Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I'm very new to Maple (and coding in general). I'd like to know a very large coefficient of a certain 𝑞-series involving the Dedekind 𝜂-function. For example

s:=series(subs(q=q^6, eta^4), q, N);

where eta := series(q^(1/24)*product(1 - q^n, n = 1 .. 100), q, N). I know the command coeftayl(s, q=0, N) but for certain 𝑞-series it doesn't recognize the numerical value of this coefficient when 𝑁 is too large (even after subtracting the principal part of 𝑠, if there is any) - instead it realizes the coefficient as a HUGE limit of something. Cheers.

what is the wrong in this operations for isentropic process ( isentropic-process) 

 

Restart: with(RealDomain) : interface(dispalyprecision=4) : ; Isentropical := proc(N,v) local K,PTR,KM1,KP1,GO, M,MS,C,PPT,TTT,RRT,AAS,eq,o ; K : = G() : KM1 : = k - 1 : KP1 : = K + 1 : GO := 1 : If N=1 then M := v Elif N=2 then PPT := v : M := sqrt ( 2 * (PPT^(-KM/K) -1 ) : Elif N=3 then MS := v : M := sqrt ( 1 / (KP1/ (2*MS^2) –KM1/2 ) : Elif N=4 then C := v : M := sqrt ( 2 / (KM1* (1 /(C^2) -1 )) ) : Elif N=5 then TTT := v : M := sqrt ( 2 * (1/TTT-1 ) / KM1 : Elif N=6 then RRT := v : M := sqrt ( 2 * (1/RRT^KM1 -1 ) / KM1 : Elif N=7 then AAS := v : eq :=AAS- (2*(1+KM1*M^2/2)/ KP1) ^ (KP1/ (2*KM1)) /M : M := fsolve(eq,M,0..1) : GO :=2 : Elif N=8 then AAS := v : eq :=AAS- (2*(1+KM1*M^2/2)/ KP1) ^ (KP1/ (2*KM1)) /M : M := fsolve(eq,M,1..infinity) : GO :=2 : Fi:fi GO<>2 then ASS := (2 *(1+ KM1*M^2/2/KP1) ^ (KP1/ (2*KM1)) /M fi: PTR := (1+ KM1*M^2/2/KP1) : PPT := PTR^(-K/KM1) : TTT:=PTR^ (-1) : RRT:+PTR^(-1/KM1) : If N <> 3 then MS := sqrt ( KP1 / ( 2 / ( M^2)+KM1) ) If N <> 3 then C := sqrt( 1 / (2 / (KM1*M^2) + 1 ) ) O := evalf([m,1./PPT,MS,C,1./TTT,1./RRT,AAS]) end : irp := proc (N, v) local f; f:=Isentropic1(N,v) : printf(cat(`% 9.4f `$7, ` \ n`) , f[ii$ii=1..7]) end : G := ( ) -> 1.4 : For mi form .1 to .5 do irp(1.mi) od : > > > Eq := table( [ (M2) = M2 , (MS2) = (K+1) /2 (2 / ( M2)+ (K-1) ) (C2) = 1 / (2 / (K-1)*M2+1 ) (PP0) = (1+(K-1)*M2/2)^(-K/(K-1) ) (RR0) = (1+(K-1)*M2/2)^(-1/(K-1) ) (TT0) = (1+(K-1)*M2/2)^(-1) (AAS) = (2 *(1 +(K-1)*M2/2 ) / (K+1) )^( (k-1) /(2*(k-1)))/ squt(M2) ]) : if vL=M then M2v := solve ( M2 -Eq[M2 ] , M2 ) : M2v := eval(M2v ,M2 = VR^2 ) : elif vL=MS then M2v := solve( M2 -Eq[MS2 ] , M2 ) : M2v := eval(M2v ,MS2 = VR^2 ) : elif vL=C then M2v := solve( M2 -Eq[C2 ] , M2 ) : M2v := eval(M2v ,C2 = VR^2 ) : elif vL=PP0 then M2v := solve( M2 -Eq[PP0] , M2 ) : M2v := eval(M2v ,PP0 = VR ) : elif vL=RR0 then M2v := solve( M2 -Eq[RR0] , M2 ) : M2v := eval(M2v ,RR0 = VR ) : elif vL=TT0 then M2v := solve( M2 -Eq[TT0] , M2 ) : M2v := eval(M2v ,TT0 = VR ) : elif vL=AASsub then M2v := fsolve( M2 -Eq[AAS] , M2 ) : M2 :=0..1 : elif vL=AASup then M2v := fsolve( M2 -Eq[AAS] , M2 ) : M2 :=1..infinity : fi: Eqsva1 := eva1(Eq, M2 = M2v) : Eqava1 [M] := sqrt(EqsVa1[M2] ) : Eqsva1[MS] := sqrt(EqsVa1[MS2] ) : Eqava1 [C] := sqrt(EqsVa1[C2] ) : 1var := [M, MS, C, PP0, RR0, TT0, AAS] : [seq(1var[i]=EqsVA1[1var[i] ] , I=1…nope(1var))] end: Egs :=[M=0.5, MS=0.53452, C=0.2182, P0P=0.84302, RR0=0.88517, TT0=0.95238, AASsub=1.33985, AASsup=0.95238] : For i from 1 to nops(Egs) do print(I,Isentropic2(Egs[i])) od : (process)

What is the problem with the initialconsiditions that caused this error?

"Error, (in dsolve/numeric/DAE/initial) missing initial conditions for the following: {Integer}"

Thanks.

 Dear all

Is there a nice idea to determine the Lyapunov function of the following system

Lyapunov_function.mw

Some parameters used in the code:

b fixed parameter

a any parameter in R

Many thanks for your help

 

 

I was trying to learn more about the commands in this package and found it to be someone non satisfying:


 

Download sockets_strangeness.mw

 

У меня есть код для активации Maple, но я не знаю какой имя сервера которое у меня требует для активации.

 I'd like to get all at most 15 vertices Non-isomorphic  connected  bipartite graphs. One way is to use the function NonIsomorphicGraphs(k, output = graphs, outputform = graph, restrictto = connected).

with(GraphTheory):

k:=8;
s1:=[NonIsomorphicGraphs(k,restrictto = connected,output=graphs,outputform=graph)]:
bipartitegraph:=select[flatten](x->IsBipartite(x)=true, s1):
nops(bipartitegraph);

But when k=9, it is slow, I doubted that the code 

By Checking out the encyclopedia,http://oeis.org/A033995 , we knew the following number of bipartite graphs datas of , at most 14, they are not many(the datas contain  no-connected conditions)

 

so I read the help document about  

awesome.

Ps: I know  in SageMath  we can get all bipartite graphs quikly even though n>=10  by  using the 

for g in graphs.nauty_geng('-c -b 10 -g'):
 
But I hope it can be realized in Maple. 

Thanks!

 

I am thinking of running maple in google cloud. Does Maplesoft available in google cloud

If I know the direction of up and down

how to control normal distribution to fill in missing data to the direction I want in maple?

just like fill in missing pixel in bitmap file.

Is Maple capable of printing functional html links? That is can a Maple code output an html link that actually works?

Hi all;

I need to compute the stabilizing feedback for the system of nonlinear ODEs

stabilizing_Feedback.mw

 

Many thanks for your help

I tried to solve the following equation to find an explicit expression for x in terms of n. But the answer is a long relation in terms of RootOf and _Z. 

 

(1/4)*((-x^2+1)*(-4*Pi*(x^2-1)+n*(x^4-2*x^2+5))*cosh(n*x)*sinh(Pi*x)+sinh(n*x)*((-x^2+1)*(-4*n*(x^2-1)+Pi*(x^4-2*x^2+5))*cosh(Pi*x)-2*x*(x^4-2*x^2-3)*sinh(Pi*x)))/(x^2-1)^2=0

 

Any comment is welcomed.

F(0) := a; F(1) := b; F(2) := c; F(3) := d

for k from 0 to 1 do F(k+4) := -(N[1]*G(k)+Re*(sum(F(k-m)*(m+1)*(m+2)*(m+3)*F(m+3), m = 0 .. k))-Re*(sum((k-m+1)*F(k-m+1)*(m+1)*(m+2)*F(m+2), m = 0 .. k)))/((1+N[1])*(k+1)*(k+2)*(k+3)*(k+4)) end do

How to plot a graph for this equation with different values of N_1 and Re number

Dear Users!

Hoped everyone fine here. I have three main questions regarding the maple code given bellow:

restart; with(LinearAlgebra); with(plots);

alpha := 1; beta := 1; theta := 1/2;

UU := sinh(x)*sinh(y)*sinh(z)*exp(-1.*t);

NN := 3; L := 0; R := 1; T := 1; N := NN; Mx := NN; My := NN; Mz := NN; `&Delta;x` := (R-L)/Mx; `&Delta;y` := (R-L)/My; `&Delta;z` := (R-L)/Mz; `&Delta;t` := (R-L)/N;

kappa[1] := 1; kappa[2] := 2/x^2; kappa[3] := 1/x^2; kappa[X] := x^2+y^2+z^2+1; kappa[Y] := x^2+y^2+z^2+1; kappa[Z] := x^2+y^2+z^2+1; kappa[4] := 0; NL := 3;

ics := [seq(seq(seq([u[i, j, k, 0] = eval(UU, [x = i*`&Delta;x`, y = j*`&Delta;y`, z = k*`&Delta;z`, t = 0]), u[i, j, k, -1] = eval(u[i, j, k, 1]-2*`&Delta;t`*(eval(diff(UU, t), t = 0)), [x = i*`&Delta;x`, y = j*`&Delta;y`, z = k*`&Delta;z`, t = 0])][], i = 0 .. Mx), j = 0 .. My), k = 0 .. Mz)];

bcs := [seq(seq(seq([u[0, j, k, n] = eval(UU, [x = 0, y = j*`&Delta;y`, z = k*`&Delta;z`, t = n*`&Delta;t`]), u[Mx, j, k, n] = eval(UU, [x = L, y = j*`&Delta;y`, z = k*`&Delta;z`, t = n*`&Delta;t`])][], j = 0 .. My), k = 0 .. Mz), n = 1 .. N), seq(seq(seq([u[i, 0, k, n] = eval(UU, [x = i*`&Delta;x`, y = 0, z = k*`&Delta;z`, t = n*`&Delta;t`]), u[i, My, k, n] = eval(UU, [x = i*`&Delta;x`, y = L, z = k*`&Delta;z`, t = n*`&Delta;t`])][], i = 1 .. Mx-1), k = 0 .. Mz), n = 1 .. N), seq(seq(seq([u[i, j, 0, n] = eval(UU, [x = i*`&Delta;x`, y = j*`&Delta;y`, z = 0, t = n*`&Delta;t`]), u[i, j, Mz, n] = eval(UU, [x = i*`&Delta;x`, y = j*`&Delta;y`, z = L, t = n*`&Delta;t`])][], i = 1 .. Mx-1), j = 1 .. My-1), n = 1 .. N)];
Sol := {u[1, 1, 1, 1] = 0.2366497936e-1, u[1, 1, 1, 2] = 0.7589975856e-2, u[1, 1, 1, 3] = 0.6029906475e-3, u[1, 1, 2, 1] = 0.3778786317e-1, u[1, 1, 2, 2] = 0.7126415819e-2, u[1, 1, 2, 3] = -0.1197885714e-2, u[1, 2, 1, 1] = 0.3778786315e-1, u[1, 2, 1, 2] = 0.7126415820e-2, u[1, 2, 1, 3] = -0.1197885718e-2, u[1, 2, 2, 1] = 0.6038763054e-1, u[1, 2, 2, 2] = 0.4264591907e-2, u[1, 2, 2, 3] = -0.3509477851e-2, u[2, 1, 1, 1] = 0.3171958616e-1, u[2, 1, 1, 2] = -0.1327161715e-1, u[2, 1, 1, 3] = -0.4628647419e-2, u[2, 1, 2, 1] = 0.4979852397e-1, u[2, 1, 2, 2] = -0.3060811899e-1, u[2, 1, 2, 3] = -0.344914876e-4, u[2, 2, 1, 1] = 0.4979852397e-1, u[2, 2, 1, 2] = -0.3060811898e-1, u[2, 2, 1, 3] = -0.3449150010e-4, u[2, 2, 2, 1] = 0.7882396741e-1, u[2, 2, 2, 2] = -0.6192340018e-1, u[2, 2, 2, 3] = 0.1156615222e-1}

Using set of points given in ics, bcs and Sol

1. I want to contruct a vector at any time level (by fixing fourth suffix like u[i,j,k,n]) for i = 0..Mx,j=0..My,k=0..Mz and then find its L2 and L[infinity] norms.

2. Next I want contruct a vector by fixing two suffixes like u[i,j,k,n]) for i = 0..Mx,j=0..My and plot a surface in 3D

3. Finally I want to construct a vector by fixing three suffixes like u[i,j,k,n]) for i = 0..Mx, and plot a curve in 2D.

I'm waiting for your positive respone. I shall be very thankfull to you in advance.

Special request to:
@acer @Carl Love @Kitonum @Preben Alsholm

Hi everyone, I have a mechanical problem, I solved it using hybrid method (differential transformation method for time and finite difference method for space) I need some help please.

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