Dear All,

I am facing some problems. I want to draw some plots: I have considered the 4th order momentum equation and the 2nd order energy equation; it requires 6 boundary conditions, which I have provided, but till asking for errors (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 7, got 6.

eqn1 := {((kappa[1].phi[1]+kappa[2].phi[2]+kappa[3].phi[3])/(phi[1]+phi[2]+phi[3])+(p-1).kappa[f]+(p-1).(kappa[1].phi[1]+kappa[2].phi[2]+kappa[3].phi[3])-(p-1).(phi[1]+phi[2]+phi[3]).kappa[f])/((kappa[1].phi[1]+kappa[2].phi[2]+kappa[3].phi[3])/(phi[1]+phi[2]+phi[3])+(p-1).kappa[f]-(p-1).(kappa[1].phi[1]+kappa[2].phi[2]+kappa[3].phi[3])+(phi[1]+phi[2]+phi[3]).kappa[f]).(diff(theta(eta), eta, eta)+4/3.N.(diff((1+(K-1).theta(eta))^3.(diff(theta(eta), eta)), eta)))+Pr.(((1-phi[3]).((1-phi[2])*(1-phi[1]+phi[1].(`ρc__s1`/`ρc__f`))+phi[2].(`ρc__s2`/`ρc__f`))+phi[3].(`ρc__s3`/`ρc__f`)).(R.f(eta)+alpha.eta).(diff(theta(eta), eta))+Q.theta(eta)+R.Ec.((diff(f(eta), eta, eta))^2)) = 0, diff(f(eta), eta, eta, eta, eta)-(1-phi[1])^2.5.((1-phi[2])^2.5).((1-phi[3])^2.5).((1-phi[3]).((1-phi[2]).(1-phi[1]+phi[1].(`ρ__s1`/`ρ__f`))+phi[2].(`ρ__s2`/`ρ__f`))+phi[3].(`ρ__s3`/`ρ__f`)).(alpha.(eta.(diff(f(eta), eta, eta, eta))+3.*(diff(f(eta), eta, eta)))+(diff(f(eta), eta, eta, eta)).f(eta)-(diff(f(eta), eta)).(diff(f(eta), eta, eta))).R-(1-phi[1])^2.5.((1-phi[2])^2.5).((1-phi[3])^2.5).A.B.e^(-B.eta) = 0, f(-1) = S, f(1) = 1, theta(-1) = 1, theta(1) = 0, (D(f))(-1) = 0, (D(f))(1) = 0}

sys1 := eval(eqn1, {A = 1, B = .5, Ec = .1, K = 1.5, N = .5, Pr = 2, Q = .4, R = 1, S = -.1, p = 3, alpha = .2, `ρ__f` = 997.1, `ρ__s1` = 0, `ρ__s2` = 0, `ρ__s3` = 5180, `ρc__f` = 997.1.4179, `ρc__s1` = 0, `ρc__s2` = 0, `ρc__s3` = 5180.670, phi[1] = 0., phi[2] = 0., phi[3] = 0.3e-1, kappa[1] = 0, kappa[2] = 0, kappa[3] = 9.7, kappa[f] = .613})

sol1 := dsolve(sys1, numeric);
Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 7, got 6
with(plots);
t1 := odeplot(sol1, [eta, diff(f(eta), eta)], eta = -1 .. 1, numpoints = 65, thickness = 0, color = green, linestyle = solid);
plots[plots:-display]({t1})

Download A1.mw

Dear all,

is there a versioning concept similiar to Eclipse ?

I did expect the following two plot statements (MaplePrimes is only rendering one statement) to produce the same plot. What did I do wrong when using mod in plot?

Download mod_in_plot.mw

In my Maple 2020, I noticed my program got stuck (overnight so let's say for at least 8 hours) on factorization of relatively small integer, so I tried the command standalone:

ifactor(630743190664091077)

and it just froze. For comparsion I tried other SW and programming libraries and basically all of them had the answer instantly. Also looking at the Maple's methods, if I force pollard or lenstra, it also gets the answer instantly. If my understanding is correct, it gets stuck on the method 'morrbril' which is part of the default mix (I tried also mpqs and it gave FAIL, but at least instantly). 

Is that something that still happens by default in newer versions? Seems to me if it gets stuck on 18 decimal digit integer, maybe it's not the best default method...

restart;
with(geometry);
with(plots);
Bl := color = black;
y0 := x -> -ln(1 - exp(-x));
y0 := proc (x) options operator, arrow; -ln(1-exp(-x)) end proc

y1 := x -> -ln(-1 + exp(-x));
y1 := proc (x) options operator, arrow; -ln(-1+exp(-x)) end proc

y2 := x -> -ln(1 + exp(-x));
y2 := proc (x) options operator, arrow; -ln(1+exp(-x)) end proc

p := plot(y0(x), x = 0.02 .. 4, scaling = constrained, color = blue);
p1 := plot(y2(x), x = -4 .. 4, scaling = constrained, color = green);
p2 := plot(y1(x), x = -4 .. 0, scaling = constrained, color = red);
display({p, p1, p2}, view = [-4 .. 4, -4 .. 5]);
Calculate its area; Thank you.

Why Maple can not do this basic combining of two terms? What do  I need to do to help Maple do it? Am I not using the correct command?

Download how_to_combine_august_28_2024.mw

For reference, using another software, this is what it gives

Is this valid:

Int(sqrt(x^2+sqrt(x^4+1))/(x+1)/sqrt(x^4+1),x=0..infinity) =
(1/8)*ln((52+36*2^(1/2))*(2+2*2^(1/2))^(1/2)+80*2^(1/2)+113)*(2+2*2^(1/2))^(1/2);

?

SimpleMarsBlyProcedure.mw

Hello Orbital Mechanics and astrodynamics designers of Maple Primes! I am trying to fly to Mars and enter into orbit around it! I know there are a few of you out there that have thought about doing that! Think of all the great mathematicians who have "dabbled" with orbits and astrodynamics! Anyway, here is my problem: I have a simple keplerian model for doing a flyby around Mars and I have a simple model for Reaction Control Thrusters (RCS) to help put the spacecraft into orbit around Mars.  The first thruster burn happens as the spacecraft enters Mars' Sphere Of Influence (SOI) when it is less than 577000 km away and that burn is needed.  I do that with a piecewise continous function with the conditions set up to fire the thrusters.  But in that same piecewise continous function, I have a 2nd thruster firing with the times called out to fire again.  But this time I want to fire the thruster at periapse (P) in order to go into orbit around Mars.  I believe that the Rosenbrock and/or RKF45 are not responding to the 2nd conditions in the piecewise function I have set up for the thruster firing times.  I have to fire the thruster at periapse and I know that time I reach the periapse point.  Also, in my Maple file you will see that I can "cant" the spacecraft to better control the direction of my burns.  

The problem I am encountering seems to be more about the piecewise functions with multiple conditions and expressions.  Please take a look at my Maple file and see if any of you Orbital Mechanics and/or astrodynamicsts familar with Maple can see what I am doing wrong here.  You don't have to be a astrodyamicist per se, just perhaps you have run across this problem of piecewise functions in dsolve with method = rosenbrock or RKF45. 

Thank you. 

In this post about a non-linear system of equations solutions were sougth. It turned out that there were no non-trivial solutions for the given numerical values. However, with different numerical values there should be solutions.

In analogy to the fundamental theorem of algebra (which clearly states the number of roots),
I wonder if Maple provides commands that can estimate an upper bound of roots/solutions for a system of multivariate equations by analysing the structure of the system of equations rather than attempting to solve it.

I am not sure if rules, methods or theorems exist at all for multivariate problems. Maybe it is a stupid question but for me this was non-trivial for the case given above.

In the Standard interface, the length of an expression that display in the worksheet can be limited using the Options dialog: Options Dialog - Precision Tab - Maple Help. However, I would like to know if I can change this option programmatically. The closest interface variables are elisiontermsbefore, elisiontermsafter and termelisionthreshold, but as the aforementioned help page states, they control the “term elision” and are not the same as “expression length limit”. So, is this possible? 

Writng the Pde wave function solution in a textbook form ?
golfvergelijking_oplossing_gebruiken_om_integraaluisom_te_halen_voorbeeld.mw

Below is the code in Maple 2022, and then I describe the problem.
restart;
with(plots);
a := 0.5;
j := BesselJ(0, sqrt(2*I)*sqrt(x^2 + y^2)*a)/BesselJ(0, sqrt(2*I)*a);
A := sqrt(Re(j)^2 + Im(j)^2);
densityplot(A, x = -1 .. 1, y = -sqrt(-x^2 + 1) .. sqrt(-x^2 + 1), grid = [68, 68], style = patchnogrid, scaletorange = 0 .. 1);

Thus, I have a real function of two variables: $A(x, y)$. At zero it is minimal (value 0.996). At the boundary of the unit circle it is maximal with a value equal to 1. In theory, scaletorange = 0 .. 1 should give a picture with almost perfectly white everywhere in the circle since the function values ​​are very close to 1. However, both with scaletorange and without it, the command produces a picture with a significantly dark circle in the center...

I am looking for something similar to color functions of plot3D. plot.options is directing me to plot,color where I cannot find an example. I tried

plot(floor(x),x=-3..3,color=floor(x))

Error, (in plot) invalid color specification: floor(x)

Suppose I have a list of differential equations:

L:=[x*diff(f(x),x)+2*x+1=0, 4*(diff(f(x),x$2))^2+7*diff(f(x),x)-2=0, x*diff(f(x),x)+2*x+1=0, 3*(diff(f(x),x))^2-f(x)-1=0];

how can I rewrite this list such that 
L:=[[x*diff(f(x),x)+2*x+1=0,2], [4*(diff(f(x),x$2))^2+7*diff(f(x),x)-2=0,1], [3*(diff(f(x),x))^2-f(x)-1=0,1]];
i.e., rewrite this list as the [equation, Number of occurrences in the list]

Hi all guys, it is simple equation, I wanna get the expression of w=()^(1/4) which consists zg & fg. I use solve command but fails, could you please help me?

Download solve_an_equation.mw