Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

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

Hi everyone,

I am trying to solve a system of coupled ODEs numerically. My worksheet runs and produces results, but when I look at the graphs, it seems that the boundary conditions are not being satisfied correctly. Could anyone help me identify the issue and  fix my implementation?

BCs_help.mw

I need to export an image in high resolution in JPEG, JPG, and PDF formats. Right now, I'm using screenshots, which results in low clarity. Could you please help me with the correct syntax to generate a high-resolution, downloadable image in these formats? I'm attaching the file below:

q_new.mw

Hi

I'm trying to duplicate this graph in Maple. Any suggestions on how to place the textplot labels (n=0, n=1, etc.) to the right of 0.8, just like in the original graph?

how to place the textplot labels (n=0, n=1, etc.)

Thanks

S7MAA_Dveloppement_Limit.mw

I constructed a density function, and I am certain it shows me what I want.  The problem I am having is parsing the Elliptic functions. Is there a way to "get rid" of the ones I don't want or need.

I generated a plot of the function -- the plot tells me what I expected based on simulation. I need to know if there is a way to express the density function (y) as a function of t and without the elliptic functions..  Even a numerical solution would be fine.

I assume the denomenator term is correct. I also assume that I don't need complex values. My input file is below.

Basics.mw

I have set a style for my Maple 2023 sheets

2D-Input, Font: Times Roman 28 pt.

In the the past when I reopened the file, it would come back with the same 2D input font.

Starting today, when I reopen the file, the whole sheet is changed to. 

Maple-Input, Font: Courier New 12 pt. 

You can see it flash on the original stylem then reset to the Courier font. 

I tried resetting the Display options, but no luck.

Any thoughts?

I tried to open some existing worksheets. 

If I enter, e.g.,r f:=x, I get 

"Typesetting:-mprintslash([(f := x)],[x])"

I cannot change the style set. 

It seems that when I open old worksheets, some of the text imput, e.g., processes, is lost.

I upgraded to Maple 2025, but have the same issues. 

Any suggestions?

The two profit functions intersect at a certain point, but the graph is not clearly visible in the range of Cb​ from 30,000 to around 60,000. How can I adjust the plot to make this range more visible? What can i do such that two lines are seen distinct in that area?

Sheet:Q_12.mw

I'm solving the 1D heat equation using two different approaches, both involving Fourier transforms.

  1. First Attempt: Using pdsolve the Fourier method. This code either takes a very long time or doesn't produce a plot at all.
  2. Second Attempt: Manual Fourier transform. This one works fine and quickly plots the result.

Why does the first version using pdsolve(..., method = Fourier) result in slow or non-responsive behaviorplot3d, while the second version (manual transform) runs efficiently? Is the pdsolve result too symbolic or unevaluated for plotting? How can I make the first approach plot correctly?

Thanks for any insights!

ft1.mw

In this system of differential equation i have two questions
1- i want find thus parameter containing in S[1] and S[2] to be 1 or -1 how find find all other parameter inside thus for finding that?

2-when equalibroium point are complex the conservative quantity not shown thus point ? why is not shown in  diagram there is trick which i don't know How i can show in global? 
L1.mw

finding each parameter to set the point be one like this picture

 

 

Hi. how can i plot this function (FF) ?

restart

 

NULL

FF := evalf((5.00000*10^(-1))*sqrt(2.00000*10^0)*sqrt((-(2.86309*10^0)*P1-(1.66947*10^5)*(-(1.78626*10^(-6))*P1+(-1.03200*10^(-6)-I*(2.12871*10^(-209)))*P1)*exp(-(3.24175*10^(-1))*x)-(1.66947*10^5)*(-(4.18761*10^(-119))*P1+(-2.41935*10^(-119)-I*(4.99043*10^(-322)))*P1)*exp((3.24175*10^(-1))*x)+(4.83452*10^3+I*(9.71800*10^2))*((4.91783*10^(-20)+I*(4.44752*10^(-19)))*P1-(7.23576*10^(-19))*P1)*exp((4.17729*10^(-2)+I*(3.63246*10^(-2)))*x)+(4.83452*10^3+I*(9.71800*10^2))*((-1.86327*10^(-5)+I*(5.29561*10^(-5)))*P1+(2.76726*10^(-4))*P1)*exp((-4.17729*10^(-2)-I*(3.63246*10^(-2)))*x)+(4.83452*10^3-I*(9.71800*10^2))*((-1.86327*10^(-5)-I*(5.29561*10^(-5)))*P1+(2.76726*10^(-4))*P1)*exp((-4.17729*10^(-2)+I*(3.63246*10^(-2)))*x)+(-1.00000*10^(-200)-I*(1.00000*10^(-403)))*P1+(-7.80021*10^(-2750)-I*(3.11940*10^(-2750)))*((-3.43175*10^2733+I*(1.99678*10^2732))*P1+(5.08514*10^2734)*P1)*exp((4.17729*10^(-2)-I*(3.63246*10^(-2)))*x))^(2.00000*10^0)+(-(1.53846*10^5)*(-(6.46014*10^(-7))*P1+(-3.73229*10^(-7)-I*(7.69863*10^(-210)))*P1)*exp(-(3.24175*10^(-1))*x)-(1.53846*10^5)*(-(1.51448*10^(-119))*P1+(-8.74976*10^(-120)-I*(1.80482*10^(-322)))*P1)*exp((3.24175*10^(-1))*x)+(2.51785*10^0)*P1+(-6.25305*10^3+I*(3.19024*10^3))*((-1.86327*10^(-5)+I*(5.29561*10^(-5)))*P1+(2.76726*10^(-4))*P1)*exp((-4.17729*10^(-2)-I*(3.63246*10^(-2)))*x)+(-6.25305*10^3+I*(3.19024*10^3))*((4.91783*10^(-20)+I*(4.44752*10^(-19)))*P1-(7.23576*10^(-19))*P1)*exp((4.17729*10^(-2)+I*(3.63246*10^(-2)))*x)+(-6.25305*10^3-I*(3.19024*10^3))*((-1.86327*10^(-5)-I*(5.29561*10^(-5)))*P1+(2.76726*10^(-4))*P1)*exp((-4.17729*10^(-2)+I*(3.63246*10^(-2)))*x)+(5.94458*10^(-2750)+I*(1.03769*10^(-2749)))*((-3.43175*10^2733+I*(1.99678*10^2732))*P1+(5.08514*10^2734)*P1)*exp((4.17729*10^(-2)-I*(3.63246*10^(-2)))*x)+(-4.53057*10^(-1)-I*(9.34527*10^(-204)))*P1+(4.43548*10^4)*(-(1.78626*10^(-6))*P1+(-1.03200*10^(-6)-I*(2.12871*10^(-209)))*P1)*exp(-(3.24175*10^(-1))*x)+(4.43548*10^4)*(-(4.18761*10^(-119))*P1+(-2.41935*10^(-119)-I*(4.99043*10^(-322)))*P1)*exp((3.24175*10^(-1))*x)+(-1.53846*10^5-I*(3.36949*10^(-198)))*((-1.28153*10^(-7)-I*(3.64224*10^(-7)))*P1+(1.90328*10^(-6))*P1)*exp((-4.17729*10^(-2)+I*(3.63246*10^(-2)))*x)+(1.20721*10^(-220)+I*(7.88859*10^(-221)))*((-4.28969*10^203+I*(2.49597*10^202))*P1+(6.35642*10^204)*P1)*exp((4.17729*10^(-2)-I*(3.63246*10^(-2)))*x)+(-1.53846*10^5+I*(3.36949*10^(-198)))*((3.38241*10^(-22)+I*(3.05893*10^(-21)))*P1-(4.97664*10^(-21))*P1)*exp((4.17729*10^(-2)+I*(3.63246*10^(-2)))*x)+(-1.53846*10^5+I*(3.36949*10^(-198)))*((-1.28153*10^(-7)+I*(3.64224*10^(-7)))*P1+(1.90328*10^(-6))*P1)*exp((-4.17729*10^(-2)-I*(3.63246*10^(-2)))*x))^(2.00000*10^0)+(-(1.53846*10^5)*(-(6.46014*10^(-7))*P1+(-3.73229*10^(-7)-I*(7.69863*10^(-210)))*P1)*exp(-(3.24175*10^(-1))*x)-(1.53846*10^5)*(-(1.51448*10^(-119))*P1+(-8.74976*10^(-120)-I*(1.80482*10^(-322)))*P1)*exp((3.24175*10^(-1))*x)-(3.45235*10^(-1))*P1-(1.22592*10^5)*(-(1.78626*10^(-6))*P1+(-1.03200*10^(-6)-I*(2.12871*10^(-209)))*P1)*exp(-(3.24175*10^(-1))*x)-(1.22592*10^5)*(-(4.18761*10^(-119))*P1+(-2.41935*10^(-119)-I*(4.99043*10^(-322)))*P1)*exp((3.24175*10^(-1))*x)+(-1.41853*10^3+I*(4.16204*10^3))*((4.91783*10^(-20)+I*(4.44752*10^(-19)))*P1-(7.23576*10^(-19))*P1)*exp((4.17729*10^(-2)+I*(3.63246*10^(-2)))*x)+(-1.41853*10^3+I*(4.16204*10^3))*((-1.86327*10^(-5)+I*(5.29561*10^(-5)))*P1+(2.76726*10^(-4))*P1)*exp((-4.17729*10^(-2)-I*(3.63246*10^(-2)))*x)+(-1.53846*10^5-I*(3.36949*10^(-198)))*((-1.28153*10^(-7)-I*(3.64224*10^(-7)))*P1+(1.90328*10^(-6))*P1)*exp((-4.17729*10^(-2)+I*(3.63246*10^(-2)))*x)+(-1.41853*10^3-I*(4.16204*10^3))*((-1.86327*10^(-5)-I*(5.29561*10^(-5)))*P1+(2.76726*10^(-4))*P1)*exp((-4.17729*10^(-2)+I*(3.63246*10^(-2)))*x)+(-1.53846*10^5+I*(3.36949*10^(-198)))*((-1.28153*10^(-7)+I*(3.64224*10^(-7)))*P1+(1.90328*10^(-6))*P1)*exp((-4.17729*10^(-2)-I*(3.63246*10^(-2)))*x)+(-1.53846*10^5+I*(3.36949*10^(-198)))*((3.38241*10^(-22)+I*(3.05893*10^(-21)))*P1-(4.97664*10^(-21))*P1)*exp((4.17729*10^(-2)+I*(3.63246*10^(-2)))*x)+(1.20721*10^(-220)+I*(7.88859*10^(-221)))*((-4.28969*10^203+I*(2.49597*10^202))*P1+(6.35642*10^204)*P1)*exp((4.17729*10^(-2)-I*(3.63246*10^(-2)))*x)+(-4.53057*10^(-1)-I*(9.34527*10^(-204)))*P1+(-1.85563*10^(-2750)+I*(7.25748*10^(-2750)))*((-3.43175*10^2733+I*(1.99678*10^2732))*P1+(5.08514*10^2734)*P1)*exp((4.17729*10^(-2)-I*(3.63246*10^(-2)))*x))^(2.00000*10^0)+(6.00000*10^0)*(-(2.25126*10^5)*(-(1.78626*10^(-6))*P1+(-1.03200*10^(-6)-I*(2.12871*10^(-209)))*P1)*exp(-(3.24175*10^(-1))*x)+(2.25126*10^5)*(-(4.18761*10^(-119))*P1+(-2.41935*10^(-119)-I*(4.99043*10^(-322)))*P1)*exp((3.24175*10^(-1))*x)+(1.79100*10^3-I*(5.22310*10^2))*((-1.86327*10^(-5)+I*(5.29561*10^(-5)))*P1+(2.76726*10^(-4))*P1)*exp((-4.17729*10^(-2)-I*(3.63246*10^(-2)))*x)+(-1.79100*10^3+I*(5.22310*10^2))*((4.91783*10^(-20)+I*(4.44752*10^(-19)))*P1-(7.23576*10^(-19))*P1)*exp((4.17729*10^(-2)+I*(3.63246*10^(-2)))*x)+(1.79100*10^3+I*(5.22310*10^2))*((-1.86327*10^(-5)-I*(5.29561*10^(-5)))*P1+(2.76726*10^(-4))*P1)*exp((-4.17729*10^(-2)+I*(3.63246*10^(-2)))*x)+(2.06743*10^(-2750)+I*(2.41391*10^(-2750)))*((-3.43175*10^2733+I*(1.99678*10^2732))*P1+(5.08514*10^2734)*P1)*exp((4.17729*10^(-2)-I*(3.63246*10^(-2)))*x))^(2.00000*10^0))-250)

.7071067810*((-2.86309*P1-166947.0000*(-0.1786260000e-5*P1+(-0.1032000000e-5-0.2128710000e-208*I)*P1)*exp(-.3241750000*x)-166947.0000*(-0.4187610000e-118*P1+(-0.2419350000e-118-0.4990430000e-321*I)*P1)*exp(.3241750000*x)+(4834.52000+971.80000*I)*((0.4917830000e-19+0.4447520000e-18*I)*P1-0.7235760000e-18*P1)*exp((0.4177290000e-1+0.3632460000e-1*I)*x)+(4834.52000+971.80000*I)*((-0.1863270000e-4+0.5295610000e-4*I)*P1+0.2767260000e-3*P1)*exp((-0.4177290000e-1-0.3632460000e-1*I)*x)+(4834.52000-971.80000*I)*((-0.1863270000e-4-0.5295610000e-4*I)*P1+0.2767260000e-3*P1)*exp((-0.4177290000e-1+0.3632460000e-1*I)*x)+(-0.1000000000e-199-0.1000000000e-402*I)*P1+(-0.7800210000e-2749-0.3119400000e-2749*I)*((-0.3431750000e2734+0.1996780000e2733*I)*P1+0.5085140000e2735*P1)*exp((0.4177290000e-1-0.3632460000e-1*I)*x))^2.00000+(-153846.0000*(-0.6460140000e-6*P1+(-0.3732290000e-6-0.7698630000e-209*I)*P1)*exp(-.3241750000*x)-153846.0000*(-0.1514480000e-118*P1+(-0.8749760000e-119-0.1804820000e-321*I)*P1)*exp(.3241750000*x)+2.51785*P1+(-6253.05000+3190.24000*I)*((-0.1863270000e-4+0.5295610000e-4*I)*P1+0.2767260000e-3*P1)*exp((-0.4177290000e-1-0.3632460000e-1*I)*x)+(-6253.05000+3190.24000*I)*((0.4917830000e-19+0.4447520000e-18*I)*P1-0.7235760000e-18*P1)*exp((0.4177290000e-1+0.3632460000e-1*I)*x)+(-6253.05000-3190.24000*I)*((-0.1863270000e-4-0.5295610000e-4*I)*P1+0.2767260000e-3*P1)*exp((-0.4177290000e-1+0.3632460000e-1*I)*x)+(0.5944580000e-2749+0.1037690000e-2748*I)*((-0.3431750000e2734+0.1996780000e2733*I)*P1+0.5085140000e2735*P1)*exp((0.4177290000e-1-0.3632460000e-1*I)*x)+(-.4530570000-0.9345270000e-203*I)*P1+44354.80000*(-0.1786260000e-5*P1+(-0.1032000000e-5-0.2128710000e-208*I)*P1)*exp(-.3241750000*x)+44354.80000*(-0.4187610000e-118*P1+(-0.2419350000e-118-0.4990430000e-321*I)*P1)*exp(.3241750000*x)+(-153846.0000-0.3369490000e-197*I)*((-0.1281530000e-6-0.3642240000e-6*I)*P1+0.1903280000e-5*P1)*exp((-0.4177290000e-1+0.3632460000e-1*I)*x)+(0.1207210000e-219+0.7888590000e-220*I)*((-0.4289690000e204+0.2495970000e203*I)*P1+0.6356420000e205*P1)*exp((0.4177290000e-1-0.3632460000e-1*I)*x)+(-153846.0000+0.3369490000e-197*I)*((0.3382410000e-21+0.3058930000e-20*I)*P1-0.4976640000e-20*P1)*exp((0.4177290000e-1+0.3632460000e-1*I)*x)+(-153846.0000+0.3369490000e-197*I)*((-0.1281530000e-6+0.3642240000e-6*I)*P1+0.1903280000e-5*P1)*exp((-0.4177290000e-1-0.3632460000e-1*I)*x))^2.00000+(-153846.0000*(-0.6460140000e-6*P1+(-0.3732290000e-6-0.7698630000e-209*I)*P1)*exp(-.3241750000*x)-153846.0000*(-0.1514480000e-118*P1+(-0.8749760000e-119-0.1804820000e-321*I)*P1)*exp(.3241750000*x)-.3452350000*P1-122592.0000*(-0.1786260000e-5*P1+(-0.1032000000e-5-0.2128710000e-208*I)*P1)*exp(-.3241750000*x)-122592.0000*(-0.4187610000e-118*P1+(-0.2419350000e-118-0.4990430000e-321*I)*P1)*exp(.3241750000*x)+(-1418.53000+4162.04000*I)*((0.4917830000e-19+0.4447520000e-18*I)*P1-0.7235760000e-18*P1)*exp((0.4177290000e-1+0.3632460000e-1*I)*x)+(-1418.53000+4162.04000*I)*((-0.1863270000e-4+0.5295610000e-4*I)*P1+0.2767260000e-3*P1)*exp((-0.4177290000e-1-0.3632460000e-1*I)*x)+(-153846.0000-0.3369490000e-197*I)*((-0.1281530000e-6-0.3642240000e-6*I)*P1+0.1903280000e-5*P1)*exp((-0.4177290000e-1+0.3632460000e-1*I)*x)+(-1418.53000-4162.04000*I)*((-0.1863270000e-4-0.5295610000e-4*I)*P1+0.2767260000e-3*P1)*exp((-0.4177290000e-1+0.3632460000e-1*I)*x)+(-153846.0000+0.3369490000e-197*I)*((-0.1281530000e-6+0.3642240000e-6*I)*P1+0.1903280000e-5*P1)*exp((-0.4177290000e-1-0.3632460000e-1*I)*x)+(-153846.0000+0.3369490000e-197*I)*((0.3382410000e-21+0.3058930000e-20*I)*P1-0.4976640000e-20*P1)*exp((0.4177290000e-1+0.3632460000e-1*I)*x)+(0.1207210000e-219+0.7888590000e-220*I)*((-0.4289690000e204+0.2495970000e203*I)*P1+0.6356420000e205*P1)*exp((0.4177290000e-1-0.3632460000e-1*I)*x)+(-.4530570000-0.9345270000e-203*I)*P1+(-0.1855630000e-2749+0.7257480000e-2749*I)*((-0.3431750000e2734+0.1996780000e2733*I)*P1+0.5085140000e2735*P1)*exp((0.4177290000e-1-0.3632460000e-1*I)*x))^2.00000+6.00000*(-225126.0000*(-0.1786260000e-5*P1+(-0.1032000000e-5-0.2128710000e-208*I)*P1)*exp(-.3241750000*x)+225126.0000*(-0.4187610000e-118*P1+(-0.2419350000e-118-0.4990430000e-321*I)*P1)*exp(.3241750000*x)+(1791.00000-522.31000*I)*((-0.1863270000e-4+0.5295610000e-4*I)*P1+0.2767260000e-3*P1)*exp((-0.4177290000e-1-0.3632460000e-1*I)*x)+(-1791.00000+522.31000*I)*((0.4917830000e-19+0.4447520000e-18*I)*P1-0.7235760000e-18*P1)*exp((0.4177290000e-1+0.3632460000e-1*I)*x)+(1791.00000+522.31000*I)*((-0.1863270000e-4-0.5295610000e-4*I)*P1+0.2767260000e-3*P1)*exp((-0.4177290000e-1+0.3632460000e-1*I)*x)+(0.2067430000e-2749+0.2413910000e-2749*I)*((-0.3431750000e2734+0.1996780000e2733*I)*P1+0.5085140000e2735*P1)*exp((0.4177290000e-1-0.3632460000e-1*I)*x))^2.00000)^(1/2)-250.

(1)

NULL

with(plots, implicitplot, complexplot)

[implicitplot, complexplot]

(2)

 

implicitplot(FF, x = 0 .. 200, P1 = 0 .. 800)

 

NULL

 

NULL

Download PLOT11.mw

In the attached file, I would like to determine the real part of the complex term2. I'm asking for your help.test.mw

restart

term1 := exp(I*t/2^k)

exp(I*t/2^k)

(1)

term2 := product(term1, k = 1 .. n)

(cos(2*t*(1/2)^(n+1))-I*sin(2*t*(1/2)^(n+1)))/(cos(t)-I*sin(t))

(2)

``

Download test.mw

The problem seems to be more with the editor than the MultiSet, but I can't think of a way how to ask the question outside of this context (I am very much not a programmer). MultiSet is a set with multiplicities, i.e. each of its element can belong more than once, for example

constructs MultiSet with a appearing twice, b - five times, and c - four times. Remove is the operation of removing element from a MultiSet, possibly with prescribed multiplicity, for example in

we asked Maple to remove three of b's, and therefore the MultiSet M was left with only two of them (the lone 2 in the output says how many are left, then M is displayed to ilustrate that). Both screenshots are taken from the linked maplesoft page on Remove.

However, when I repeat the same example on Maple 2025 (on a PC), I get something quite different

so that b is deleted from M altogether. I checked that this does not happen on Maple 2019 on another PC. While writing this question and playing with other examples of the same kind, I noticed (viewing what Maple stores in memory) that it seems that "Remove(M,b,3)" is executed twice whenever the cursor enters its line (without me executing it, and without producing output). The same happens with Insert. When I don't touch the line (e.g. if Remove is inside of a loop), everythig works as expected.

It seems that if a command directly changes an object (i.e. I don't need to redefine said object) then Maple executes it silently whenever the cursor touches it. I can't think of other commands that directly change objects (again, not a programmer, can't even think how to phrase it correctly). The question is as in the title: why and how Maple 2025 does that? I did check for options that look like enabling automatic execution but found nothing active and/or related. Any help will be much appreciated.

Suppose I have a variable (a) and I want it to print true in red if it is greater than one and false in blue otherwise. What would be the corresponding code?

i don't know how plot thus system and how is gonna give me the best shape sometime they add cos term and sometime they add sin term which i don't know the different between them the 2D and 3D even when i change the interval of t is not give me one of thus type  picture and i used the same parameter and i don't know where is problem?

restart;

with(plots):

K[1] := 2/`ξ__1`^2; K[2] := (2*`ξ__1`*`γ__1`*`γ__2`+`ξ__2`*`γ__1`^2-`ξ__3`)/(`ξ__1`^2*`ξ__2`)

2/xi__1^2

 

(2*xi__1*gamma__1*gamma__2+xi__2*gamma__1^2-xi__3)/(xi__1^2*xi__2)

(1)

`ξ__1` := 1; `ξ__2` := 1; `ξ__3` := 1; `γ__1` := 2.2; `γ__2` := 1; epsilon := 2.8; theta := 1

1

 

1

 

1

 

2.2

 

1

 

2.8

 

1

(2)

de1 := diff(u(t),t) = v(t);
de2 := diff(v(t),t) = - K[1]*u(t)^3 + K[2]*u(t) + epsilon*sin(theta*t);

diff(u(t), t) = v(t)

 

diff(v(t), t) = -2*u(t)^3+8.24*u(t)+2.8*sin(t)

(3)

ic := u(0)=0, v(0)=0;

u(0) = 0, v(0) = 0

(4)

dsol := dsolve({de1,de2,ic}, numeric);

proc (x_rkf45) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x_rkf45) else _xout := evalf(x_rkf45) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _pars := []; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 28, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..65, {(1) = 2, (2) = 2, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 17, (19) = 30000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0, (64) = -1, (65) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 0.30058408214858914e-1, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..2, {(1) = .1, (2) = .1}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = 0, (2) = 0}, datatype = integer[8]), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = 0, (2) = 0}, datatype = integer[8])]), ( 8 ) = ([Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..2, {(1, 1) = .0, (1, 2) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = u(t), Y[2] = v(t)]`; YP[2] := -2*Y[1]^3+8.24*Y[1]+2.8*sin(X); YP[1] := Y[2]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, 0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = u(t), Y[2] = v(t)]`; YP[2] := -2*Y[1]^3+8.24*Y[1]+2.8*sin(X); YP[1] := Y[2]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 27 ) = (""), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0), ( 28 ) = (0)  ] ))  ] ); _y0 := Array(0..2, {(1) = 0., (2) = 0.}); _vmap := array( 1 .. 2, [( 1 ) = (1), ( 2 ) = (2)  ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); _i := false; if _par <> [] then _i := `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then _i := `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) or _i end if; if _i then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch:  end try else try procname(procname("right")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch:  end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if elif type(_xin, `=`) and lhs(_xin) = "setdatacallback" then if not type(rhs(_xin), 'nonegint') then error "data callback must be a nonnegative integer (address)" end if; _dtbl[1][28] := rhs(_xin) else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error  end try; if _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(0..0, {}), (3) = [t, u(t), v(t)], (4) = []}); _vars := _dat[3]; _pars := map(lhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol := 1; _ndsol := _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_rkf45) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error  end try end proc

(5)

odeplot(dsol, [[t, u(t)], [t,v(t)]], t=0..12*Pi,
        color=["Red", "Green"], size=[600,300], thickness=2);

 

odeplot(dsol, [u(t),v(t)], t=0..12*Pi, color="Blue");

 

odeplot(dsol, [t, u(t), v(t)], t=0..12*Pi, color="Blue", axes=framed);

 

odeplot(dsol, [u(t),v(t)], t=0..12*Pi, color="Blue", frames=100);

 

NULL

NULL

chaotic-2.mw

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