I want to define a piecewise function. How do I test if a variable t is in a definite open or closed real range?

I am using the smart plot (i.e plot without giving the x=from..to) since I am generating these plots programmatically and better let Maple figure the best range to use.

But found Maple hangs on some solutions.

Here is an example

restart;
sol:=1/2/cos(x)*(sin(x)^2+(sin(x)^4+36*cos(x))^(1/2));
plot(sol);

I waited for 30 minutes and nothing happened.

If I change the above command to 

plot(sol,x=-Pi..Pi);

then it finishes instantly. It looks like Maple is stuck trying to find correct x and y ranges to use.

Is this known limitation  or smart plot or is this a bug?

Maple 2024.1 on windows 10.

What exactly is the difference between the differential operator d_[] from the physics package and diff() ? Why is it not possible for me to differentiate a scalar function g or a coordinate r with the help of the operator? d_[1] should correspond to d/dx (X = (x, y, z, t)) or not? 

Download example_d_[].mw

restart;
with(Plot);
params := {alpha = 2.5, k = 3, w = 2, beta[3] = 3, beta[4] = 1.7};
xi := beta[3]*(2*alpha*k*t + x)*sqrt(1/(36*alpha*beta[4] + 36*gamma*beta[4]));
params := {alpha = 2.5, k = 3, w = 2, beta[3] = 3, beta[4] = 1.7}

          xi := beta[3] (2 alpha k t + x) 

                                                 (1/2)
            /                 1                 \     
            |-----------------------------------|     
            \36 alpha beta[4] + 36 gamma beta[4]/     


sol1n := u(x, t) = U(xi)*exp((-sqrt(1/(36*alpha*beta[4] + 36*gamma*beta[4]))*x + w*t + theta)*I);
                     /                          
                     |                          
 sol1n := u(x, t) = U|beta[3] (2 alpha k t + x) 
                     \                          

                                        (1/2)\    /  /
   /                 1                 \     |    |  |
   |-----------------------------------|     | exp|I |
   \36 alpha beta[4] + 36 gamma beta[4]/     /    \  \
                                       (1/2)                \\
  /                 1                 \                     ||
 -|-----------------------------------|      x + w t + theta||
  \36 alpha beta[4] + 36 gamma beta[4]/                     //



plot3d(rhs(sol1n), x = 0 .. 250, t = 0 .. 4);

how plot the the solution of PDE of this kind of function?

Download plot.mw

Hello

Here is the ODE

sys := {diff(w(t), t) = y(t)*z(t), diff(x(t), t) = a*w(t), diff(y(t), t) = x(t)*z(t) + w(t), diff(z(t), t) = -x(t)*y(t), w(0) = w0, x(0) = x0, y(0) = y0, z(0) = z0}

with initial parameters a=2, w0 = -0.727367040, x0 = -0.728244724, y0 = -0.237753623 and z0 = 0.014225402.

With these parameters I have no problem to plot the solution.

nsys := subs({a=2,w0 = -0.727367040, x0 = -0.728244724, y0 = -0.237753623, z0 = 0.014225402},sys);

numsol := dsolve(nsys, numeric, method = rkf45);

vars:=[x,y,z,w];

with(plots):

col := [red, magenta, cyan, blue]:
display(
  seq(
    plots:-odeplot(numsol, [t, vars[i](t)], t=0..3, color=col[i], legend=vars[i](t))
    , i=1..numelems(vars)
  )
)

How to use animate (or explore?)  with a slider for each parameter (a,x0,y0,z0,w0)? And if I want to add a tfinal as well for the simulation (in place of 3)? ( I am newbie as far as using plot and related functions in Maple).  

Many thanks. 

sometimes (not often) I get this pop-up window when I open new worksheet and run something first time in it.

And it can last for 10-20 seconds until connection is made.

I have my preferences set to  create new engine for each worksheet.

The strange thing when this happened now, is that I only had 4 worksheets open and was not running anything in any of them. So Maple was not "busy". Task manage showed 8 mservers.exe processes on it at the time. Which is not unormal.

I have 128 GB and PC was not busy at the time this happened.

Any idea what can cause this to happen?

Windows 10 home edition, Maple 2024.1

When making this plot, using smart plot (i.e. not giving the plot command the x=from..to and also not giving it y=from...to

p:=plot(0,color=red);

I need to programatically find the x=-10..10 and y=-1..1 from the variable p. But if I do

rhs~(indets(p, identical("originalview")=anything));

it gives

              {[-10. .. 10., 0. .. 0.]}

But clearly looking at the plot the y axis is from -1..1

The reason I need to determine the view from the above plot, is that I need to use same view windows size in another plot not using smart plot (phase plot) which requires one to provide explicit x and y ranges. i.e I'd like the phase plot to have same view size in terms of x range and y range.

I printed the PLOT structure but do not see another field to look at. 

Any idea or trick to find y=-1..1 values in this example ? I am using Maple 2024.1

lprint(p)
PLOT(CURVES(Matrix(200,2,{(1, 1) = -10., (2, 1) = -9.89484789949749, (3, 1) = 
-9.80335561909548, (4, 1) = -9.70046298090452, (5, 1) = -9.59688830351759, (6,
1) = -9.49380589849246, (7, 1) = -9.39823531356784, (8, 1) = -9.29927750854271,
(9, 1) = -9.19693520502513, (10, 1) = -9.09492111457286, (11, 1) = 
-8.98998708341709, (12, 1) = -8.89756113165829, (13, 1) = -8.79351140100503, (
14, 1) = -8.6890344321608, (15, 1) = -8.58835151356784, (16, 1) = 
-8.49692177788945, (17, 1) = -8.38820297889447, (18, 1) = -8.29610389547739, (
19, 1) = -8.18897076683417, (20, 1) = -8.09413979497487, (21, 1) = 
-7.99009518894472, (22, 1) = -7.89102011959799, (23, 1) = -7.78764567839196, (
24, 1) = -7.69271567135678, (25, 1) = -7.59032083417085, (26, 1) = 
-7.4839613758794, (27, 1) = -7.39137515477387, (28, 1) = -7.29137949949749, (29
, 1) = -7.18807420301508, (30, 1) = -7.08701012462312, (31, 1) = 
-6.9892254321608, (32, 1) = -6.88065220301508, (33, 1) = -6.78309432763819, (34
, 1) = -6.67893047236181, (35, 1) = -6.58454253768844, (36, 1) = 
-6.48135159396985, (37, 1) = -6.38425695778894, (38, 1) = -6.28276508643216, (
39, 1) = -6.18353823115578, (40, 1) = -6.07965690954774, (41, 1) = 
-5.97960685025126, (42, 1) = -5.87729121407035, (43, 1) = -5.77582280301507, (
44, 1) = -5.68258387135678, (45, 1) = -5.57572153366834, (46, 1) = 
-5.48014258492462, (47, 1) = -5.37823549045226, (48, 1) = -5.28069739798995, (
49, 1) = -5.17239388140703, (50, 1) = -5.07861099396985, (51, 1) = 
-4.97216657788945, (52, 1) = -4.87515404824121, (53, 1) = -4.76903758693467, (
54, 1) = -4.67747702713568, (55, 1) = -4.57320023718593, (56, 1) = 
-4.47247400603015, (57, 1) = -4.37181357688442, (58, 1) = -4.27152345929648, (
59, 1) = -4.17517605326633, (60, 1) = -4.07102195577889, (61, 1) = 
-3.97175554874372, (62, 1) = -3.86728232964824, (63, 1) = -3.77270890854271, (
64, 1) = -3.66818757386935, (65, 1) = -3.56807434874372, (66, 1) = 
-3.46820480201005, (67, 1) = -3.36389067336683, (68, 1) = -3.26781355276382, (
69, 1) = -3.16941743919598, (70, 1) = -3.06077643819095, (71, 1) = 
-2.96241091055276, (72, 1) = -2.86181373366834, (73, 1) = -2.7595089959799, (74
, 1) = -2.66547103417085, (75, 1) = -2.5652296120603, (76, 1) = 
-2.46575123417085, (77, 1) = -2.35934029145729, (78, 1) = -2.26543724422111, (
79, 1) = -2.15709262110553, (80, 1) = -2.05931995175879, (81, 1) = 
-1.96257900603015, (82, 1) = -1.85855141105528, (83, 1) = -1.75410300301508, (
84, 1) = -1.65907041708543, (85, 1) = -1.5581500321608, (86, 1) = -1.4596616, (
87, 1) = -1.35289910050251, (88, 1) = -1.26051985527638, (89, 1) = 
-1.15441893366834, (90, 1) = -1.05467848944724, (91, 1) = -.955901429145728, (
92, 1) = -.857045790954773, (93, 1) = -.756219297487437, (94, 1) = 
-.649344903517589, (95, 1) = -.551351549748743, (96, 1) = -.454619526633167, (
97, 1) = -.351214585929648, (98, 1) = -.248034748743718, (99, 1) = 
-.155424717587939, (100, 1) = -.0457214572864313, (101, 1) = .0460731437185924,
(102, 1) = .153437240201004, (103, 1) = .255905869346734, (104, 1) = 
.347398149748743, (105, 1) = .4502907879397, (106, 1) = .553865465326634, (107,
1) = .656947870351759, (108, 1) = .752518455276382, (109, 1) = .851476260301508
, (110, 1) = .953818563819095, (111, 1) = 1.05583265427136, (112, 1) = 
1.16076668542714, (113, 1) = 1.25319263718593, (114, 1) = 1.3572423678392, (115
, 1) = 1.46171933668342, (116, 1) = 1.56240225527638, (117, 1) = 
1.65383199095477, (118, 1) = 1.76255078994975, (119, 1) = 1.85464987336683, (
120, 1) = 1.96178300201005, (121, 1) = 2.05661397386935, (122, 1) = 
2.1606585798995, (123, 1) = 2.25973364924623, (124, 1) = 2.36310809045226, (125
, 1) = 2.45803809748744, (126, 1) = 2.56043293467337, (127, 1) = 
2.66679239296482, (128, 1) = 2.75937861407035, (129, 1) = 2.85937426934673, (
130, 1) = 2.96267956582914, (131, 1) = 3.06374364422111, (132, 1) = 
3.16152833668342, (133, 1) = 3.27010156582915, (134, 1) = 3.36765944120603, (
135, 1) = 3.47182329648241, (136, 1) = 3.56621123115578, (137, 1) = 
3.66940217487437, (138, 1) = 3.76649681105528, (139, 1) = 3.86798868241206, (
140, 1) = 3.96721553768844, (141, 1) = 4.07109685929648, (142, 1) = 
4.17114691859297, (143, 1) = 4.27346255477387, (144, 1) = 4.37493096582915, (
145, 1) = 4.46816989748744, (146, 1) = 4.57503223517588, (147, 1) = 
4.6706111839196, (148, 1) = 4.77251827839196, (149, 1) = 4.87005637085427, (150
, 1) = 4.97835988743719, (151, 1) = 5.07214277487437, (152, 1) = 
5.17858719095477, (153, 1) = 5.27559972060302, (154, 1) = 5.38171618190955, (
155, 1) = 5.47327674170854, (156, 1) = 5.57755353165829, (157, 1) = 
5.67827976281407, (158, 1) = 5.7789401919598, (159, 1) = 5.87923030954774, (160
, 1) = 5.97557771557789, (161, 1) = 6.07973181306533, (162, 1) = 
6.1789982201005, (163, 1) = 6.28347143919598, (164, 1) = 6.37804486030151, (165
, 1) = 6.48256619497488, (166, 1) = 6.5826794201005, (167, 1) = 
6.68254896683417, (168, 1) = 6.78686309547739, (169, 1) = 6.8829402160804, (170
, 1) = 6.98133632964824, (171, 1) = 7.08997733065327, (172, 1) = 
7.18834285829146, (173, 1) = 7.28894003517588, (174, 1) = 7.39124477286432, (
175, 1) = 7.48528273467337, (176, 1) = 7.58552415678392, (177, 1) = 
7.68500253467337, (178, 1) = 7.79141347738694, (179, 1) = 7.88531652462311, (
180, 1) = 7.9936611477387, (181, 1) = 8.09143381708543, (182, 1) = 
8.18817476281407, (183, 1) = 8.29220235778895, (184, 1) = 8.39665076582915, (
185, 1) = 8.49168335175879, (186, 1) = 8.59260373668342, (187, 1) = 
8.69109216884422, (188, 1) = 8.79785466834171, (189, 1) = 8.89023391356784, (
190, 1) = 8.99633483517588, (191, 1) = 9.09607527939699, (192, 1) = 
9.1948523396985, (193, 1) = 9.29370797788945, (194, 1) = 9.39453447135678, (195
, 1) = 9.50140886532663, (196, 1) = 9.59940221909548, (197, 1) = 
9.69613424221106, (198, 1) = 9.79953918291458, (199, 1) = 9.9027190201005, (200
, 1) = 10.},datatype = float[8],storage = rectangular,order = Fortran_order,
shape = []),COLOUR(RGB,.47058824,0.,.54901961e-1,_ATTRIBUTE("source" = 
"mathdefault"))),AXESLABELS("",""),VIEW(-10. .. 10.,DEFAULT,_ATTRIBUTE("source"
= "mathdefault")),_ATTRIBUTE("input" = [table([(1)=plot,(2)=[0]]), 
"originalview" = [-10. .. 10., 0. .. 0.], "originalaxesticks" = AXESTICKS(
DEFAULT,DEFAULT,_ATTRIBUTE("source" = "mathdefault"))]))

Update

This below is a proc that takes PLOT data struct and returns correct x,y ranges.  It seems to work ok on few tests I did. Bug reports are welcome.

Download get_x_y_range.mw

Update

Warning.  plottools:-getdata(p,'rangesonly') is buggy. I replaced this with 

                  rhs~(indets(p, identical("originalview")=anything))[];

which gives more accurate Y ranges used. Here is example showing that getdata(p,'rangesonly') returns wrong y ranges for a plot compared to how it shows on the screen, So in the function above, better use the second method instead. This whole getdata(p,'rangesonly'); should be looked at by Maplesoft and fix to make it return correct values that agrees with screen view.

Download fixed_plot_Y_range.mw

Hi 

I teach Pre-Calulus High School level, and our school recently upgraded to Maple 2024. Like in Maple 2023 we use Assistant-Tools-import DATA and chosing an Excel file from which to import to do regression on.  In the new 2024 we have experienced, that Maple cannot read in DATA, meaning it cannot read column of DATA into a Maple document. However if we copy into Excel document on the machine locally, then there is no issue and the data is imported. 

Any idear what can cause this?  

before run file remove all (:) i want calculate equation but with a condition for example: when a=4 then find other parameter in my equation with respect to a=4 find other

usesol.mw

sigma1:=10^(-5):sigma2:=10^(5):sigma3:=3.7*10^(6):alpha:=5*10^(-7):beta1:=0.5*10^(-4):beta2:=0.5*10^(-4):beta3:=0.5*10^(-4):ky:=1:kz:=10^4:mu1:=10:mu2:=11:mu3:=0.86:mu4:=0.2:mu5:=1:v1:=0.5:v2:=1:alphaa:=0.6:alphas:=0.24:alphad:=0.16:A:=0.5:mus:=0.17:k:=0.2:#parameters 
dsys:={diff(x1(t),t)=sigma1*y(t)-beta1*x1(t)*y(t)/(ky+x1(t)+x2(t))-v1*x1(t)-mu1*x1(t)+(2*alphad+alphaa)*k*A*S(t),diff(x2(t),t)=v1*x1(t)-beta2*x2(t)*y(t)/(ky+x1(t)+x2(t))+alpha*v2*x1(t)*z(t)-mu2*x2(t),diff(y(t),t)=sigma2*(beta1*x1(t)*y(t)/(ky+x1(t)+x2(t))+beta2*x2(t)*y(t)/(ky+x1(t)+x2(t)))-mu4*y(t)-mu5*y(t)^2,diff(z(t),t)=sigma3+y(t)*beta3/(kz+y(t))-mu3*z(t)-v2*z(t)*x2(t),diff(S(t),t)=(k*(alphas-alphad)-mus)*S(t) }; #SYS ODE

rhs; with(DEtools);# to find the equilibrium points
fx1 = sigma1*y-beta1*x1*y-v1*x1-mu1*x1+(2*alphad+alphaa)*k*A*s; fx2 = alpha*v2*x1*z-beta2*x2*y-mu2*x2+v1*x1; fy = sigma2*(beta1*x1*y+beta2*x2*y)-mu4*y-mu5*y^2; fz = sigma3+y*(kz+y)-mu3*z-v2*z*x2; fs = (k*(alphas-alphad)-mus)*s;

eqs := solve({fs, fx1, fx2, fy, fz}, {s, x1, x2, y, z})

L := map(subs, [eqs], [x1, x2, y, z, s])

J := unapply(VectorCalculus:-Jacobian([fx1, fx2, fy, fz, fs], [x1, x2, y, z, s]), x1, x2, y, z, s); J(x1, x2, y, z, s)

Verification_known_T_R_30_07_2024.mw That`s the worksheet.

For some strange reason the command simplify doesn`t work. Beforehand it managed to simplify quite bulky expressions.

Thank you in advance!

I would like to solve this system of differential equations y_1 , y_2. However, there should be no exact solutions for this problem. Is there a way to get a numerical solution of such coupled equations in maple and if so, how? I know the dsolve() command, but it did not work here. The boundary conditions are f(0)-1 = K(0) = 0 and f'(inf) = K'(inf) = 0. It would be nice if someone could help me or tell me where to look to solve something like this.

Download coupled_deq.mw

Recently there have been some questions about the unit packages. I would like to add another one that has been on my desk for a while.

The Simple environement overloads the command frem and piecewise. The "most powerful" (can we say so?) environement Standard does not

{with(Units:-Simple)[]} minus {with(Units:-Standard)[]}
                       {frem, piecewise}

For example calculating the remainder of a length in mm does not work in the Standard environment

restart;
with(Units:-Simple):
convert(frem(1.234*Unit(m),Unit(cm)),units,mm);
                      4.000000000 Unit(mm)

restart;
with(Units:-Standard):
convert(frem(1.234*Unit(m),Unit(cm)),units,mm)
Error, invalid input: frem received 1.234*Units:-Unit(m), which is not valid for its 1st argument, x

Why is that?

In the Programming Guide, Ch. 3 "Maple Expressions", subsection 3.13 "Other Expressions" there is a section called "Composition".

There is the following snippet

In particular, although the inverses of the circular functions are commonly denoted by a power-like notation in written mathematics, in Maple, for example, sin^(-1) denotes the reciprocal of the sin function, while sin@@(-1) denotes the arcsine (arcsin).

I opened a new worksheet to check this. I found the results confusing.

Consider (1) and (2). 

(1) is in accordance with the quoted snippet: sin^(-1) is the reciprocal of the sine function. But when we use this same expression as a function call, the function that is called is arcsine. Does this make sense to be this way?

Next, consider (3), (4), and (5), which I expected to be the same expressions as (1), (2) and (2), respectively. The only difference is that (1) and (2) use 2D math and (3), (4), and (5) use Maple input.

Both results using Maple input give as output the reciprocal of sine.

Why is there this difference between the 2D version and the Maple input version?

Consider (4) and (5). Why is it that we need to add parentheses for the argument x to be applied to the function?

Finally, what is the reasoning behind the syntax sin@@(-1) denoting arcsine?

@@ represents repeated composition. sin@@3 represents the function sin(sin(sin))). 

Is sin@@(-1) equal to arcsine simply by convention or is there some logical reason?

Download Repeated_Composition.mw