Maple 2018 Questions and Posts

These are Posts and Questions associated with the product, Maple 2018

Hi,

The help page TimeSeriesAnalysis, ExponentialSmoothingModel contains an error.
The command that generates the output (7) should be
esm2 := ExponentialSmoothingModel(seasonal={"A","M"},constraints=admissible)
instead of
esm2 := ExponentialSmoothingModel(seasonal={A,M},constraints=admissible)

PS : there is no tag relative to TimeSeriesAnalysys

 Hello!
  As we  known, in Graphtheory , a loop is an edge that joins a vertex to itself (for example  fig1 vertex1) and multiple edges (for example Fig2)are two or more edges that join the same two vertices.  But in Maple,  G := Graph({{a, b}, {a, c}, {b, c}}). The Edges(G) function returns a set  (not list )of the edges of G.  So, for example I can't create loop{1,1} by G:=Graph({{1,1},{1,2},{1,5},{2,5},{2,3},{5,4},{3,4},{4,6}})   . But in my research, I consider a graph which exist loops or multiple edges. I want to create  it  .How should I do?  Thanks in advance.

my code like this

with(GraphTheory):
G:=Graph({{1,2},{1,5},{2,5},{2,3},{5,4},{3,4},{4,6}}):
G:=Graph({{1,1},{1,2},{1,5},{2,5},{2,3},{5,4},{3,4},{4,6}}):DrawGraph(G,style=spring);
G2:=Graph({{1,2}}):
DrawGraph(G2);
G3:=Graph({{1,2},{1,2}}):
DrawGraph(G3);

 

How I can get integral by part.

I want to calculate these integral.

Thank you

integral_part.pdf

 

How I can take Laplace Transform from equation.

Thanks

LAPLACE

Right now I am going through Bishop's ML book and as a part of the first exercise I need to define a polynomial that goes like this.

y(x,w) = w_0 + w_1 * x + w_2 * x^2 ... + w_m * x^m = sum (k=0 to m) w_k * x^k

Here is how I've written it out in Maple.

f := proc (x, w) options operator, arrow; sum(w[k]*x^k, k = 0 .. nops(w)) end proc

Sorry for the raw code, Maple Math won't accept the code I've written as a valid Maple expression for some reason. When I try to use this I get an error that says too many levels of recursion.

f(2, [a, b, c]);
Error, (in limit/mrv/limsimpl) too many levels of recursion

Where am I going wrong here?
 

Please look at this codes!!!

i cant understand the idea of how maple works with parameters...

Problem.JPG

if u watch it exactly u can see that first maple understands that diff(a__1,t) is equall 1; but anfter that it couldnt load the value 1.
why?

what is hapening?

what can i do for this problem. its not the main code. i just send u an example of what  i want and what maple does. plz help me. tnx 

Hi,

When multiple request to DocumentTools:-Tabulate(...) are enclosed in the same group of commands (which typically happens when they are within a procedure), only the last one is displayed.
Is it possible to overcome this behaviour?

Thanks in advance

Hello, everyone: I have a question of drawing graph。
restart:
with(GraphTheory):
with(SpecialGraphs):
H := HypercubeGraph(3):
DrawGraph(H,
style = spring);


How  do I change  the vertex style   to polygon without line.
the aim graph  like figure below:

Thank you very much!

 

Greeting for all 

 , How to plot gyroid surface by Maple where its equation is 

                            

Amr

I have the following ODE perturbation problem which I want maple to solve for me:

q'(\tau)=f(p(eps*\tau)+eps*q(\tau),r(eps*\tau)+s(\tau))-f(p(eps*\tau,r(eps*\tau)+s(\tau))-f(p(eps*\tau),r(eps*\tau))

 

where q(\tau)=q_0(\tau)+eps*q_1(\tau)

p(eps*\tau)=p_0(eps*\tau)+eps*p_1(eps*\tau)

s(\tau)=s_0(\tau)+eps*s_1(\tau)

r(eps*\tau)=r_0(eps*\tau)+eps*r_1(eps*\tau)

I want maple to expand every function that depends on eps in its arguments by a Taylor series around eps=0, i.e h(eps)=h(0)+eps*h'(0)

and also expand the difference above the fs with an eps-expansion around eps=0.

I did all this manually now I want to check if my calculations are correct, eventaully I want to equate same powers of eps of the RHS and LHS of the first ODE I wrote above.

 

Then how to use maple for this?

Thnaks.

 

Does there exist a Maple command that on its own calculates the residual standard error of two regression lists? 

Given the following functions, graph them and identify relative and absolute extrema (if any).

f(x)=3x^3-2x^2+5x-7     [-3,6]

How I can do ?

Thank you.

 

Substitution of . 5,6,7) into Eqs. 1–(4), gives the new equation as functions of the generalized coordinates,
u_m,n(t);  v_m,n ( t), and w_m,n ( t). These expressions are then inserted in the Lagrange equations (see Eq. 8)) a set of N second-order coupled ordinary differential equations with both quadratic   and cubic nonlinearities.

In Eq (8) q are generalized coordinate such as uvw  and q = {`u__m,n`(t), `v__m,n`(t), `w__m,n`(t)}^T.

\where the elements of the vector,q_i are the time-dependent generalized coordinates.

L_Maple
 

U = (1/2)*(int(int(int(E*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*(`∂`(w(x, y, t))/`∂`(x))^2+`∂`(w(x, y, t))/`∂`(x)*(`∂`(w__0(x, y, t))/`∂`(x))-z*(diff(w(x, y, t), x, x))+v(x, y, t)*(`∂`(v(x, y, t))/`∂`(y)+(1/2)*(`∂`(w(x, y, t))/`∂`(y))^2+`∂`(w(x, y, t))/`∂`(y)*(`∂`(w__0(x, y, t))/`∂`(y))-z*(diff(w(x, y, t), y, y))))*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*(`∂`(w(x, y, t))/`∂`(x))^2+`∂`(w(x, y, t))/`∂`(x)*(`∂`(w__0(x, y, t))/`∂`(x))-z*(diff(w(x, y, t), x, x)))/(-nu^2+1)+E*(`∂`(nu(x, y, t))/`∂`(y)+(1/2)*(`∂`(w(x, y, t))/`∂`(y))^2+`∂`(w(x, y, t))/`∂`(y)*(`∂`(w__0(x, y, t))/`∂`(y))-z*(diff(w(x, y, t), y, y))+v(x, y, t)*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*(`∂`(w(x, y, t))/`∂`(x))^2+`∂`(w(x, y, t))/`∂`(x)*(`∂`(w__0(x, y, t))/`∂`(x))-z*(diff(w(x, y, t), x, x))))*(`∂`(v(x, y, t))/`∂`(y)+(1/2)*(`∂`(w(x, y, t))/`∂`(y))^2+`∂`(w(x, y, t))/`∂`(y)*(`∂`(w__0(x, y, t))/`∂`(y))-z*(diff(w(x, y, t), y, y)))/(-nu^2+1)+E*(`∂`(u(x, y, t))/`∂`(y)+`∂`(v(x, y, t))/`∂`(x)+`∂`(w(x, y, t))/`∂`(x)*(`∂`(w(x, y, t))/`∂`(y))+`∂`(w__0(x, y, t))*`∂`(w(x, y, t))/(`∂`(x)*`∂`(y))+`∂`(w__0(x, y, t))*`∂`(w(x, y, t))/(`∂`(x)*`∂`(y))-2*z*(diff(w(x, y, t), x, y)))^2/(2*(1+nu))+E*l^2*(diff(w(x, y, t), x, y))^2/(1+nu)+E*l^2*(diff(w(x, y, t), x, y))^2/(1+nu)+E*l^2*(diff(w(x, y, t), y, y)-(diff(w(x, y, t), x, x)))^2/(2*(1+nu))+E*l^2*(diff(v(x, y, t), y, y)-(diff(u(x, y, t), x, x)))^2/(8*(1+nu))+E*l^2*(diff(v(x, y, t), x, y)-(diff(u(x, y, t), y, y)))^2/(8*(1+nu)), z = -(1/2)*h .. (1/2)*h), y = 0 .. b), x = 0 .. a))

U = (1/2)*(int(int((1/12)*(-E*(-v(x, y, t)*(diff(diff(w(x, y, t), y), y))-(diff(diff(w(x, y, t), x), x)))*(diff(diff(w(x, y, t), x), x))/(-nu^2+1)-E*(-v(x, y, t)*(diff(diff(w(x, y, t), x), x))-(diff(diff(w(x, y, t), y), y)))*(diff(diff(w(x, y, t), y), y))/(-nu^2+1)+4*E*(diff(diff(w(x, y, t), x), y))^2/(2+2*nu))*h^3+E*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*`∂`(w(x, y, t))^2/`∂`(x)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(x)^2+v(x, y, t)*(`∂`(v(x, y, t))/`∂`(y)+(1/2)*`∂`(w(x, y, t))^2/`∂`(y)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(y)^2))*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*`∂`(w(x, y, t))^2/`∂`(x)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(x)^2)*h/(-nu^2+1)+E*(`∂`(nu(x, y, t))/`∂`(y)+(1/2)*`∂`(w(x, y, t))^2/`∂`(y)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(y)^2+v(x, y, t)*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*`∂`(w(x, y, t))^2/`∂`(x)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(x)^2))*(`∂`(v(x, y, t))/`∂`(y)+(1/2)*`∂`(w(x, y, t))^2/`∂`(y)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(y)^2)*h/(-nu^2+1)+E*(`∂`(u(x, y, t))/`∂`(y)+`∂`(v(x, y, t))/`∂`(x)+`∂`(w(x, y, t))^2/(`∂`(x)*`∂`(y))+2*`∂`(w__0(x, y, t))*`∂`(w(x, y, t))/(`∂`(x)*`∂`(y)))^2*h/(2+2*nu)+2*E*l^2*(diff(diff(w(x, y, t), x), y))^2*h/(1+nu)+E*l^2*(diff(diff(w(x, y, t), y), y)-(diff(diff(w(x, y, t), x), x)))^2*h/(2+2*nu)+E*l^2*(diff(diff(v(x, y, t), y), y)-(diff(diff(u(x, y, t), x), x)))^2*h/(8+8*nu)+E*l^2*(diff(diff(v(x, y, t), x), y)-(diff(diff(u(x, y, t), y), y)))^2*h/(8+8*nu), y = 0 .. b), x = 0 .. a))

(1)

T = rho*h*(int(int((`∂`(u(x, y, t))/`∂`(t))^2+(`∂`(v(x, y, t))/`∂`(t))^2+(`∂`(w(x, y, t))/`∂`(t))^2, y = 0 .. b), x = 0 .. a))

T = rho*h*(int(int(`∂`(u(x, y, t))^2/`∂`(t)^2+`∂`(v(x, y, t))^2/`∂`(t)^2+`∂`(w(x, y, t))^2/`∂`(t)^2, y = 0 .. b), x = 0 .. a))

(2)

F = (1/2)*c*(int(int((`∂`(u(x, y, t))/`∂`(t))^2+(`∂`(v(x, y, t))/`∂`(t))^2+(`∂`(w(x, y, t))/`∂`(t))^2, y = 0 .. b), x = 0 .. a))

F = (1/2)*c*(int(int(`∂`(u(x, y, t))^2/`∂`(t)^2+`∂`(v(x, y, t))^2/`∂`(t)^2+`∂`(w(x, y, t))^2/`∂`(t)^2, y = 0 .. b), x = 0 .. a))

(3)

W = int(int(w(x, y, t)*f__1(x, y, t)*cos(omega*t), y = 0 .. b), x = 0 .. a)

W = int(int(w(x, y, z)*f__1(x, y, z)*cos(omega*t), y = 0 .. b), x = 0 .. a)

(4)

u(x, y, t) = sum(sum(`u__m,n`(t)*sin(m*Pi*x/a)*sin(n*Pi*y/b), n = 1 .. N), m = 1 .. M)

u(x, y, t) = -(1/4)*(cos(Pi*y*N/b)*cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*y*N/b)*cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y/b)+cos(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)-cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)-cos(Pi*y*N/b)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)+cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)+sin(Pi*x/a)*sin(Pi*y/b)*cos((M+1)*Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)+sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)+sin(Pi*y/b)*sin((M+1)*Pi*x/a))*`u__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))+(1/4)*(-cos(Pi*y*N/b)*sin(Pi*y/b)*sin(Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin(Pi*x/a)+sin(Pi*y*N/b)*sin(Pi*x/a)+sin(Pi*y/b)*sin(Pi*x/a))*`u__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))

(5)

v(x, y, t) = sum(sum(`v__m,n`(t)*sin(m*Pi*x/a)*sin(n*Pi*y/b), n = 1 .. N), m = 1 .. M)

v(x, y, t) = -(1/4)*(cos(Pi*y*N/b)*cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*y*N/b)*cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y/b)+cos(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)-cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)-cos(Pi*y*N/b)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)+cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)+sin(Pi*x/a)*sin(Pi*y/b)*cos((M+1)*Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)+sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)+sin(Pi*y/b)*sin((M+1)*Pi*x/a))*`v__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))+(1/4)*(-cos(Pi*y*N/b)*sin(Pi*y/b)*sin(Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin(Pi*x/a)+sin(Pi*y*N/b)*sin(Pi*x/a)+sin(Pi*y/b)*sin(Pi*x/a))*`v__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))

(6)

w(x, y, t) = sum(sum(`w__m,n`(t)*sin(m*Pi*x/a)*sin(n*Pi*y/b), n = 1 .. N), m = 1 .. M)

w(x, y, t) = -(1/4)*(cos(Pi*y*N/b)*cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*y*N/b)*cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y/b)+cos(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)-cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)-cos(Pi*y*N/b)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)+cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)+sin(Pi*x/a)*sin(Pi*y/b)*cos((M+1)*Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)+sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)+sin(Pi*y/b)*sin((M+1)*Pi*x/a))*`w__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))+(1/4)*(-cos(Pi*y*N/b)*sin(Pi*y/b)*sin(Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin(Pi*x/a)+sin(Pi*y*N/b)*sin(Pi*x/a)+sin(Pi*y/b)*sin(Pi*x/a))*`w__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))

(7)

diff(`∂`(T(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`), t)-`∂`(T(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)+`∂`(U(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)+`∂`(U(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)+`∂`(F(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`) = `∂`(W(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`), j = 1, () .. (), N

(D(`∂`))(T(x, y, t))*(diff(T(x, y, t), t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)-`∂`(T(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)+2*`∂`(U(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)+`∂`(F(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`) = `∂`(W(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`), j = 1, () .. (), N

(8)

NULL


 

Download L_Maple

 

 

Hi, 

I was able to determine a cubic spline fit, F(v), to x1 and y1. Now I have vector x2 which I would like to use F(v) to calculate y2 as another Vector[row]. I am having trouble accomplishing this task. Any help is greatly appreciated. Thanks.
 

restart

 x1 := Vector[row]([0.8e-1, .28, .48, .68, .88, 1, 1.2, 1.4, 1.6, 1.8, 2, 2.2, 2.4, 2.6, 2.8, 3, 3.2, 3.4, 3.6, 3.8, 4, 4.2]);

 y1 := Vector[row]([-10.081, -10.054, -10.018, -9.982, -9.939, -9.911, -9.861, -9.8, -9.734, -9.659, -9.601, -9.509, -9.4, -9.293, -9.183, -9.057, -8.931, -8.806, -8.676, -8.542, -8.405, -8.265]);

 

m := ArrayTools[Dimensions](x1);

maxx := rhs(m[1]);

 

F := proc (v) options operator, arrow; CurveFitting:-Spline(x1, y1, v, degree = 3) end proc;

 

x2 := Vector[row]([seq(log10(2*10^x1[k]), k = 1 .. maxx)])

 

y2:=?

 

Pts1 := plot(x1, y1, style = point, symbol = diamond, gridlines = true, color = red);

plt_sp := plot(F(v), v = x1[1] .. x1[maxx], color = blue);

plots:-display(Pts1, plt_sp)``

"# How to calculate Vector y2 using spline fit F with x2"? "    x1:=Vector[row]([0.08,0.28,0.48,0.68,0.88,1,1.2,1.4,1.6,1.8,2,2.2,2.4,2.6,2.8,3,3.2,3.4,3.6,3.8,4,4.2]):    y1:=Vector[row]([-10.081,-10.054,-10.018,-9.982,-9.939,-9.911,-9.861,-9.8,-9.734,-9.659,-9.601,-9.509,-9.4,-9.293,-9.183,-9.057,-8.931,-8.806,-8.676,-8.542,-8.405,-8.265]):    m:=ArrayTools[Dimensions](x1):  maxx:=rhs(m[1]):      F:=v->CurveFitting:-Spline(x1,y1, v,degree=3):    x2:=Vector[row]([seq(log10(2*10^(x1[k])),k=1..maxx)]):                   #` PLOT RESULTS`   Pts1:=plot(x1,y1,style=point,symbol = diamond, gridlines=true, color = red):       plt_sp:=plot(F(v),v=x1[1]..x1[maxx],color = blue):     plots:-display(Pts1,plt_sp);     "

 

``

``


 

Download splfit.mw

In Maple 2018, I was playing around with some sums of infinite series, and I came across a result that made me wonder if Maple was perhaps using some other definition or understanding of the sum of a series in its calculation. Take a look at the screenshot linked below:

https://ibb.co/hMdkQHn

That first series is most certainly divergent since the limit as n approaches infinity of n^2/(n+1) is not equal to 0. And just to confirm my own sanity, I even checked some of the partial sums of the series, which sure enough are diverging. And yet for the infinite sum, Maple is giving this finite result.

I even checked a more familiar alternating series, the alternating harmonic series, which Maple does correctly calculate to be ln(2).

What am I missing here? Is Maple using a different definition for the sum of the series than the limit of the partial sums as n approaches infinity? Or is there a mistake with how I've written something that I'm not noticing?

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