Questions - MaplePrimes

singularity error in dsolve...

Asked by: torabi 60

February 15 2019

0 1

how I can remove this error in dsolve?

Error, (in dsolve/numeric/bvp) singularity encountered
dsolv.mw

I do not know how to do these.i need help...

Asked by: kyawhan 5

February 15 2019

1 3

Given these functions identify their symmetries:

a) f(x)=4x^2-1/2

b)s(t)=t^3-4t

c) g(k)=-|2k-7|

d) x-y^2=3

e) h(a)=1/a-1

How can decrease the evaluation time of NLPSolve o...

Asked by: Gillee 47

February 15 2019

2 2

Hi,

I am trying to curve fit data using NLPSolve. I noticed that the evaluation time for NLPSolve seems really long. Did I mess up in using NLPSolve?

Thanks you for any suggests or comments.

restart; kernelopts(version); interface(version); multithread_capability := kernelopts(multithreaded); Number_of_CPUs := kernelopts(numcpus)

(1)

"#` How` can I decrease the evaluation time of NLPSolve or are there better methods"?"" ""

SoS:=proc(E0::float,E00::float,alpha::float,beta:: float)::float;

	Experimental Data

Enter Initial Guesses for HN equation

(2.1)

Run Optimizer

[0.648163470800135894e-2, Vector[column](%id = 18446747242105787086)]

(3.1)

Plot Wicket Plot with Optimized HN Parameters

(4.1)

Download HN_fit_of_DMA_data_ss_proc_v5a.mw

A remark about Statistics:-Sampling(..., method=[e...

Asked by: mmcdara 420

February 15 2019

1 8

Hi,

Recently a few questions concerning the sampling of the Cauchy distribution and the sampling of a truncated Normal distribution have been posted (mainly by @jalale).
This post is concerned by the sampling of a truncated (standard) Cauchy distribution.

In a first part the efficiency fo two methods is adressed in the case of a non-truncated Cauchy distribution:

The "standard" Maple's command Statistics:-Sample(Cauchy(0, 1), N)
And a general method a priori very efficient if one knows the ICDF (Inverse Cumulative Function Distribution). It happens that this ICDF is just cot(U*Pi) where U is a Uniform RV over [0, 1].

The second part adresses the sampling of a truncatedCauchy distribution with two methods:

The "standard" Maple's command Statistics:-Sample(Cauchy(0, 1), N, method=[envelope, range=...])
The method based on the use of the ICDF

Results:

Test1 (non-truncated Cauchy distribution)

"Standard" Maples sampling outperforms the ICDF based method in terms of :
- memory occupation: ICDF is twice more demanding
- cpu time: ICDF is ten times slower

Test2 (truncated Cauchy distribution)

ICDF based method i outperforms "Standard" Maples sampling oin terms of :
- memory occupation: Maples "envelope sampling" method is twice more demanding
- cpu time: Maples "envelope sampling" method is two times slower

But, beyond these simple observations, a disturbing problem is: the "envelope sampling" method seems to not return the correct distribution (at least when used this waymethod=[envelope, range=a..b] with a < b)
This is confirmed by the two last plot where histogram and PDF are uperimposed.

Do you think this problem can be avoided by another parameterization of the "envelope sampling" method or that it reveals some underlying problem with it?

PS: I did not investigate further for other distributions .

>

Sampling the Cauchy distribution

Maple's default sampling method outperformes the adhoc method

>

restart

>	with(Statistics):

>	C := RandomVariable(Cauchy(0, 1))

(1)

>	f := unapply(CDF(C, t), t);

(2)

>	finv := unapply(-solve(f(t)=u, t), u)

(3)

>	# "natural" way to proceed N := 10^6: S1 := CodeTools:-Usage(Sample(C, N)):

memory used=7.71MiB, alloc change=39.63MiB, cpu time=69.00ms, real time=69.00ms, gc time=8.72ms

>	# Let's try the sampling strategy based on the inverse of the CDF # Usually it starts from sampling a Uniform RV on [0, 1] and # next applies finv to the result. # # Smart but inefficient U := RandomVariable(Uniform(0., 1)): S2 := CodeTools:-Usage(finv~(Sample(U, N))):

memory used=145.02MiB, alloc change=7.63MiB, cpu time=4.94s, real time=3.04s, gc time=2.61s

>	# Much more efficient # # Given the special form of finv it's simpler to sample a Unirorm RV # on [0, Pi] and apply "cot" to the result pi := evalf(Pi): U := RandomVariable(Uniform(0., pi)): S2 := CodeTools:-Usage(cot~(Sample(U, N))):

memory used=15.28MiB, alloc change=0 bytes, cpu time=652.00ms, real time=237.00ms, gc time=577.78ms

Sampling a truncated Cauchy distribution

Example 1:
with(Statistics) + method=[envelope, range=-10..10]

The adhoc method outperforms Maple's default sampling method

>	S1 := CodeTools:-Usage(Sample(C, N, method=[envelope, range=-10..10])): Histogram(S1);

memory used=8.88MiB, alloc change=-7.63MiB, cpu time=322.00ms, real time=260.00ms, gc time=93.77ms

>	p := Probability(C < -10, numeric); q := 1-Probability(C > +10, numeric); U := RandomVariable(Uniform(ppi, qpi)): S2 := CodeTools:-Usage(cot~(Sample(U, N))): Histogram(S2);

memory used=15.28MiB, alloc change=7.63MiB, cpu time=170.00ms, real time=113.00ms, gc time=92.11ms

Sampling a truncated Cauchy distribution

Example 2:
with(Statistics) + method=[envelope, range=-1..1]

The adhoc method outperformes Maple's default sampling method

>	S1 := CodeTools:-Usage(Sample(C, N, method=[envelope, range=-1..1])): scaling := Probability(C < +1, numeric) - Probability(C < -1, numeric); plots:-display( Histogram(S1), plot(PDF(C, t)/scaling, t=-1..1, thickness=3, color=red) );

memory used=8.08MiB, alloc change=0 bytes, cpu time=246.00ms, real time=215.00ms, gc time=46.62ms

>	p := Probability(C < -1, numeric); q := 1-Probability(C > +1, numeric); U := RandomVariable(Uniform(ppi, qpi)): S2 := CodeTools:-Usage(cot~(Sample(U, N))): plots:-display( Histogram(S2), plot(PDF(C, t)/scaling, t=-1..1, thickness=3, color=red) );

memory used=15.28MiB, alloc change=7.63MiB, cpu time=163.00ms, real time=106.00ms, gc time=85.93ms

>

Download CAUCHY_adhoc-sampling.mw

Laplacian and Euler Lagrange equation...

Asked by: maple2015 105

February 15 2019

1 0

Hi

Please download the attachment.

I try to find a relation between EL and Lap(EL) in polar coordinate for one variable function w(r), where Lap is laplacian and EL is Euler Lagrange equation. Please check the Maple code and help me to do some manipulations to find a general relation (if any relation exists!).

In fact I need the inverse of Euler Lagrange equation to obtain f(r) for an arbitrary function g(r) in equation below

EL(f) = Lap(EL(g))

Or f=inverseEL(Lap(EL(g)))

Thank you for taking your time

Download EL.mw

How to perform cumulative summation of an integral...

Asked by: Haqphy12015 10

February 14 2019

1 11

Dear Experts,

I am new user. I need your help!

I have numerical values of omega (w) and a2F(w) (500 rows). I need to do cumulative summation to get lambda(w) using lambd=2 int (a2F(w)/w dw). Please help me how can I do it?

Best Wishes,

Enamul Haque

The fastest and concise way to implement a discret...

Asked by: emendes 120

February 14 2019

3 16

Hello

I am revising the unstable period orbits of the Logistic map, y[n]=4*y[n-1]*(1-y[n]), in Maple. Although I have implemented the equation and use a loop for the iterations, I wonder whether there is a faster and concise way to code the equation in Maple.

Here it is what I did:

y[0] := (-sqrt(5)+5)*(1/8);

for n to 10 do y[n] := 4*y[n-1]*(1-y[n-1]) end do;
soly := [seq(simplify(expand(y[n]), radical), n = 0 .. 10)];
dat := [seq([n, Re(evalf(soly[n]))], n = 1 .. 10)]; plot(dat, labels = ["k", "x(k)"], style = pointline,title="Period 2");

Since only few iterations are needed, the solution is symbolic (and then convert to float).

Many thanks.

Ed

Ordinary differential equations...

Asked by: Gabriel samaila 15

February 14 2019

0 16

Hi guys,

This is the first time of solving partial differential equation, can some please help me point out some errows in my code.

>

ODEs := `<,>`(diff(v(y), y, y)+(diff(v(y), y))/y-(Ha^2/(1-eta)^2+1/y^2)*v(y)-Re*v(y)*(diff(v(y), y)) = 0, diff(theta(y), y, y)+Ec*Pr*(diff(v(y), y)-v(y)/y)^2-Pr*Re*v(y)*(diff(theta(y), y))+Nb*(diff(theta(y), y))*(diff(phi(y), y))+Nt*(diff(theta(y), y))^2 = 0, diff(phi(y), y, y)-Re*Sc*v(y)*(diff(phi(y), y))+Nt*(diff(theta(y), y, y)+(diff(theta(y), y))/y)/Nb = 0)

$ODEs := Matrix(3, 1, {(1, 1) = diff(diff(v(y), y), y)+(diff(v(y), y))/y-(Ha^2/(1-eta)^2+1/y^2)*v(y)-Re*v(y)*(diff(v(y), y)) = 0, (2, 1) = diff(diff(theta(y), y), y)+Ec*Pr*(diff(v(y), y)-v(y)/y)^2-Pr*Re*v(y)*(diff(theta(y), y))+Nb*(diff(theta(y), y))*(diff(phi(y), y))+Nt*(diff(theta(y), y))^2 = 0, (3, 1) = diff(diff(phi(y), y), y)-Re*Sc*v(y)*(diff(phi(y), y))+Nt*(diff(diff(theta(y), y), y)+(diff(theta(y), y))/y)/Nb = 0})$

(1)

>

BCs := Matrix(6, 1, {(1, 1) = phi(eta) = 1, (2, 1) = v(eta) = 1, (3, 1) = theta(eta) = 1, (4, 1) = phi(1) = 0, (5, 1) = theta(1) = 0, (6, 1) = v(1) = 0})

(2)

>

param_names := [eta, Ha, Ec, Nt, Nb, Re, Sc, Pr];

(3)

>

$pdSolve := subs(_P = param_names, proc ({ eta::realcons := .5, Ha::realcons := 1, Sc::realcons := .8, Nt::realcons := .1, Nb::realcons := .1, Re::realcons := 2, Ec::realcons := 0.1e-1, Pr::realcons := 10 }) userinfo(1, Solve, `~`[`=`](param_names, _P)); dsolve(eval(`union`(convert(ODEs, set), convert(BCs, set)), `~`[`=`](param_names, _P)), numeric) end proc);$

$proc ({ Ec::realcons := 0.1e-1, Ha::realcons := 1, Nb::realcons := .1, Nt::realcons := .1, Pr::realcons := 10, Re::realcons := 2, Sc::realcons := .8, eta::realcons := .5 }) userinfo(1, Solve, `~`[`=`](param_names, [eta, Ha, Ec, Nt, Nb, Re, Sc, Pr])); dsolve(eval(`union`(convert(ODEs, set), convert(BCs, set)), `~`[`=`](param_names, [eta, Ha, Ec, Nt, Nb, Re, Sc, Pr])), numeric) end proc$

(4)

>

Fig. 3 (changing values of Ha):

>

P:= Ha:
vals:= [1, 5, 10, 20]:
sols:= [seq(Solve(P= v), v= vals)]:
colors:= [red, green, blue]:
for F in [v,theta,phi](y) do
   print(plots:-display(
      [seq(
         plots:-odeplot(sols[k], [y,F], color= colors[k], legend= [P= vals[k]]),
         k= 1..nops(vals)
      )],
      labeldirections= [horizontal,vertical]
   ))
od:

Error, pdeplot is not a command in the plots package

>

Download chapter5.mw

Difference Quotient...

Asked by: rjerome 5

February 14 2019

1 2

How can I use Maple to solve a difference quotient problem? How do I enter the basic difference quotient formula and the quadratic equation to be used in the problem?

How can I optimize the given nonlinear system equa...

Asked by: mamehrashi 0

February 14 2019

0 11

1.47449729919434*10^10*c[0, 1]*c[0, 2]*c[2, 2]*c[3, 0]+3.38624318440755*10^8*c[0, 1]*c[0, 3]*c[1, 0]*c[2, 1]+1.54309415817260*10^10*c[0, 1]*c[0, 3]*c[1, 3]*c[2, 0]+1.69527735464914*10^14*c[0, 2]*c[0, 3]*c[1, 3]*c[3, 3]+5.64571777979530*10^11*c[0, 1]*c[1, 3]*c[3, 0]*c[3, 1]+5.64571777979530*10^11*c[0, 1]*c[1, 1]*c[3, 0]*c[3, 3]+3.44365358352662*10^11*c[0, 1]*c[1, 1]*c[3, 1]*c[3, 2]+4.56141047477722*10^11*c[0, 1]*c[0, 2]*c[2, 1]*c[3, 3]+1.47449729919434*10^10*c[0, 1]*c[0, 2]*c[2, 0]*c[3, 2]+1.00292015075684*10^10*c[0, 1]*c[0, 2]*c[2, 1]*c[3, 1]+4.96419365552208*10^14*c[1, 1]*c[2, 3]*c[3, 1]*c[3, 2]+2.41547661753786*10^16*c[1, 1]*c[2, 3]*c[3, 2]*c[3, 3]+3.09237360954284*10^11*c[0, 2]*c[1, 1]*c[1, 3]*c[3, 1]+2.07077209298372*10^13*c[0, 2]*c[2, 2]*c[2, 3]*c[3, 0]+2.77395036220550*10^11*c[0, 2]*c[1, 1]*c[1, 2]*c[3, 2]+3.25883571082134*10^15*c[1, 2]*c[2, 3]*c[3, 1]*c[3, 2]+2.77442234357198*10^11*c[0, 2]*c[1, 1]*c[2, 1]*c[2, 3]+7.80736282336175*10^14*c[2, 0]*c[2, 1]*c[3, 2]*c[3, 3]+3.25883571082134*10^15*c[1, 2]*c[2, 2]*c[3, 1]*c[3, 3]+5.35593751087840*10^15*c[1, 2]*c[2, 3]*c[3, 0]*c[3, 3]+3.63255405301248*10^15*c[1, 1]*c[2, 3]*c[3, 1]*c[3, 3]+3.25883571082134*10^15*c[1, 2]*c[2, 1]*c[3, 2]*c[3, 3]+1.48022406855142*10^13*c[1, 0]*c[2, 1]*c[2, 2]*c[3, 3]+5.19766484559825*10^15*c[0, 1]*c[2, 3]*c[3, 2]*c[3, 3]+3.63255405301248*10^15*c[1, 3]*c[2, 1]*c[3, 1]*c[3, 3]+1.03156027712140*10^14*c[0, 3]*c[1, 2]*c[1, 3]*c[2, 3]+6.84418565576730*10^13*c[1, 1]*c[1, 2]*c[1, 3]*c[3, 3]+1.36253689407226*10^13*c[0, 1]*c[1, 2]*c[2, 3]*c[3, 2]+4.50722523384354*10^11*c[0, 1]*c[0, 2]*c[1, 2]*c[3, 3]+4.63272867590191*10^14*c[1, 1]*c[1, 3]*c[2, 3]*c[3, 2]+9.56722337372450*10^9*c[0, 1]*c[0, 2]*c[1, 2]*c[1, 3]+7.56283392524430*10^14*c[0, 3]*c[1, 1]*c[2, 3]*c[3, 3]+1.51879056084535*10^13*c[0, 3]*c[1, 1]*c[2, 3]*c[3, 1]+8.15436050904650*10^14*c[1, 1]*c[2, 3]*c[3, 0]*c[3, 3]+1.51879056084535*10^13*c[0, 1]*c[1, 1]*c[2, 3]*c[3, 3]+3.05712170936082*10^11*c[0, 1]*c[1, 1]*c[1, 3]*c[2, 3]+2.21942429315476*10^9*c[0, 1]*c[0, 2]*c[1, 0]*c[3, 2]+1.50960286458333*10^9*c[0, 1]*c[0, 2]*c[1, 1]*c[3, 1]+6.37602806091310*10^9*c[0, 1]*c[1, 1]*c[1, 2]*c[1, 3]+2.22015380859375*10^7*c[0, 0]*c[1, 0]*c[1, 1]*c[3, 0]+2.24812825520834*10^6*c[0, 0]*c[0, 1]*c[1, 0]*c[2, 1]+2.24812825520834*10^6*c[0, 0]*c[0, 1]*c[1, 1]*c[2, 0]+4.45556640625000*10^5*c[0, 0]*c[0, 1]*c[0, 2]*c[1, 0]+1.80236816406250*10^7*c[0, 0]*c[0, 2]*c[0, 3]*c[1, 0]+9.99813988095240*10^6*c[0, 1]*c[1, 0]*c[1, 1]*c[2, 0]+1.64310515873016*10^7*c[0, 0]*c[0, 1]*c[1, 0]*c[3, 1]+1.09924316406250*10^7*c[0, 0]*c[0, 1]*c[0, 2]*c[1, 2]+1.22578938802084*10^7*c[0, 0]*c[0, 1]*c[0, 3]*c[1, 1]+6.74438476562500*10^5*c[0, 0]*c[0, 1]*c[1, 0]*c[2, 0]+3.27484130859375*10^7*c[0, 0]*c[0, 1]*c[2, 0]*c[3, 0]+4.96419365552208*10^14*c[1, 1]*c[2, 2]*c[3, 1]*c[3, 3]+1.48022406855142*10^13*c[1, 2]*c[2, 0]*c[2, 1]*c[3, 3]+1.48022406855142*10^13*c[1, 2]*c[2, 0]*c[2, 3]*c[3, 1]+7.00457388588595*10^14*c[1, 2]*c[2, 0]*c[2, 3]*c[3, 3]+9.01806926154510*10^12*c[1, 2]*c[2, 1]*c[2, 2]*c[3, 1]+4.26195329427362*10^14*c[1, 1]*c[2, 2]*c[2, 3]*c[3, 2]+8.70017911044035*10^14*c[1, 1]*c[3, 0]*c[3, 2]*c[3, 3]+1.64960358855012*10^13*c[1, 2]*c[1, 3]*c[3, 0]*c[3, 1]+8.70017911044035*10^14*c[1, 3]*c[3, 0]*c[3, 1]*c[3, 2]+4.11701503132284*10^16*c[1, 3]*c[3, 0]*c[3, 2]*c[3, 3]+1.32823657812862*10^13*c[2, 0]*c[2, 1]*c[2, 2]*c[2, 3]+2.49782355477406*10^13*c[0, 1]*c[0, 3]*c[3, 1]*c[3, 3]+1.86077008928572*10^7*c[0, 0]*c[0, 1]*c[0, 2]*c[0, 3]+4.50750425170068*10^11*c[0, 3]*c[1, 2]*c[1, 3]*c[2, 0]+2.41765159606934*10^10*c[0, 0]*c[0, 2]*c[2, 0]*c[3, 3]+1.28155946659681*10^15*c[2, 0]*c[2, 3]*c[3, 0]*c[3, 3]+7.80736282336175*10^14*c[2, 0]*c[2, 3]*c[3, 1]*c[3, 2]+2.95015059452266*10^13*c[2, 0]*c[2, 3]*c[3, 0]*c[3, 1]+1.64424324035644*10^10*c[0, 1]*c[0, 3]*c[2, 0]*c[3, 1]+7.80736282336175*10^14*c[2, 0]*c[2, 2]*c[3, 1]*c[3, 3]+3.38624318440755*10^8*c[0, 1]*c[0, 3]*c[1, 1]*c[2, 0]+6.83811849201320*10^14*c[0, 2]*c[2, 1]*c[2, 3]*c[3, 3]+4.96419365552208*10^14*c[1, 1]*c[2, 1]*c[3, 2]*c[3, 3]+4.50722523384354*10^11*c[0, 1]*c[0, 2]*c[1, 3]*c[3, 2]+2.74640085129511*10^12*c[0, 3]^2*c[1, 3]*c[3, 0]+4.53797990504672*10^10*c[0, 2]^2*c[2, 0]*c[2, 3]+2.76260943995885*10^10*c[0, 2]^2*c[2, 1]*c[2, 2]+5.63905988420760*10^10*c[0, 3]^2*c[1, 0]*c[3, 1]+2.74640085129511*10^12*c[0, 3]^2*c[1, 0]*c[3, 3]+5.63905988420760*10^10*c[0, 3]^2*c[1, 1]*c[3, 0]+1.67039675031390*10^12*c[0, 3]^2*c[1, 1]*c[3, 2]+1.67039675031390*10^12*c[0, 3]^2*c[1, 2]*c[3, 1]

Why is the sign incorrect when I differentiate a c...

Asked by: struckmeier 15

February 13 2019

3 3

When I try to calculate the derivative of a covariant metric with respect to the corresponding contravariant metric, or vice versa, the result is correct up to the sign, which is wrong:

diff(g_[nu, tau], g_[~mu, ~eta]);

Maple's result: g_[eta, nu] g_[mu, tau]

Correct result: -g_[eta, nu] g_[mu, tau]

diff(g_[~nu, ~tau], g_[mu, eta]);

Maple's result: g_[~eta, ~nu] g_[~mu, ~tau]

Correct result: -g_[~eta, ~nu] g_[~mu, ~tau]

I've loaded DifferentialGeometry, Tensor, Physics. Is this my fault, or Maple's?

Which code is more useful for embedded plot compon...

Asked by: Ramakrishnan 274

February 13 2019

3 5

Dear friends,

I have attached a document with two commands in slider0 for plotting the same graph in two plot components.
use DocumentTools in
a := Do(%Slider0/100);
b := Do(%Slider1/100);
Do(%Plot0 = plot(sin(a*x)+cos(b*x^2),x=0..10,y=-3..3));
SetProperty("Plot1",value,plot(sin(a*x)+cos(b*x^2),x=0..10,y=-3..3));
end use;

I am just curious to know which one is better and when?

Download DoubtOnLatestCodesinEmbeddedPlot.mw

Thanks for answers.

Ramakrishnan V

how to get multi kink solution from function is it...

Asked by: bashar27 10

February 13 2019

0 2

restart;
A[0] := 0;
0
A[1] := sqrt(2*(k[1]^2-w[1]^2))/n;
(1/2)
/ 2 2\
\2 k[1] - 2 w[1] /
------------------------
n
A[2] := sqrt(2*(k[2]^2-w[2]^2))/n;
(1/2)
/ 2 2\
\2 k[2] - 2 w[2] /
------------------------
n
c[1] := 1;
1
c[2] := 1;
1
c[3] := 1;
1
c[4] := 1;
1
c[5] := 1;
1
c[6] := 1;
1
k[1] := 10.5;
10.5
k[2] := 3.5;
3.5
w[1] := 5.05;
5.05
w[2] := .5;
0.5
m := 1.9;
1.9
n := 1.75;
1.75
xi[1] := -t*w[1]+x*k[1];
-5.05 t + 10.5 x
xi[2] := -t*w[2]+x*k[2];
-0.5 t + 3.5 x
a := m/sqrt(2*(k[1]^2-w[1]^2));
0.1459402733
b := m/sqrt(k[2]^2-w[2]^2);
0.5484827558
g := a*(c[2]*exp(a*xi[1])+c[3]*exp(-a*xi[1]));
0.1459402733 exp(-0.7369983802 t + 1.532372870 x)

+ 0.1459402733 exp(0.7369983802 t - 1.532372870 x)
h := c[1]+c[2]*exp(a*xi[1])+c[3]*exp(-a*xi[1]);
1 + exp(-0.7369983802 t + 1.532372870 x)

+ exp(0.7369983802 t - 1.532372870 x)
G := b*(c[5]*exp(b*xi[2])+c[6]*exp(-b*xi[2]));
0.5484827558 exp(-0.2742413779 t + 1.919689645 x)

+ 0.5484827558 exp(0.2742413779 t - 1.919689645 x)
H := c[4]+c[5]*exp(b*xi[2])+c[6]*exp(-b*xi[2]);
1 + exp(-0.2742413779 t + 1.919689645 x)

+ exp(0.2742413779 t - 1.919689645 x)
u := A[0]+A[1]*[g/h]+A[2]*[G/H];
[(2.799416849 (0.5484827558 exp(-0.2742413779 t + 1.919689645 x)

+ 0.5484827558 exp(0.2742413779 t - 1.919689645 x)))/(1

+ exp(-0.2742413779 t + 1.919689645 x)

+ exp(0.2742413779 t - 1.919689645 x)) + (7.439442594

(0.1459402733 exp(-0.7369983802 t + 1.532372870 x)

+ 0.1459402733 exp(0.7369983802 t - 1.532372870 x)))/(1

+ exp(-0.7369983802 t + 1.532372870 x)

+ exp(0.7369983802 t - 1.532372870 x))]
plot3d(u, x = -20 .. .20, t = -20 .. .20);

t := 0;
0
plot(u, x = -15 .. 15);

Error, (in plot) found points with fewer or more than 2 components

help for get some good figure...

Asked by: bashar27 10

February 13 2019

0 1

fgure set 1;
Error, missing operation
Typesetting:-mambiguous(fgure Typesetting:-mambiguous(set 1,

Typesetting:-merror("missing operation")))
restart;
l := 4;
4
m := 1;
1
n := 2;
2
k := 1/sqrt(-6*beta*l^2+24*beta*m*n);
1
----------------
(1/2)
4 (-3 beta)
w := alpha/(5*beta*sqrt(l^2-4*m*n));
(1/2)
alpha 2
------------
20 beta

B[0] := -(1/25)*alpha*(5*l^3/(5*sqrt(l^2-4*m*n))-20*l*m*n/(5*sqrt(l^2-4*m*n))-l^2+2*m*n)*sqrt(-6*beta*l^2+24*beta*m*n)*(5*sqrt(l^2-4*m*n))/((l^2-4*m*n)^2*beta);
/ (1/2) \ (1/2) (1/2)
alpha \8 2 - 12/ (-3 beta) 2
- -------------------------------------------
40 beta
B[1] := -(12/5)*m*alpha*(5*l/(5*sqrt(l^2-4*m*n))-1)/sqrt(-6*beta*l^2+24*beta*m*n);
/ (1/2) \
3 alpha \2 - 1/
- --------------------
(1/2)
5 (-3 beta)
B[2] := -12*m^2*alpha/(sqrt(-6*beta*l^2+24*beta*m*n)*(5*sqrt(l^2-4*m*n)));
(1/2)
3 alpha 2
- -----------------
(1/2)
20 (-3 beta)
theta := sqrt(l^2-4*m*n);
(1/2)
2 2
xi[0] := 1;
1
F := -l/(2*m)-theta*tanh((1/2)*theta*(xi+xi[0]))/(2*m);
(1/2) / (1/2) \
-2 - 2 tanh\2 (xi + 1)/
beta := -2;
-2
alpha := -3;
-3

1

xi := k*x-t*w;
1 (1/2) 3 (1/2)
-- 6 x - -- t 2
24 40
u := B[0]+B[1]*F+B[2]*F*F;
3 / (1/2) \ (1/2) (1/2) 3 / (1/2) \ (1/2) /
- -- \8 2 - 12/ 6 2 + -- \2 - 1/ 6 |-2
80 10 \

(1/2) / (1/2) /1 (1/2) 3 (1/2) \\\ 3
- 2 tanh|2 |-- 6 x - -- t 2 + 1||| + --
\ \24 40 /// 40

(1/2) (1/2)
6 2

2
/ (1/2) / (1/2) /1 (1/2) 3 (1/2) \\\
|-2 - 2 tanh|2 |-- 6 x - -- t 2 + 1|||
\ \ \24 40 ///
plot3d(u, x = -30 .. .30, t = -30 .. .30);

t := 0;
0
plot([u], x = -30 .. 30);

case2222;
case2222
restart;
l := 2;
2
m := 1;
1
n := 2;
2
k := 1/sqrt(-6*beta*l^2+24*beta*m*n);
(1/2)
6
------------
(1/2)
12 beta
w := alpha/(5*beta*sqrt(l^2-4*m*n));
1
-- I alpha
10
- ----------
beta

B[0] := -(1/25)*alpha*(5*l^3/(5*sqrt(l^2-4*m*n))-20*l*m*n/(5*sqrt(l^2-4*m*n))-l^2+2*m*n)*sqrt(-6*beta*l^2+24*beta*m*n)*(5*sqrt(l^2-4*m*n))/((l^2-4*m*n)^2*beta);
(1/2)
alpha 6
------------
(1/2)
5 beta
B[1] := -(12/5)*m*alpha*(5*l/(5*sqrt(l^2-4*m*n))-1)/sqrt(-6*beta*l^2+24*beta*m*n);
/1 1 \ (1/2)
|- + - I| alpha 6
\5 5 /
----------------------
(1/2)
beta
B[2] := -12*m^2*alpha/(sqrt(-6*beta*l^2+24*beta*m*n)*(5*sqrt(l^2-4*m*n)));
1 (1/2)
-- I alpha 6
10
-----------------
(1/2)
beta
theta := sqrt(l^2-4*m*n);
2 I
xi[0] := 1;
1
C := -2;
-2
F := -l/(2*m)-theta*tanh((1/2)*theta*xi)/(2*m)+sech((1/2)*theta*xi)/(C*cosh((1/2)*theta*xi)-2*m*sinh((1/2)*theta*xi)/theta);
sec(xi)
-1 + tan(xi) + --------------------
-2 cos(xi) - sin(xi)

beta := -2;
-2
alpha := 3;
3

xi := k*x-t*w;
1 (1/2) (1/2) 3
- -- 6 (-2) x - -- I t
24 20
u := B[0]+B[1]*F+B[2]*F*F;
3 (1/2) (1/2) / 3 3 \ (1/2) (1/2) /
- -- 6 (-2) + |- -- - -- I| 6 (-2) |-1
10 \ 10 10 / \

/1 (1/2) (1/2) 3 \ / /1 (1/2)
- tan|-- 6 (-2) x + -- I t| + |sec|-- 6
\24 20 / \ \24

(1/2) 3 \\// /1 (1/2) (1/2) 3 \
(-2) x + -- I t|| |-2 cos|-- 6 (-2) x + -- I t|
20 // \ \24 20 /

/1 (1/2) (1/2) 3 \\\ 3 (1/2)
+ sin|-- 6 (-2) x + -- I t||| - -- I 6
\24 20 /// 20

(1/2) / /1 (1/2) (1/2) 3 \ / /1
(-2) |-1 - tan|-- 6 (-2) x + -- I t| + |sec|--
\ \24 20 / \ \24

(1/2) (1/2) 3 \\//
6 (-2) x + -- I t|| |
20 // \
/1 (1/2) (1/2) 3 \
-2 cos|-- 6 (-2) x + -- I t|
\24 20 /

/1 (1/2) (1/2) 3 \\\
+ sin|-- 6 (-2) x + -- I t|||^2
\24 20 ///
plot3d(Re(u), x = -30 .. .30, t = -30 .. .30);

t := 0;
0
plot([Re(u)], x = -30 .. 30);

plot3d(Im(u), x = -10 .. .10, t = -10 .. .10);
Error, (in plot3d) bad range arguments: x = -10 .. .10, 0 = -10 .. .10
t := 0;
0
plot([Im(u)], x = -30 .. 30);

fgure set 2;
Error, missing operation
Typesetting:-mambiguous(fgure Typesetting:-mambiguous(set 2,

Typesetting:-merror("missing operation")))
restart;
l := 4;
4
m := 1;
1
n := 2;
2
k := 1/sqrt(6*beta*l^2-24*beta*m*n);
(1/2)
3
------------
(1/2)
12 beta
w := alpha/((5*sqrt(l^2-4*m*n))*beta);
(1/2)
alpha 2
------------
20 beta

B[0] := (1/25)*alpha*(5*l^3/(5*sqrt(l^2-4*m*n))-20*l*m*n/(5*sqrt(l^2-4*m*n))+l^2-6*m*n)*sqrt(6*beta*l^2-24*beta*m*n)*(5*sqrt(l^2-4*m*n))/((l^2-4*m*n)^2*beta);
/ (1/2) \ (1/2) (1/2)
alpha \8 2 + 4/ 3 2
----------------------------------
(1/2)
40 beta
B[1] := -(12/5)*m*alpha*(5*l/(5*sqrt(l^2-4*m*n))-1)/sqrt(6*beta*l^2-24*beta*m*n);
/ (1/2) \ (1/2)
alpha \2 - 1/ 3
- -------------------------
(1/2)
5 beta
B[2] := -12*m^2*alpha/(sqrt(6*beta*l^2-24*beta*m*n)*(5*sqrt(l^2-4*m*n)));
(1/2) (1/2)
alpha 3 2
- -------------------
(1/2)
20 beta

1 (1/2)
-- I alpha 6
10
-----------------
(1/2)
beta
theta := sqrt(l^2-4*m*n);
(1/2)
2 2
xi[0] := 1;
1
F := -l/(2*m)-theta*tanh((1/2)*theta*(xi+xi[0]))/(2*m);
(1/2) / (1/2) \
-2 - 2 tanh\2 (xi + 1)/
beta := -2;
-2
alpha := -3;
-3

1

xi := k*x-t*w;
1 (1/2) (1/2) 3 (1/2)
- -- 3 (-2) x - -- t 2
24 40
u := B[0]+B[1]*F+B[2]*F*F;
3 / (1/2) \ (1/2) (1/2) (1/2) 3 / (1/2) \
-- \8 2 + 4/ (-2) 3 2 - -- \2 - 1/
80 10

(1/2) (1/2) /
3 (-2) |-2
\

(1/2) / (1/2) / 1 (1/2) (1/2) 3 (1/2)
- 2 tanh|2 |- -- 3 (-2) x - -- t 2
\ \ 24 40

\\\ 3 (1/2) (1/2) (1/2) /
+ 1||| - -- 3 (-2) 2 |-2
/// 40 \

(1/2) / (1/2) / 1 (1/2) (1/2) 3 (1/2)
- 2 tanh|2 |- -- 3 (-2) x - -- t 2
\ \ 24 40

\\\
+ 1|||^2
///
plot3d(Re(u), x = -30 .. .30, t = -30 .. .30);
Error, (in plot3d) bad range arguments: x = -30 .. .30, 0 = -30 .. .30
t := 0;
0
plot([Re(u)], x = -30 .. 30);

plot3d(Im(u), x = -1 .. 1, t = -1 .. 1);
Error, (in plot3d) bad range arguments: x = -1 .. 1, 0 = -1 .. 1
t := 0;
0
plot([Im(u)], x = -30 .. 30);

case2222;
case2222
restart;
l := 2;
2
m := 1;
1
n := 2;
2
k := 1/sqrt(-6*beta*l^2+24*beta*m*n);
(1/2)
6
------------
(1/2)
12 beta
w := alpha/(5*beta*sqrt(l^2-4*m*n));
1
-- I alpha
10
- ----------
beta

B[0] := -(1/25)*alpha*(5*l^3/(5*sqrt(l^2-4*m*n))-20*l*m*n/(5*sqrt(l^2-4*m*n))-l^2+2*m*n)*sqrt(-6*beta*l^2+24*beta*m*n)*(5*sqrt(l^2-4*m*n))/((l^2-4*m*n)^2*beta);
(1/2)
alpha 6
------------
(1/2)
5 beta
B[1] := -(12/5)*m*alpha*(5*l/(5*sqrt(l^2-4*m*n))-1)/sqrt(-6*beta*l^2+24*beta*m*n);
/1 1 \ (1/2)
|- + - I| alpha 6
\5 5 /
----------------------
(1/2)
beta
B[2] := -12*m^2*alpha/(sqrt(-6*beta*l^2+24*beta*m*n)*(5*sqrt(l^2-4*m*n)));
1 (1/2)
-- I alpha 6
10
-----------------
(1/2)
beta
theta := sqrt(l^2-4*m*n);
2 I
xi[0] := 1;
1
C := -2;
-2
F := -l/(2*m)-theta*tanh((1/2)*theta*xi)/(2*m)+sech((1/2)*theta*xi)/(C*cosh((1/2)*theta*xi)-2*m*sinh((1/2)*theta*xi)/theta);
sec(xi)
-1 + tan(xi) + --------------------
-2 cos(xi) - sin(xi)

beta := -2;
-2
alpha := 3;
3

xi := k*x-t*w;
1 (1/2) (1/2) 3
- -- 6 (-2) x - -- I t
24 20
u := B[0]+B[1]*F+B[2]*F*F;
3 (1/2) (1/2) / 3 3 \ (1/2) (1/2) /
- -- 6 (-2) + |- -- - -- I| 6 (-2) |-1
10 \ 10 10 / \

/1 (1/2) (1/2) 3 \ / /1 (1/2)
- tan|-- 6 (-2) x + -- I t| + |sec|-- 6
\24 20 / \ \24

(1/2) 3 \\// /1 (1/2) (1/2) 3 \
(-2) x + -- I t|| |-2 cos|-- 6 (-2) x + -- I t|
20 // \ \24 20 /

/1 (1/2) (1/2) 3 \\\ 3 (1/2)
+ sin|-- 6 (-2) x + -- I t||| - -- I 6
\24 20 /// 20

(1/2) / /1 (1/2) (1/2) 3 \ / /1
(-2) |-1 - tan|-- 6 (-2) x + -- I t| + |sec|--
\ \24 20 / \ \24

(1/2) (1/2) 3 \\//
6 (-2) x + -- I t|| |
20 // \
/1 (1/2) (1/2) 3 \
-2 cos|-- 6 (-2) x + -- I t|
\24 20 /

/1 (1/2) (1/2) 3 \\\
+ sin|-- 6 (-2) x + -- I t|||^2
\24 20 ///
plot3d(Re(u), x = -30 .. .30, t = -30 .. .30);

t := 0;
0
plot([Re(u)], x = -30 .. 30);

plot3d(Im(u), x = -10 .. .10, t = -10 .. .10);
Error, (in plot3d) bad range arguments: x = -10 .. .10, 0 = -10 .. .10
t := 0;
0
plot([Im(u)], x = -30 .. 30);

Sets????...

Asked by: tomleslie 4000

February 13 2019

0 2

You use curly braces, ie '{}' as a container. Within Maple such curly braces designate a set, and Maple will always display sets in "lexicographic" order.

Since order has no meaning for entries in a set, trying to "sort" a set is meaningless. You can only sort lists, Arrays etc where the concept of order meaningful

See the attached for examples of sorting sets, lists, Arrays, and note that sorting of sets doesn't do anything useful

For future reference

This should be a "Question", not a "Post" (and if I knew how to move it I would!)
When posting on this site, try to avoid using third party sites like dropbox. Upload code (not pictures of code) using the big green up-arrow in the Mapleprimes toolbar

>

  restart;
  alpha:=[2,3,4,5];
#
# Try sorting sets - won't work because
# order is meaningless in a set
#
  sort( {abs(alpha[1]-30),abs(alpha[2]-30),abs(alpha[3]-30),abs(alpha[4]-30)}, `<`);
  whattype(%);
  sort( {abs(alpha[1]-30),abs(alpha[2]-30),abs(alpha[3]-30),abs(alpha[4]-30)}, `>`);
  whattype(%);
#
# Do the same thing with lists, where order is significant
#
  sort( [abs(alpha[1]-30),abs(alpha[2]-30),abs(alpha[3]-30),abs(alpha[4]-30)], `<`);
  whattype(%);
  sort( [abs(alpha[1]-30),abs(alpha[2]-30),abs(alpha[3]-30),abs(alpha[4]-30)], `>`);
  whattype(%);
#
# You can also sort entries in an Array()
#
  sort(Array([abs(alpha[1]-30),abs(alpha[2]-30),abs(alpha[3]-30),abs(alpha[4]-30)]), `<`);
  whattype(%);
  sort(Array([abs(alpha[1]-30),abs(alpha[2]-30),abs(alpha[3]-30),abs(alpha[4]-30)]), `>`);
  whattype(%);