I have been having problem in solving this question because of the 'Whittaker'.

Can anyone please asist me how to integrate below problem with the 'Whitaker?

f := exp(-1.5*t)*(GAMMA(2)*t^(2-alpha)/GAMMA(3-alpha)-t^(1-alpha)/GAMMA(2-alpha)+t^2-t);
               /   (2 - alpha)        (1 - alpha)           \
               |  t                  t                 2    |
   exp(-1.5 t) |---------------- - ---------------- + t  - t|
               \GAMMA(3 - alpha)   GAMMA(2 - alpha)         /
int(f, t);
 

2.^(3.-1.*alpha)*3.^(alpha-3.)*(t^(-.5000000000*alpha)*3.^(-.5000000000*alpha)*2.^(.5000000000*alpha)*(alpha-3.)*(-2.+alpha)*exp(-.7500000000*t)*WhittakerM(-.5000000000*alpha, -.5000000000*alpha+.5000000000, 1.500000000*t)/(3.-1.*alpha)+t^(-.5000000000*alpha)*3.^(-.5000000000*alpha)*2.^(.5000000000*alpha)*(1.500000000*t-1.*alpha+2.)*(alpha-3.)*exp(-.7500000000*t)*WhittakerM(-.5000000000*alpha+1., -.5000000000*alpha+.5000000000, 1.500000000*t)/(3.-1.*alpha))/GAMMA(3.-1.*alpha)-1.*2.^(2.-1.*alpha)*3.^(-2.+alpha)*(t^(-.5000000000*alpha)*3.^(-.5000000000*alpha)*2.^(.5000000000*alpha)*exp(-.7500000000*t)*WhittakerM(-.5000000000*alpha, -.5000000000*alpha+.5000000000, 1.500000000*t)+t^(-.5000000000*alpha)*3.^(-.5000000000*alpha)*2.^(.5000000000*alpha)*(-2.+alpha)*exp(-.7500000000*t)*WhittakerM(-.5000000000*alpha+1., -.5000000000*alpha+.5000000000, 1.500000000*t)/(2.-1.*alpha))/GAMMA(2.-1.*alpha)+.1481481481+(0.9876543210e-1*(-6.750000000*t^2-9.*t-6.))*exp(-1.500000000*t)-(.2222222222*(-2.-3.*t))*exp(-1.500000000*t)

I want infinite series expansion of incomplete upper gamma function.

I'm trying to use CodeTools[Profile] to investigate my memory leak and the effect or lack there of of 'forget' to improve it.

I copied my code from an example:

with(CodeTools[Profiling]);
 [Allow, Build, Coverage, GetProfileTable, Ignore, IsProfiled, 

   LoadProfiles, Merge, PrintProfiles, Profile, Remove, 

   SaveProfiles, Select, SortBy, UnProfile]

Profile([PickAngles(1.0, 1.0, 1.0)]);
Error, (in CodeTools:-Profiling:-Profile) unexpected argument(s)

The 'unexpected argument' is the 'result' from 'PickAngles'. I've tried with and w/o the '[]' but it does the same thing failing to recognize that 'PickAngles' is a procedure.

The example I used is here:

https://www.maplesoft.com/support/help/maple/view.aspx?path=CodeTools%2FProfiling%2FProfile procedure.

I did what to make of the subscript Profiles in the example so I used '[Profiles]' and that worked or seemed to.

Dear Users!

I hope you are doing well. In the attached file I want to convert the system of ODEs (attained the system against the value of M) into matrix form and need the matrices A, B and vector b. Remember the order of A, B and b vary as M vary. I am waiting for your kind response. Please take care and thanks

System_of_ODEs.mw

I can import maple, but I get an error when importing namespace/symbols:

import maple.namespace as mpl

The below is not properly rendering in my browser. You probably have to open the worksheet
 

Edit: Asking differently: Which symbol from the palettes can be used for equivalence (in a logic context)?

Edit2: Title changed. Original title: Why does Maple replace the equivalence symbol by an implication symbol

Download De_Morgans_law.mw

hi

I have a linear system with varibles trying to plot 3d the solutions x, y, z

here is my code: linear_var.mw

please any comment might help.

*******************************

restart;

Omega:=10:N:=0.5:M:=sqrt(N(N+1)):

a11:=0.5*(1+2*N)+M*cos(phi):
a12:=-0.5*((1+theta)^3+(1-theta)^3):a13:=-0.5*(N+M*cos(phi))*((1+theta)^3-(1-theta)^3): a21:=M*sin(phi): a22:=(-(1+2*N)+0.5*M*cos(phi))*((1+theta)^3+(1-theta)^3): a23:=-(Omega+0.5*((1+theta)^3-(1-theta)^3)*M*sin(phi)): a31:=0.25*((1+theta)^3-(1-theta)^3): a32:=Omega: a33:=-0.5-(N+0.25)*((1+theta)^3+(1-theta)^3): b1:=-0.5*a31: b2:=0: b3:=0.25+((1+theta)^3+(1-theta)^3)/8:

slove([a11*x+a12*y+a13*z=b1,a21*x+a22*y+a23*z=b2,a31*x+a32*y+a33*z=b3[,[x,y,z]);
Error, unable to match delimiters
Typesetting:-mambiguous(Typesetting:-mambiguous(slovelparlsqba11

  sdotx + a12sdoty + a13sdotzequalsb1commaa21sdotx + a22sdoty + 

  a23sdotzequalsb2commaa31sdotx + a32sdoty + a33sdotzequalsb3lsqb

  comma(xyz)rparsemi, 

  Typesetting:-merror("unable to match delimiters")))

plot3d(x, theta = .1 .. 5, phi = 0 .. 2*Pi, axes = boxed);
plot3d(y, theta = .1 .. 5, phi = 0 .. 2*Pi, axes = boxed); plot3d(z, theta = .1 .. 5, phi = 0 .. 2*Pi, axes = boxed);

I would like solving systems of congruences like the following one:

154x+69y = 0 mod 7^3

13x+716y = 0 mod 13^3

23x+3059y = 0 mod 23^3

I need the minimal non-trivial solution. I know that the solution of the system above is x=1103, y=26390.

How could I find the solution with Maple?

# ----------------------------------THE DESIGN OF THE MAPLET SCREEN---------------------
with(Maplets[Elements]):
HCC:=Maplet(Window('title'="HEAT CONDUCTIVITY CONTROL",["WITH THIS APPLICATION THE CONDUCTIVITY COEFFICIENT OF A ONE-DIMENSIONAL OBJECT, APPROXIMATING THE TEMPRATURE OF THE OBJECT TO A TARGET TEMPRETURE AT A CERTAIN FINAL TIME, IS CONTROLLED. ",[["l",TextField[l](3)],["T",TextField[T](3)],["f(x,t)",TextField[f](15)],["phi(x)",TextField[ph](5)]],[["k(0)",TextField[k0](3)],["g0(t)",TextField[g0](10)],["k(l)",TextField[kl](3)],["g1(t)",TextField[g1](10)],["mu(x)",TextField[mu](10)]],[["alpha",TextField[alpha](3)],["kaplus(x)",TextField[kaplus](5)],["N",TextField[N](3)],["kstart(x)",TextField[kstart](3)],["beta",TextField[beta](3)],["eps",TextField[eps](3)]] ,[Button("Calculate the Control",Evaluate('kutu'=ms(N,l,alpha,T,ph,f,g0,g1,mu,kaplus,k0,kl,kstart,beta,eps))),[TextBox['kutu'](30..30)],Button("Draw the Control",Evaluate('Draw'='plot(kutu,x=0..l)')),Plotter['Draw'](),[[Button("Distance to
Target",Evaluate('kutu2'=ms8(N,l,alpha,T,ph,f,g0,g1,mu,kaplus,k0,kl,kstart,beta,eps))),TextField['kutu2'](12)],[Button("Approximation to kaplus",Evaluate('kutu3'='evalf(int((kutu-kaplus)^2,x=0..l))')),TextField['kutu3'](12)]]],Button("Shutdown",Shutdown())])):
# -------------------------PROCEDURE FOR CALCULATION OF THE CONTROL FUNCTION-----------
with(inttrans):
with(linalg):
ms:=proc(N,l,alpha,T,ph,f,g0,g1,mu,kaplus,k0,kl,kstart,beta,eps):
with(inttrans):
with(linalg):
w:=simplify(x^2/2*g1/(l*kl)+(x^2/2-x*l)*g0/(l*k0)):
phdal:=ph-subs(t=0,w):
fdal:=simplify(f-diff(w,t)+diff(kaplus*diff(w,x),x)):
# ---------------------------------Solution of the Heat Problem------------------------------------
dp:=proc(ka)
with(inttrans):
with(linalg):
phi:=Vector(1..N):
phi[1]:=1/sqrt(l):
for i from 2 to N do
phi[i]:=evalf(sqrt(2/l)*cos((i-1)*Pi*x/l)):
od:
K:=Array(1..N,1..N):
for j from 1 to N do
for k from 1 to N do
K[j,k]:=evalf(-int(ka*diff(phi[k],x$2)*phi[j],x=0..l)):
od:
od:
F:=Vector(1..N):
for n from 1 to N do
F[n]:=evalf(int(fdal*phi[n],x=0..l)):
od:
A:=Vector(1..N):
for m from 1 to N do
A[m]:=evalf(int(phdal*phi[m],x=0..l)):
od:
KL:=Matrix(1..N,1..N):
for j1 from 1 to N do
for k1 from 1 to N do
if (j1=k1) then KL[j1,k1]:=s+K[j1,k1] else KL[j1,k1]:=K[j1,k1] fi:
od:
od:
FL:=Vector(1..N):
for i1 from 1 to N do
FL[i1]:=evalf(laplace(F[i1],t,s));
od:
S:=Vector(1..N):
for i2 from 1 to N do
S[i2]:=(A[i2]+FL[i2]);
od:
C:=Vector(1..N):
C:=evalm(inverse(KL)&*S):
c:=Vector(1..N):
for i3 from 1 to N do
c[i3]:=evalf(invlaplace(C[i3],s,t)):
od:
v:=evalf(add(c[n1]*phi[n1],n1=1..N)):
uyak:=v+w;
end:
# ---------------------------------Solution of the Adjoint Problem------------------------------------
ap:=proc(ka)
with(inttrans):
with(linalg):
utau:=evalf(subs(t=T-tau,dp(ka))):
phe:=evalf(2*(subs(tau=0,utau)-mu));
phie:=Vector(1..N):
phie[1]:=1/sqrt(l):
for i4 from 2 to N do
phie[i4]:=evalf(sqrt(2/l)*cos((i4-1)*Pi*x/l)):
od:
Kc:=Array(1..N,1..N):
for j2 from 1 to N do
for k2 from 1 to N do
Kc[j2,k2]:=evalf(-int(ka*diff(phie[k2],x$2)*phie[j2],x=0..l)):
od:
od:
Fc:=Vector(1..N):
for m1 from 1 to N do
Fc[m1]:=0:
od:
Ac:=Vector(1..N):
for cm1 from 1 to N do
Ac[cm1]:=evalf(int(phe*phie[cm1],x=0..l)):
od:
KLC:=Matrix(1..N,1..N):
for cj1 from 1 to N do
for ck1 from 1 to N do
if (cj1=ck1) then KLC[cj1,ck1]:=s+Kc[cj1,ck1] else KLC[cj1,ck1]:=Kc[cj1,ck1] fi:
od:
od:
FLC:=Vector(1..N):
for ci1 from 1 to N do
FLC[ci1]:=evalf(laplace(Fc[ci1],tau,s));
od:
Sc:=Vector(1..N):
for ci2 from 1 to N do
Sc[ci2]:=(Ac[ci2]+FLC[ci2]);
od:
CC:=Vector(1..N):
CC:=evalm(inverse(KLC)&*Sc):
cc:=Vector(1..N):
for ci3 from 1 to N do
cc[ci3]:=evalf((invlaplace(CC[ci3],s,tau))):
od:
ve:=evalf(add(cc[cn]*phie[cn],cn=1..N)):
eta:=evalf(subs(tau=T-t,ve));
end:
# ---------------------------------Calculation of the Gradient----------------------------------
T�rev:=proc(alpha,ka)
T�re:=simplify(evalf(-int(diff(dp(ka),x)*diff(ap(ka),x),t=0..T)+2*alpha*(ka-kaplus)));
end:
# ----------------------------Calculation of the Cost Functional--------------------------------
Jka:=proc(ka)
IJ1:=evalf(int((subs(t=T,dp(ka))-mu)^2,x=0..l));
end:
Sta:=proc(ka)
IJ2:=simplify(evalf((int((ka-kaplus)^2,x=0..l))));
end:
II:=proc(ka)
IJ:=simplify(evalf(Jka(ka)+alpha*Sta(ka))):
end:# 
# -----------------------------------Minimizing Process--------------------------------------------
a[0]:=kstart:
ka[0]:=kstart:
say�:=0:
for im from 0 to 60 do
a[im+1]:=simplify(evalf(ka[im-say�]-beta*T�rev(alpha,ka[im-say�]))): 
fark:=evalf(II(ka[im-say�])-II(a[im+1])): 
if(fark>0 and fark<eps) then break elif (fark>0) then 
j:=im+1: ka[j-say�]:=a[im+1]:   elif(fark<=0) then  say�:=say�+1: beta:=beta/(1.2): ka[im-say�+2]:=ka[im-say�+1]:   else fi:
od:
optcont:=a[im+1]:
end:
# -------------------------END OF THE PROCEDURE FOR CALCULATION OF THE CONTROL FUNCTION-----------
# ------PROCEDURE FOR CALCULATION OF THE DISTANCE TO THE TARGET FUNCTION-----------
ms8:=proc(N,l,alpha,T,ph,f,g0,g1,mu,kaplus,k0,kl,kstart,beta,eps):
with(inttrans):
with(linalg):
w8:=simplify(x^2/2*g1/(l*kl)+(x^2/2-x*l)*g0/(l*k0)):
phdal8:=ph-subs(t=0,w8):
fdal8:=simplify(f-diff(w8,t)+diff(kaplus*diff(w8,x),x)):
phi8:=Vector(1..N):
phi8[1]:=1/sqrt(l):
for i8 from 2 to N do
phi8[i8]:=evalf(sqrt(2/l)*cos((i8-1)*Pi*x/l)):
od:
K8:=Array(1..N,1..N):
for j8 from 1 to N do
for k8 from 1 to N do
K8[j8,k8]:=evalf(-int(ms(N,l,alpha,T,ph,f,g0,g1,mu,kaplus,k0,kl,kstart,beta,eps)*diff(phi8[k8],x$2)*phi8[j8],x=0..l)):
od:
od:
F8:=Vector(1..N):
for m28 from 1 to N do
F8[m28]:=evalf(int(fdal8*phi8[m28],x=0..l)):
od:
A8:=Vector(1..N):
for m8 from 1 to N do
A8[m8]:=evalf(int(phdal8*phi8[m8],x=0..l)):
od:
KL8:=Matrix(1..N,1..N):
for j18 from 1 to N do
for k18 from 1 to N do
if (j18=k18) then KL8[j18,k18]:=s+K8[j18,k18] else KL8[j18,k18]:=K8[j18,k18] fi:
od:
od:
FL8:=Vector(1..N):
for i148 from 1 to N do
FL8[i148]:=evalf(laplace(F8[i148],t,s));
od:
S8:=Vector(1..N):
for i48 from 1 to N do
S8[i48]:=(A8[i48]+FL8[i48]);
od:
C8:=Vector(1..N):
C8:=evalm(inverse(KL8)&*S8):
c8:=Vector(1..N):
for i58 from 1 to N do
c8[i58]:=evalf(invlaplace(C8[i58],s,t)):
od:
v8:=evalf(add(c8[n8]*phi8[n8],n8=1..N)):
uyak8:=v8+w8;
IJ18:=evalf(int((subs(t=T,uyak8)-mu)^2,x=0..l));
end:
# ------END OF THE PROCEDURE FOR CALCULATION OF THE DISTANCE TO THE TARGET FUNCTION-----------
Maplets[Display](HCC):

Hi!

I'm having problems with my maple not saving. I get no error message and no windows pop up.
The error occurred after the summer holidays in Maple 2022. I use Windows 11, everything is up to date. Have no Anti-virus programs.

  I have tried the following after I discovered the error:
- To install Maple 2023
- Uninstall and delete all maple folders, then reinstall Maple 2023
- Pressed Ctrl + s
- Press "Save as..."
- Pressed on the floppy disk/save icon
- Restarted computer and updated windows
- Run Maple as administrator

The only thing I can be allowed to do is:
- Ctrl + p
- Print to PDF/printer

Really hope you can help!

Dear power users, I am making the switch from Mathcad towards Maple and would like to know what is the most efficient alternative in Maple for a solve block. I have attached a work document to illustrate better my question.SolveBlockQuestion.mw Any help is highly appreciated.

Say I have ,

sol1 := C*vout*vin/(Iout*L*k^2)

and I want to simplify this expression by replacing  with .

Then I need to simplify it further by noting that , and that , so that the answer is only in terms of , , and .

I tried eval(sol1, vin/Iout = omega*Lm) initially to step through the first substitution, but that just returned the same expression.

Thank you.

I don't know where my last exchange with @mz6687  has been moved (not to the initial question  https://www.mapleprimes.com/questions/237066-Determinant-The-System-Hangs for what I see).
Nevertheless here is the reply I was sending to @mz6687  which ended with the message "Page not found".
Are_you_ok_with_that.mw

Could the one who moved the question meanwhile be so kind as to attach this reply?
TIA

If one writes Pi or Catalan, the output is Pi or Catalan, and writing evalf(Pi) or evalf(Catalan) we get approximations.

I would like to define other constants behaving in the same way. How to do it?

How to export Maplet file to .exe file to run independently without installing Maple software?