> kappa__0 + kappa__1*(D(Xi)/Xi)(phi) + h__1*(Xi/D(Xi))(phi);

proc (phi) options operator, arrow; kappa__0+kappa__1*(D(Xi)/Xi)(phi)+h__1*(Xi/D(Xi))(phi) end proc

Xi:= subs(
    L= `ℓ`,  #just an alternate typescript abbreviation for script "L"
        (varepsilon__1*JacobiCN(zeta__1*phi, L) + varepsilon__2*JacobiSN(zeta__2*phi, L))
        / (varepsilon__3*JacobiCN(zeta__3*phi, L) + varepsilon__4*JacobiSN(zeta__4*phi, L))

proc (phi) options operator, arrow; (varepsilon__1*JacobiCN(zeta__1*phi, `ℓ`)+varepsilon__2*JacobiSN(zeta__2*phi, `ℓ`))/(varepsilon__3*JacobiCN(zeta__3*phi, `ℓ`)+varepsilon__4*JacobiSN(zeta__4*phi, `ℓ`)) end proc

#Use preset values for h__1, kappa__0, varepsilon__2, varepsilon__4, zeta__1, and Psi.
Eq21a:= eval(  
        (h__1, kappa__0, varepsilon__2, varepsilon__4, zeta__1) =~ 0,
        Psi= kappa__1/12*sqrt(-6*rho__1 - 12*rho__3)

simplify(solve({Eq21a}, {omega}));

{omega = -(1/24)*kappa__1*(-6*rho__1-12*rho__3)^(1/2)*(zeta__3^2*rho__3^2*(rho__1+2*rho__3)*(`ℓ`^2-1/2)*kappa__1^2-(3/2)*rho__2^2)/rho__3^2}




This is an open-ended question; I don't have a definite opinion about it: Is something as crude as the empirical rule worth studying to the extent implied by the above Post when one has Maple, which has much more sophisticated functions for assessing whether data come from a Normal distribution?

That being said, I think that everyone should learn and memorize the central probabilities for 1, 2, and 3 standard deviations. That can help in everyday life or help one to understand nearly any research that uses statistics.

@delvin What do you mean by "fixed"? You simply typed a - where you should've typed =. That's all there is to it.

Regarding tanh: You can simply enter tanh(a+b) and tanh(a-b). Maple knows these functions, and you don't need to provide any further definition.

@delvin This is your input for pde2 from your attached worksheet:

pde2:= beta[3]*beta[4]*diff(U(xi), xi, xi) - (beta[4]*diff(U(xi),xi))*(u(xi[n - 1])-2*U(xi)+u(xi[n + 1]));

If you want that to be equivalent to the displayed equation at the top of your worksheet, then change the central (minus sign) to = (equals sign).

Regarding tanh, are you asking because you think that perhaps Maple's definition is different from what you expect? If so, what do you expect?

@aimLow The fact that your error messages are accompanied by your input in a red-dashed rectangle indicates that those two lines have a syntax error specific to 2-D Input. In such cases, Maple cannot translate the input into equivalent 1-D Maple-code input. The error is not related to your use of sum. If you tell me what output you expect from each command, I might be able to help further.

@Kitonum Maple understands indefinite sums, and they can't be adequately replaced with add, for example:

sum(i^2, i);
            1/3*i^3 - 1/2*i^2 + 1/6*i                     


@sursumCorda If you tell me for your most-recent case what you expect the quotients to be, I may be able to adjust my program. What does Mathematica return? The package Groebner might have something that helps.

The direct problem is that regardless of the elimination order used, the 2nd remainder has a denominator containing the 3rd variable.

As I said, my knowledge of this area of math is limited. It may be that this problem cannot be solved by using quo and rem as the only algebraic operations. It may require Groebner or something similar.

What does the operator symbol N (in "blackboard bold") in paragraph 1 mean? 

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