MaplePrimes Posts

MaplePrimes Posts are for sharing your experiences, techniques and opinions about Maple, MapleSim and related products, as well as general interests in math and computing.

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  • Hi,

    look at this Maple code.

    short_list_prime_factorization_fun.mw

    short_list_prime_factorization_fun.pdf

    Have a good day

    Matthew

    Hi,

    check out this maple code

    positive_odd_integer_factorization_data.pdf

    positive_odd_integer_factorization_data.mw

    that is all

    Regards,

    Matthew

    Hi,

    have some Maple code to share.

    prime_triplet_0_4_6.mw

    prime_triplet_0_4_6.pdf

    Enjoy

    Matthew

    ps Prime numbers are fun

    see https://t5k.org/

     

    We are a week away from the submission deadline for the Maple Conference!  
    Presentation proposal applications are due July 25, 2025.

    We are inviting submissions of presentation proposals on a range of topics related to Maple, including Maple in education, algorithms and software, and applications. We also encourage submission of proposals related to Maple Learn. You can find more information about the themes of the conference and how to submit a presentation proposal at the Call for Participation page.

    We hope to see there.

    Hi,

    Don't laugh.

    Some of you are not familair with Wagstaff Prime Numbers

    see Wolfram Math World

    also, this Maple code is esentially, a loop and the isprime() function

    for your edification

    b

    have a look

    just wanted to contribute my two cents to the Maple community

    good day

    Thank you for your patience and understanding during the recent outage of MaplePrimes. The outage was caused by a server issue. We have obtained and configured a replacement to prevent disruptions moving forward. We are sorry for any inconvenience this may have caused.

    Back in 2017, when the concept of Maple Flow was first proposed at Maplesoft, we developed an aspirational brochure to ignite our creative energy. I still have a printed few copies – here’s one that’s sat behind my monitor.

    At that time, the product that did not yet exist was called “Maple Whiteboard” and the brochure described what we had gradually come to appreciate that engineers wanted from a calculation tool:

    • simplicity at its beating heart – just learn a few basic game mechanics, and then everything else “flows” (ahem). 
    • units support from the get-go
    • documentation features to describe the analysis
    • connectivity with other software
    • engineering-focused math functions

    The first working version of Maple Whiteboard was crude…but the basic building blocks were in place and the concept worked. This image dates from 2019.

    We unveiled Maple Flow to the public in 2021 (coming up with the name was a trial in of itself). Here’s what it looked like.

    The target audience loved the new product—they liked what it could do now and were excited about its future potential. Our initial assumptions had been validated!

    Maple Flow has evolved dramatically since the fever dream of the initial brochure and early prototypes. Even though it's much more powerful now, we've made sure it’s still simple to use.

    Today, I’m delighted to announce the launch of Maple Flow 2025. This release is a major turning point for the product. You'll see a clean, new interface, faster performance, and more tools for documentation and moving your work from other programs.

    Let me touch on my personal highlights.

    A new interface headlines the release! It’s clean and simple, with logically ordered buttons in organized groups.

    The ribbon is contextual; for example, click on an image, and you’ll see tools for adding shapes and text.

    There's always room for improvement and refinement. Let me know what you think!.

    You can now insert a table of contents into your document. The page numbers automatically update, and headings are hyperlinked – just click and you jump to that part of the worksheet.

    Hyperlinks in the table of contents are preserved when you export the worksheet to PDF – that’s an awesome navigation feature when you distribute your work.

    This feature gives me a visual dopamine hit every time I use it. Look how easy it is to use!

    We've decided to release a tool we’ve been using internally for some time. The Maple Flow Migration Assistant is a free addon that helps you convert your Mathcad 13, 14 and 15 worksheets to Maple Flow. 


    You can convert single Mathcad worksheets or point to a folder for bulk conversion. You also get many function translations.

    Automatically converting executable code between two different high-level math tools is difficult; some manual reworking is probably needed for anything that’s not simple arithmetic (we documented what the Migration Assistant does here). But if you’ve already decided to make the switch from Mathcad 13, 14 or 15, then the Migration Assistant is a great time saver.

    Large worksheets now evaluate faster! These are benchmarks from our internal testing suite.

    You can now run Maple Flow worksheets through Excel via a simple function call. You can change parameters and get updated results.

    To help you set up that function call, an interface walks you through the process.

    You can use this feature to develop a simple spreadsheet reporting dashboard or perform parameter sweeps on your Flow analyses.

    Large analysis projects can be difficult to manage. 

    • The results of one worksheet might need to be used in another,
    • there may be equations that are reused everywhere, 
    • or you might need to split your project into small chunks that different people can work on separately

    Well, now we’ve made that whole process easier! You can now treat Flow worksheets as “black box” functions that you can call from other Flow worksheets. You can even change parameter values, and return updated results

     

    The AI Formula Assistant made its debut in Maple 2025 and it sparked a lot of interest (and some interesting conversations about the future of AI in math software). 

    By popular demand, we've brought this feature into Flow. You can now look up an engineering formula with a simple natural language query,


     

    That's enough of my personal highlights. If you want to know more, visit the What's New pages for a complete rundown and grab a trial.

    If you haven’t tried Maple Flow yet, now is the right time to jump in. We have several time-limited launch offers to make the transition to Flow as frictionless as possible; these include offers for users who are

    • deploying a small suite of licenses
    • switching from other tools
    • in large organizations that need a full implementation plan.

    As ever, we can only keep Maple Flow on track if you let me know what you want - send all your feedback my way.

    We are excited to announce that the Maple Conference will be held Novemeber 5-7, 2025!

    Please join us at this free virtual event as it will be an excellent opportunity to meet other members of the Maple community, get the latest news about our products, and hear from the experts about the challenges and opportunities that our technology brings to teaching, learning, and research. More importantly, it's a chance for you to share the work you've been doing with Maple and Maple Learn. 

    The Call for Participation is now open. We are inviting submissions of presentation proposals on a range of topics related to Maple, including Maple in education, algorithms and software, and applications. We also encourage submission of proposals related to Maple Learn. 

    You can find more information about the themes of the conference and how to submit a presentation proposal at the Call for Participation page. Applications are due July 25, 2025.

    After the conference, all accepted presenters and invited speakers will be invited to submit related content to the Maple Transactions journal for consideration.

    Registration for attending the conference will open in July.  Watch for further announcements in the coming weeks.

    We hope all of you in the Maple Primes community will join us for this event!

    Kaska Kowalska
    Contributed Program Co-Chair

    Maple 2025.1

    We have just released an update to Maple. Maple 2025.1 includes several enhancements to the new interface, as well as various small corrections throughout the product. As always, we recommend that all Maple 2025 users install this update.

    In particular, please note that this update includes a fix to the problem where new documents were opening in a new window instead of a new tab.  Thanks for helping us, and other users, by letting us know!

    This update is available through Tools>Check for Updates in Maple, and is also available from the Maple 2025.1 download page on web site, where you can also find more details.

    MapleSim 2025

    We are happy to announce that we just released MapleSim 2025. This release includes a new component library to support the modeling of motor drives and updates to several in-product apps that make it even easier to perform optimization and analysis.

    See What’s New in MapleSim for details.

    claude.ai can write and explain many facits in the feild of prime number theory. Look what was created.

    https://claude.ai/public/artifacts/b5b0697c-01a2-4e42-843b-7ddecc63c568

    Thanks to @salim-barzani, I became interested in the Laplace Adomian Decompositon method to solve partial differential equations. It produces a sum of analytical components that converge to the exact solution. Probably it is not that efficient for numerical solutions, but the possibility of finding an exact solution to nonlinear PDEs by finding a formula for the components and therefore the infinite sum is interesting.

    The version here covers many of the common forms of PDEs, but is still a work in progress. The method for finding the Adomian polynomials could be improved by using one of the reccurence formulas in the literature. Extension to more PDE forms, ODEs etc are possible and I will attempt some of these before uploading an improved version to the application centre. In the meantime, feedback about bugs, usability etc. are appreciated.

    Laplace Adomian Decomposition method to solve partial differential equations.
     D.A. Harrington, June 2025, v 1.16.
     Procedure LAD is in the startup code region.

    Arguments:

    1. 

    Partial differential equation in one "time" variable and several other variables (called spatial variables here). Specified as an equation, or an expression implicitly equal to zero.
    Comprising: (1) one time derivative term of order m (denoted L), (2) linear terms that are derivatives in the spatial variables (R), (3) nonlinear terms with derivatives in the spatial variables (N). Together, (1)-(3) is a multivariate polynomial in the dependent variable, its derivatives, and any parameters. (4) inhomogenous terms in the time and spatial variables that do not contain the dependent variable or its derivatives (G). The general form is L = R+N-G.
    Any symbolic parameters are assumed to be real. Any numeric coefficients or parameters should be of type algebraic. Floating point values will be converted to rationals with convert(value, rational).

    2. 

    Function to solve for, e.g., u(x, y, t).

    3. 

    m initial condition(s) (at time zero). For m > 1, these must be in a list, and are the values of the function and its successive derivatives with respect to time, evaluated at time zero.

    4. 

    name of time variable.

    5. 

    number of iterations.

    6. 

    (optional) order for a fractional derivative, specified as fracorder = name or fracorder = numeric*value (floating point values are converted to type rational). The permissible values alpha are related to the value of m: m-1 < alpha and alpha <= m, i.e., an mth order time derivative is specified in the pde and m initial conditions are provided, as well as the value of alpha in the correct range. A symbolic alpha is assumed to be in this range.

    infolevel[LAD] may be set to different values to print out additional information as follows. Greater numbers include the information from smaller values.

    1. 

    The nonlinear expansion variables (those in the Adomian polynomials).

    2. 

    The different parts of the the pde (L, R, N, G) in jet notation.

    3. 

    Progress is indicated, as the time at each iteration.

    4. 

    Values of the components of the solution as they are produced (one per iteration).

    restart

    It may be useful to load the Physics package if derivatives contain abs. LAD converts these to a form without abs but with the conjugate of the dependent variable. The Physics package affects the internal simplifications and may affect the form of the output or the running time.

    PDEtools:-declare(U(x, t), quiet)

    Example from A-M. Wazwaz, Applied Mathematics and Computation 111 (2000) 53. Sec. 4.

    pde := diff(U(x, t), t)+U(x, t)^2*(diff(U(x, t), x)); inx := 3*x

    diff(U(x, t), t)+U(x, t)^2*(diff(U(x, t), x))

    3*x

    infolevel[LAD] := 2

    approx := LAD(pde, U(x, t), inx, t, 10)

    LAD: L = U[t]; R = 0; N = -U^2*U[x]; G = 0.

    LAD: nonlinear expansion variables (conjugated functions denoted by C) are: [U, U[x]]

    175692092397588*t^10*x^11-5650915252554*t^9*x^10+184670433090*t^8*x^9-6155681103*t^7*x^8+210450636*t^6*x^7-7440174*t^5*x^6+275562*t^4*x^5-10935*t^3*x^4+486*t^2*x^3-27*t*x^2+3*x

    By extrapolating to an infinite number of terms, we can find an exact solution. (Wazwaz calculates the coefficient of x^4*t^3 incorrectly and deduces an incorrect exact solution.) Multiplying by t gives a series in y = x*t for which guessgf can use the coefficients to find the exact solution.

    algsubs(x*t = y, expand(approx*t)); [seq(coeff(%, y, i), i = 0 .. degree(%, y))]; gfun:-guessgf(%, y)[1]; exact := (eval(%, y = x*t))/t

    175692092397588*y^11-5650915252554*y^10+184670433090*y^9-6155681103*y^8+210450636*y^7-7440174*y^6+275562*y^5-10935*y^4+486*y^3-27*y^2+3*y

    [0, 3, -27, 486, -10935, 275562, -7440174, 210450636, -6155681103, 184670433090, -5650915252554, 175692092397588]

    6*y/(1+(1+36*y)^(1/2))

    6*x/(1+(36*t*x+1)^(1/2))

    Check

    pdetest(U(x, t) = exact, [pde, U(x, 0) = inx])

    [0, 0]

    An example with inhomogeneous terms (but no nonlinear part). Ex. 3 from R. Shah et al, Entropy 21 (2019) 335.

    pde := diff(U(x, t), t)+diff(U(x, t), `$`(x, 3)) = -sin(Pi*x)*sin(t)-Pi^3*cos(Pi*x)*cos(t); inx := sin(Pi*x); exact := sin(Pi*x)*cos(t); pdetest(U(x, t) = exact, [pde, U(x, 0) = inx])

    diff(U(x, t), t)+diff(diff(diff(U(x, t), x), x), x) = -sin(Pi*x)*sin(t)-Pi^3*cos(Pi*x)*cos(t)

    sin(Pi*x)

    sin(Pi*x)*cos(t)

    [0, 0]

    approx := LAD(pde, U(x, t), inx, t, 10)

    LAD: L = U[t]; R = -U[x,x,x]; N = 0; G = -sin(Pi*x)*sin(t)-Pi^3*cos(Pi*x)*cos(t).

    LAD: nonlinear expansion variables (conjugated functions denoted by C) are: []

    sin(Pi*x)-cos(Pi*x)*Pi^3*sin(t)+sin(Pi*x)*(-1+cos(t))-Pi^3*(Pi^3*(-1+cos(t))*sin(Pi*x)-cos(Pi*x)*sin(t))+(Pi^3*(-sin(t)+t)*cos(Pi*x)+sin(Pi*x)*(-1+cos(t)))*Pi^6-(1/2)*Pi^9*(Pi^3*(t^2+2*cos(t)-2)*sin(Pi*x)+2*cos(Pi*x)*(-sin(t)+t))-(1/6)*Pi^12*(Pi^3*(t^3+6*sin(t)-6*t)*cos(Pi*x)-3*sin(Pi*x)*(t^2+2*cos(t)-2))+(1/24)*(Pi^3*(t^4-12*t^2-24*cos(t)+24)*sin(Pi*x)+4*cos(Pi*x)*(t^3+6*sin(t)-6*t))*Pi^15+(1/120)*Pi^18*(Pi^3*(t^5-20*t^3-120*sin(t)+120*t)*cos(Pi*x)-5*sin(Pi*x)*(t^4-12*t^2-24*cos(t)+24))-(1/720)*Pi^21*(Pi^3*(t^6-30*t^4+360*t^2+720*cos(t)-720)*sin(Pi*x)+6*cos(Pi*x)*(t^5-20*t^3-120*sin(t)+120*t))-(1/5040)*(Pi^3*(t^7-42*t^5+840*t^3+5040*sin(t)-5040*t)*cos(Pi*x)-7*sin(Pi*x)*(t^6-30*t^4+360*t^2+720*cos(t)-720))*Pi^24+(1/40320)*Pi^27*(Pi^3*(t^8-56*t^6+1680*t^4-20160*t^2-40320*cos(t)+40320)*sin(Pi*x)+8*cos(Pi*x)*(t^7-42*t^5+840*t^3+5040*sin(t)-5040*t))+(1/362880)*Pi^30*(Pi^3*(t^9-72*t^7+3024*t^5-60480*t^3-362880*sin(t)+362880*t)*cos(Pi*x)-9*sin(Pi*x)*(t^8-56*t^6+1680*t^4-20160*t^2-40320*cos(t)+40320))

    Expand the exact solution as a series in t to the same order and verify that it is the same as above.

    series(exact-approx, t, 11, oterm = false)

    0

    An example with a complex solution

    pde := I*(diff(U(x, t), t))+diff(U(x, t), `$`(x, 2))+2*abs(U(x, t))^2*U(x, t); inx := sech(x); exact := sech(x)*exp(I*t); `assuming`([simplify(pdetest(U(x, t) = exact, [pde, U(x, 0) = inx]))], [real])

    I*(diff(U(x, t), t))+diff(diff(U(x, t), x), x)+2*abs(U(x, t))^2*U(x, t)

    sech(x)

    sech(x)*exp(I*t)

    [0, 0]

    approx := LAD(pde, U(x, t), inx, t, 10)

    LAD: L = I*U[t]; R = -U[x,x]; N = -2*U^2*C; G = 0.

    LAD: nonlinear expansion variables (conjugated functions denoted by C) are: [C, U]

    sech(x)+I*sech(x)*t-(1/2)*sech(x)*t^2-((1/6)*I)*sech(x)*t^3+(1/24)*sech(x)*t^4+((1/120)*I)*sech(x)*t^5-(1/720)*sech(x)*t^6-((1/5040)*I)*sech(x)*t^7+(1/40320)*sech(x)*t^8+((1/362880)*I)*sech(x)*t^9-(1/3628800)*sech(x)*t^10

    The series for exp(I*t) is apparent.

    collect(approx, sech); series(approx-exact, t, 11, oterm = false)

    (1+I*t-(1/2)*t^2-((1/6)*I)*t^3+(1/24)*t^4+((1/120)*I)*t^5-(1/720)*t^6-((1/5040)*I)*t^7+(1/40320)*t^8+((1/362880)*I)*t^9-(1/3628800)*t^10)*sech(x)

    0

    An example with fractional order differentiation wrt t of order alpha. For m-1 < alpha and alpha <= m, the derivative must be entered with order m and there must be a list of m initial conditions:f(x, 0), (D[2](f))(x, 0), (D[2, 2](f))(x, 0), () .. ()

     Ex. 1 from R. Shah et al, Entropy 21 (2019) 335

    pde := diff(U(x, t), t) = -2*(diff(U(x, t), x))-(diff(U(x, t), `$`(x, 3))); inx := sin(x)

    diff(U(x, t), t) = -2*(diff(U(x, t), x))-(diff(diff(diff(U(x, t), x), x), x))

    sin(x)

    Symbolic order is accepted.

    approx := LAD(pde, U(x, t), inx, t, 6, fracorder = alpha)

    LAD: L = U[t]; R = -2*U[x]-U[x,x,x]; N = 0; G = 0.

    LAD: nonlinear expansion variables (conjugated functions denoted by C) are: []

    sin(x)-cos(x)*t^alpha/GAMMA(1+alpha)-sin(x)*t^(2*alpha)/GAMMA(1+2*alpha)+cos(x)*t^(3*alpha)/GAMMA(1+3*alpha)+sin(x)*t^(4*alpha)/GAMMA(1+4*alpha)-cos(x)*t^(5*alpha)/GAMMA(1+5*alpha)-sin(x)*t^(6*alpha)/GAMMA(1+6*alpha)

    Giving a numerical value for the order will generally be more efficient. For alpha = 1/2, we can find an exact solution.

    approx := collect(LAD(pde, U(x, t), inx, t, 20, fracorder = 1/2), [sin, cos])

    LAD: L = U[t]; R = -2*U[x]-U[x,x,x]; N = 0; G = 0.

    LAD: nonlinear expansion variables (conjugated functions denoted by C) are: []

    (1-t+(1/2)*t^2-(1/6)*t^3+(1/24)*t^4-(1/120)*t^5+(1/720)*t^6-(1/5040)*t^7+(1/40320)*t^8-(1/362880)*t^9+(1/3628800)*t^10)*sin(x)+(-2*t^(1/2)/Pi^(1/2)+(4/3)*t^(3/2)/Pi^(1/2)-(8/15)*t^(5/2)/Pi^(1/2)+(16/105)*t^(7/2)/Pi^(1/2)-(32/945)*t^(9/2)/Pi^(1/2)+(64/10395)*t^(11/2)/Pi^(1/2)-(128/135135)*t^(13/2)/Pi^(1/2)+(256/2027025)*t^(15/2)/Pi^(1/2)-(512/34459425)*t^(17/2)/Pi^(1/2)+(1024/654729075)*t^(19/2)/Pi^(1/2))*cos(x)

    The first series is exp(-t), the second series is not so obvious, After some scaling, the second series may be passed to guessgf

    ser2 := `assuming`([simplify(expand(sqrt(Pi)*op(2, approx)/(sqrt(t)*cos(x))))], [t > 0]); [seq(coeff(ser2, t, i), i = 0 .. 9)]; ser2ex := gfun:-guessgf(%, t)[1]

    -2+(4/3)*t-(8/15)*t^2+(16/105)*t^3-(32/945)*t^4+(64/10395)*t^5-(128/135135)*t^6+(256/2027025)*t^7-(512/34459425)*t^8+(1024/654729075)*t^9

    -exp(-t)*Pi^(1/2)*erfi(t^(1/2))/t^(1/2)

    So the full solution is

    exact := exp(-t)*sin(x)+ser2ex*sqrt(t)*cos(x)/sqrt(Pi)

    exp(-t)*sin(x)-exp(-t)*erfi(t^(1/2))*cos(x)

    Check. fracdiff's default method returns an integral, method = laplace fails, but method = series works with cancellation of all terms but the "left over" last half-integral-order one.

    Ord := 20; fracdiff(exact, t, 1/2, method = series, methodoptions = [order = Ord])-series(eval(rhs(pde), U(x, t) = exact), t, Ord)

    20

    -(1048576/319830986772877770815625)*sin(x)*t^(39/2)/Pi^(1/2)+O(t^(39/2))-O(t^20)

    A second-order example (linear)

    pde := diff(U(x, t), t, t) = -c^2*(diff(U(x, t), `$`(x, 2))); inx := [exp(I*x/c), exp(I*x/c)]; exact := exp(t+I*x/c)

    diff(diff(U(x, t), t), t) = -c^2*(diff(diff(U(x, t), x), x))

    [exp(I*x/c), exp(I*x/c)]

    exp(t+I*x/c)

    pdetest(U(x, t) = exact, [pde, U(x, 0) = inx[1], (D[2](U))(x, 0) = inx[2]])

    [0, 0, 0]

    approx := LAD(pde, U(x, t), inx, t, 6)

    LAD: L = U[t,t]; R = -c^2*U[x,x]; N = 0; G = 0.

    LAD: nonlinear expansion variables (conjugated functions denoted by C) are: []

    exp(I*x/c)*(1+t)+(1/6)*exp(I*x/c)*t^2*(3+t)+(1/120)*exp(I*x/c)*t^4*(t+5)+(1/5040)*exp(I*x/c)*t^6*(7+t)+(1/362880)*exp(I*x/c)*t^8*(9+t)+(1/39916800)*exp(I*x/c)*t^10*(t+11)+(1/6227020800)*exp(I*x/c)*t^12*(13+t)

    series(exact-approx, t, 13, oterm = false)

    0

    Fractional order example

    approx := collect(LAD(pde, U(x, t), inx, t, 10, fracorder = 3/2), [exp, t])

    LAD: L = U[t,t]; R = -c^2*U[x,x]; N = 0; G = 0.

    LAD: nonlinear expansion variables (conjugated functions denoted by C) are: []

    (1+(1/20922789888000)*t^16+(1/1307674368000)*t^15+(32768/6190283353629375)*t^(29/2)/Pi^(1/2)+(16384/213458046676875)*t^(27/2)/Pi^(1/2)+(1/6227020800)*t^13+(1/479001600)*t^12+(4096/316234143225)*t^(23/2)/Pi^(1/2)+(2048/13749310575)*t^(21/2)/Pi^(1/2)+(1/3628800)*t^10+(1/362880)*t^9+(512/34459425)*t^(17/2)/Pi^(1/2)+(256/2027025)*t^(15/2)/Pi^(1/2)+(1/5040)*t^7+(1/720)*t^6+(64/10395)*t^(11/2)/Pi^(1/2)+(32/945)*t^(9/2)/Pi^(1/2)+(1/24)*t^4+(1/6)*t^3+(8/15)*t^(5/2)/Pi^(1/2)+(4/3)*t^(3/2)/Pi^(1/2)+t)*exp(I*x/c)

    There appear to be two separate series in t, with integer and half-integer powers.

    t_series := approx/exp(I*x/c); t1, t2 := selectremove(proc (w) options operator, arrow; (degree(w, t))::integer end proc, t_series)

    1+(1/20922789888000)*t^16+(1/1307674368000)*t^15+(1/6227020800)*t^13+(1/479001600)*t^12+(1/3628800)*t^10+(1/362880)*t^9+(1/5040)*t^7+(1/720)*t^6+(1/24)*t^4+(1/6)*t^3+t, (32768/6190283353629375)*t^(29/2)/Pi^(1/2)+(16384/213458046676875)*t^(27/2)/Pi^(1/2)+(4096/316234143225)*t^(23/2)/Pi^(1/2)+(2048/13749310575)*t^(21/2)/Pi^(1/2)+(512/34459425)*t^(17/2)/Pi^(1/2)+(256/2027025)*t^(15/2)/Pi^(1/2)+(64/10395)*t^(11/2)/Pi^(1/2)+(32/945)*t^(9/2)/Pi^(1/2)+(8/15)*t^(5/2)/Pi^(1/2)+(4/3)*t^(3/2)/Pi^(1/2)

    The integer-powers series is the series for exp(t) with every third term missing: missing powers 2, 5, 8, 11, ...

    t1sum := simplify(exp(t)-(sum(t^(3*i+2)/factorial(3*i+2), i = 0 .. infinity))); series(%, t, 17)

    (2/3)*exp(t)+(1/3)*(cos((1/2)*3^(1/2)*t)+3^(1/2)*sin((1/2)*3^(1/2)*t))*exp(-(1/2)*t)

    series(1+t+(1/6)*t^3+(1/24)*t^4+(1/720)*t^6+(1/5040)*t^7+(1/362880)*t^9+(1/3628800)*t^10+(1/479001600)*t^12+(1/6227020800)*t^13+(1/1307674368000)*t^15+(1/20922789888000)*t^16+O(t^17),t,17)

    And for the other one, the following scaled series shows coefficients with powers of two divided by double factorials, every third term missing: missing powers 2,5,8,11,...

    expand(sqrt(Pi)*t2/(4*t^(3/2))); all := add(2^i*t^i/doublefactorial(2*(i+1)+1), i = 0 .. 9); missing := add(eval(2^i*t^i/doublefactorial(2*(i+1)+1), i = 3*j+2), j = 0 .. 3)

    (8192/6190283353629375)*t^13+(4096/213458046676875)*t^12+(1024/316234143225)*t^10+(512/13749310575)*t^9+(128/34459425)*t^7+(64/2027025)*t^6+(16/10395)*t^4+(8/945)*t^3+(2/15)*t+1/3

    1/3+(2/15)*t+(4/105)*t^2+(8/945)*t^3+(16/10395)*t^4+(32/135135)*t^5+(64/2027025)*t^6+(128/34459425)*t^7+(256/654729075)*t^8+(512/13749310575)*t^9

    (4/105)*t^2+(32/135135)*t^5+(256/654729075)*t^8+(2048/7905853580625)*t^11

    t2sum := 4*t^(3/2)*(sum(2^i*t^i/doublefactorial(2*(i+1)+1), i = 0 .. infinity)-(sum(eval(2^i*t^i/doublefactorial(2*(i+1)+1), i = 3*j+2), j = 0 .. infinity)))/sqrt(Pi)

    4*t^(3/2)*((1/4)*(Pi^(1/2)*exp(t)-2*t^(1/2)-Pi^(1/2)*erfc(t^(1/2))*exp(t))/t^(3/2)-(4/105)*t^2*hypergeom([1], [3/2, 11/6, 13/6], (1/27)*t^3))/Pi^(1/2)

    Putting it together suggests

    exact := exp(I*x/c)*simplify(t1sum+t2sum)

    (1/3)*exp(I*x/c)*(Pi^(1/2)*exp(-(1/2)*t)*sin((1/2)*3^(1/2)*t)*3^(1/2)+Pi^(1/2)*exp(-(1/2)*t)*cos((1/2)*3^(1/2)*t)+3*Pi^(1/2)*exp(t)*erf(t^(1/2))-(16/35)*t^(7/2)*hypergeom([1], [3/2, 11/6, 13/6], (1/27)*t^3)+2*Pi^(1/2)*exp(t)-6*t^(1/2))/Pi^(1/2)

    Check.

    Ord := 20; fracdiff(exact, t, 3/2, method = series, methodoptions = [order = Ord+1])-series(eval(rhs(pde), U(x, t) = exact), t, Ord)

    20

    O(t^(39/2))-(1048576/319830986772877770815625)*exp(I*x/c)*t^(39/2)/Pi^(1/2)-O(t^(41/2))

    Numerical calculation of a soliton

    pde := I*(diff(U(x, t), t))+diff(U(x, t), `$`(x, 2))+U(x, t)^2*conjugate(U(x, t)); exact := sqrt(2*B)*sech(sqrt(B)*(2*k*t-x-x__0))*exp(I*(k*x+(-k^2+B)*t)); `assuming`([simplify(pdetest(U(x, t) = exact, pde))], [real, B > 0]); inx := eval(exact, t = 0)

    I*(diff(U(x, t), t))+diff(diff(U(x, t), x), x)+U(x, t)^2*conjugate(U(x, t))

    2^(1/2)*B^(1/2)*sech(B^(1/2)*(2*k*t-x-x__0))*exp(I*(k*x+(-k^2+B)*t))

    0

    2^(1/2)*B^(1/2)*sech(B^(1/2)*(-x-x__0))*exp(I*k*x)

    With numerical parameters it runs faster. Float parameters will be converted to rationals.

    params := {B = 2, k = -1/2, x__0 = -2}; inxnum := eval(inx, params); exactnum := eval(exact, params)

    2*sech(2^(1/2)*(-x+2))*exp(-((1/2)*I)*x)

    2*sech(2^(1/2)*(-t-x+2))*exp(I*(-(1/2)*x+(7/4)*t))

    infolevel[LAD] := 3; approx := LAD(pde, U(x, t), inxnum, t, 28)

    LAD: L = I*U[t]; R = -U[x,x]; N = -U^2*C; G = 0.

    LAD: nonlinear expansion variables (conjugated functions denoted by C) are: [C, U]

    LAD: calculating component 1 at time 0.

    LAD: calculating component 2 at time .221

    [Edited for brevity]

    LAD: calculating component 27 at time 90.414

    LAD: calculating component 28 at time 103.870

    LAD: completed at time 105.309

    For larger x and t, the approximation diverges at a point that depends on the number of iterations.

    plot3d([abs(exactnum), abs(approx)], t = 0 .. 2, x = -3 .. 3, color = [red, blue], view = [default, default, 0 .. 5], orientation = [-30, 60])

    NULL

    Download Laplace_Adomian_Decomposition_procedure8b.mw

    First impressions, I have mixed feelings - one being it's cool and new, the other feeling that it's a bit clunky.

    In my opinion Maple is starting to look like the interface is being modelled after Microsoft Office, or like the ribbon toolbars of AutoCad or Inventor.  Maple's "uniqueness" is disappearing.  I rather liked the old interface. 

    The toolbar icons are larger, taking up more space.

    The toolbar layout is indeed simpler, but also less efficient maybe.  I mean there were more useful available icons at once before, more functional is the word I guess.  Now it might be a couple of clicks away to pull up your favorite icon(s).  The icons all look very nice, that's a plus but they could be smaller.  

    Perhaps we could make a customized menu toolbar?  That is, allow users to put all the most useful icons we use or would like the most to be displayed?  This would help some of the strange organization of some of the icons and allow us to make our maple "sandbox" feel more at home. 

     

    The link below goes to the Proceedings of the Maple 2024 Conference, which includes several articles that will be of interest to the readers of Maple Primes.

    There may be one more paper coming in to the proceedings later as per policy; since most things are ready, away we go!

    Proceedings of the Maple 2024 Conferenc

    (1) The gray line above the working area is redundant.

    (2) Line Style, Color, and the "Delete" key function to delete object are not working properly.

    (3) IdentifySequence([1,3,5,7,9]) without the second argument does not work.

    (4) IdentifySequence should first identify simple patterns (Arithmetic Progression, Geometric Progression, Arithmetic-Geometric Progression, Harmonic Progression) before attempting to find a more complex formula for the nth term of the sequence.

    (5) It would be beneficial if IdentifySequence recognized sequences involving rational, irrational and symbolic numbers.

    In Optical-Illusion--Impossible-Prisms, mcarvalho provides a Maple Learn worksheet to illustrate an intriguing optical illusion.  Here I do that illustration in Maple, and in 3D! 

    The graphics below shows 4 bars.  Or is it 3 bars?

    Download the worksheet, stare at the graphics for short while to grasp the nature of the optical illusion, and then rotate the 3D graph with the mouse and see the illusion fall apart.

    optical-illusion.mw

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