Maple Questions and Posts

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

Asked by: emendes 395

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 35

February 14 2019

1 24

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 70

February 13 2019

3 4

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 399

February 13 2019

3 6

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 55

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 55

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);

An issue with package Tolerances...

Asked by: sand15 765

February 13 2019

0 11

Hi,
I face a problem using Tolerances:-NominalValue and Tolerances:-ToleranceValue on a quantity constructed from add.

Example

restart:
with(Tolerances):
x := 10 &+-1:
y := 20 &+- 2:
z := 3*x+2*y;
NominalValue(z); # returns 70 as expected
ToleranceValue(z); # returns 7 as expected

Now I define another quantity Z this way:

Z := add([3, 2] *~ [x, y]);
(or equivalently add(ListOfCoeffs[k]*ListOfVars[k], k=1..K) where ListOfCoeffs and ListOfVars are previously defined adhoc lists)

Both NominalValue(Z) and ToleranceValue(Z) return an error.
PS: already (and this probably explains that) Z does not appear as 70 +/- 7 but as 3*Interval(...)+2*Interval(...) (lprint confirmed)

How can I obtain NominalValue(Z) and ToleranceValue(Z) when Z comes from 'add' constructor?

2D contour plot and legend

by: acer 29759 Product: Maple

February 12 2019

15 1

There have been several posts, over the years, related to visual cues about the values associated with particular 2D contours in a plot.

Some people ask or post about color-bars [1]. Some people ask or post about inlined labelling of the curves [1, 2, 3, 4, 5, 6, 7]. And some post about mouse popup/hover-over functionality [1]., which got added as general new 2D plot annotation functionality in Maple 2017 and is available for the plots:-contourplot command via its contourlabels option.

Another possibility consists of a legend for 2D contour plots, with distinct entries for each contour value. That is not currently available from the plots:-contourplot command as documented. This post is about obtaining such a legend.

Aside from the method used below, a similar effect may be possible (possibly with a little effort) using contour-plotting approaches based on individual plots:-implicitplot calls for each contour level. Eg. using Kitonum's procedure, or an undocumented, alternate internal driver for plots:-contourplot.

Since I like the functionality provided by the contourlabels option I thought that I'd highjack that (and the _HOVERCONTENT plotting substructure that plot-annotations now generate) and get a relatively convenient way to get a color-key via the 2D plotting legend. This is not supposed to be super-efficient.

Here below are some examples. I hope that it illustrates some useful functionality that could be added to the contourplot command. It can also be used to get a color-key for use with densityplot.

>

restart;

>

contplot:=proc(ee, rng1, rng2)
  local clabels, clegend, i, ncrvs, newP, otherdat, others, tcrvs, tempP;
  (clegend,others):=selectremove(type,[_rest],identical(:-legend)=anything);
  (clabels,others):= selectremove(type,others,identical(:-contourlabels)=anything);
  if nops(clegend)>0 then
    tempP:=:-plots:-contourplot(ee,rng1,rng2,others[],
                                ':-contourlabels'=rhs(clegend[-1]));
    tempP:=subsindets(tempP,'specfunc(:-_HOVERCONTENT)',
                      u->`if`(has(u,"null"),NULL,':-LEGEND'(op(u))));
    if nops(clabels)>0 then
      newP:=plots:-contourplot(ee,rng1,rng2,others[],
                              ':-contourlabels'=rhs(clabels[-1]));
      tcrvs:=select(type,[op(tempP)],'specfunc(CURVES)');
      (ncrvs,otherdat):=selectremove(type,[op(newP)],'specfunc(CURVES)');
      return ':-PLOT'(seq(':-CURVES'(op(ncrvs[i]),op(indets(tcrvs[i],'specfunc(:-LEGEND)'))),
                          i=1..nops(ncrvs)),
                      op(otherdat));
    else
      return tempP;
    end if;
  elif nops(clabels)>0 then
    return plots:-contourplot(ee,rng1,rng2,others[],
                              ':-contourlabels'=rhs(clabels[-1]));
  else
    return plots:-contourplot(ee,rng1,rng2,others[]);
  end if;
end proc:

>	contplot(x^2+y^2, x=-2..2, y=-2..2, coloring=["Yellow","Blue"], contours = 9, size=[500,400], legendstyle = [location = right], legend=true, contourlabels=true, view=[-2.1..2.1,-2.1..2.1] );

>	contplot(x^2+y^2, x=-2..2, y=-2..2, coloring=["Yellow","Blue"], contours = 17, size=[500,400], legendstyle = [location = right], legend=['contourvalue',$("null",7),'contourvalue',$("null",7),'contourvalue'], contourlabels=true, view=[-2.1..2.1,-2.1..2.1] );

>

# Apparently legend items must be unique, to persist on document re-open.

contplot(x^2+y^2, x=-2..2, y=-2..2,
      coloring=["Yellow","Blue"],
      contours = 11,
      size=[500,400],
      legendstyle = [location = right],
      legend=['contourvalue',seq(cat($(` `,i)),i=2..5),
              'contourvalue',seq(cat($(` `,i)),i=6..9),
              'contourvalue'],
      contourlabels=true,
      view=[-2.1..2.1,-2.1..2.1]
);

>	contplot(x^2+y^2, x=-2..2, y=-2..2, coloring=["Green","Red"], contours = 8, size=[400,450], legend=true, contourlabels=true );

>	contplot(x^2+y^2, x=-2..2, y=-2..2, coloring=["Yellow","Blue"], contours = 13, legend=['contourvalue',$("null",5),'contourvalue',$("null",5),'contourvalue'], contourlabels=true );

>

(low,high,N):=0.1,7.6,23:
conts:=[seq(low..high*1.01, (high-low)/(N-1))]:
contplot(x^2+y^2, x=-2..2, y=-2..2,
      coloring=["Yellow","Blue"],
      contours = conts,
      legend=['contourvalue',$("null",floor((N-3)/2)),'contourvalue',$("null",ceil((N-3)/2)),'contourvalue'],
      contourlabels=true
);

>

plots:-display(
  subsindets(contplot((x^2+y^2)^(1/2), x=-2..2, y=-2..2,
                      coloring=["Yellow","Blue"],
                      contours = 7,
                      filledregions),
             specfunc(CURVES),u->NULL),
  contplot((x^2+y^2)^(1/2), x=-2..2, y=-2..2,
      coloring=["Yellow","Blue"],
      contours = 7, #grid=[50,50],
      thickness=0,
      legendstyle = [location=right],
      legend=true),
  size=[600,500],
  view=[-2.1..2.1,-2.1..2.1]
);

>

plots:-display(
  contplot(x^2+y^2, x=-2..2, y=-2..2,
      coloring=["Yellow","Blue"],
      contours = 5,
      thickness=0, filledregions),
  contplot(x^2+y^2, x=-2..2, y=-2..2,
      coloring=["Yellow","Blue"],
      contours = 5,
      thickness=3,
      legendstyle = [location=right],
      legend=typeset("<=",contourvalue)),
  size=[700,600],
  view=[-2.1..2.1,-2.1..2.1]
);

>

N:=11:
plots:-display(
  contplot(sin(x)*y, x=-2*Pi..2*Pi, y=-1..1,
      coloring=["Yellow","Blue"],
      contours = [seq(-1+(i-1)*(1-(-1))/(N-1),i=1..N)],
      thickness=3,
      legendstyle = [location=right],
      legend=true),
   plots:-densityplot(sin(x)*y, x=-2*Pi..2*Pi, y=-1..1,
      colorscheme=["zgradient",["Yellow","Blue"],colorspace="RGB"],
      grid=[100,100],
      style=surface, restricttoranges),
   plottools:-line([-2*Pi,-1],[-2*Pi,1],thickness=3,color=white),
   plottools:-line([2*Pi,-1],[2*Pi,1],thickness=3,color=white),
   plottools:-line([-2*Pi,1],[2*Pi,1],thickness=3,color=white),
   plottools:-line([-2*Pi,-1],[2*Pi,-1],thickness=3,color=white),
   size=[600,500]
);

>

N:=13:
plots:-display(
  contplot(sin(x)*y, x=-2*Pi..2*Pi, y=-1..1,
      coloring=["Yellow","Blue"],
      contours = [seq(-1+(i-1)*(1-(-1))/(N-1),i=1..N)],
      thickness=6,
      legendstyle = [location=right],
      legend=['contourvalue',seq(cat($(` `,i)),i=2..3),
              'contourvalue',seq(cat($(` `,i)),i=5..6),
              'contourvalue',seq(cat($(` `,i)),i=8..9),
              'contourvalue',seq(cat($(` `,i)),i=11..12),
              'contourvalue']),
   plots:-densityplot(sin(x)*y, x=-2*Pi..2*Pi, y=-1..1,
      colorscheme=["zgradient",["Yellow","Blue"],colorspace="RGB"],
      grid=[100,100],
      style=surface, restricttoranges),
   plottools:-line([-2*Pi,-1],[-2*Pi,1],thickness=6,color=white),
   plottools:-line([2*Pi,-1],[2*Pi,1],thickness=6,color=white),
   plottools:-line([-2*Pi,1],[2*Pi,1],thickness=6,color=white),
   plottools:-line([-2*Pi,-1],[2*Pi,-1],thickness=6,color=white),
  size=[600,500]
);

>

Download contour_legend_post.mw

How to delay command execution until variables are...

Asked by: EB1000 35

February 12 2019

0 1

Hellow

I want to create a function that sort an array with a parametric variable alpha[k]. But Maple ignores the sort command, so the array never gets sorted. Please see attached url to creen capture of the problem:

https://www.dropbox.com/s/gjy5zbm4gjwmwdv/sort.png?dl=0

Thnaks

Maple not processing math lines in worksheet...

Asked by: patrickl13 5

February 12 2019

1 2

Hi everyone, my question is how do I get maple to process these commands. It is currently not evaluating them, and output is also similar to the image above. This occurs when I open a workbook from my Professor, all the math commands that are already inserted into the worksheet output this when I try to execute them.

I have found a workaround, I simply copy and paste the code in a new command line but this is tedious and I was wondering if anyone knew how to fix this.

Thanks!

Refuse de travailler !...

Asked by: JAMET 375

February 12 2019

2 3

Fract := proc(P::posint, Q::posint)
local p,q:
for p from 1 to P-1 do
for q from 1 to Q-1 do
if (P-p)*q-P*(Q-q)=1 the return (p/q,(P-p)/(Q-q): fi:
od:od:
end;
  debug(Fract);
Fract(5, 13);
Fract(77, 200);

How can print seq op...

Asked by: minhhieuh2003 135

February 11 2019

0 7

How can type

[

Download op_seq.mw

seq('op'('S['i'])',i=1..5)]

export

[op(S[1]), op(S[2],op(S[3],op(S[4])]

Please help me

How to implicitplot3d multiple functions with diff...

Asked by: apepper 5

February 11 2019

1 3

I need to plot 2 surfaces (f, g) and a plane (Op) (two surfaces and the osculating plane to their complete intersection curve). When I use

f := x*w - z g := -z^2-w+x+2*z-1 Op := 5*x-4-4*z+3*w implicitplot3d({f, g, Op}, x = 0 .. 2, z = 0 .. 2, w = 0 .. 2, grid = [50, 50, 50])

it is very difficult to differentiate between them, so I would like to plot f, g and Op using different color schemes or something. Any ideas on how to do this?

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