MaplePrimes Questions

I just saw that Maple 2024 no longer supports importing Quandl data.

If this is a feature that I will like to use, it is possible to keep both Maple 2023 and Maple 2024 installed at the same time on Microsoft Windows 11 without conflicts?  Or should I just not upgrade to Maple 2024?  I currently have a perpetual license for Maple 2023 and am on the 15-day trial for Maple 2024.

Hi
i did calculation part by part of adomian laplace method but if we can make a loop for it is gonna be so great and take back a lot of time

restart

with(inttrans)

pde := diff(u(x, t), t)+u(x, t)*(diff(u(x, t), x)) = t^2*x+x

diff(u(x, t), t)+u(x, t)*(diff(u(x, t), x)) = t^2*x+x

(1)

eq := laplace(pde, t, s)

s*laplace(u(x, t), t, s)-u(x, 0)+laplace(u(x, t)*(diff(u(x, t), x)), t, s) = x*(s^2+2)/s^3

(2)

eq2 := subs({u(x, 0) = 0}, eq)

s*laplace(u(x, t), t, s)+laplace(u(x, t)*(diff(u(x, t), x)), t, s) = x*(s^2+2)/s^3

(3)

NULL

lap := s^alpha*laplace(u(x, t), t, s) = x*(s^2+2)/s^3-laplace(u(x, t)*(diff(u(x, t), x)), t, s)

s^alpha*laplace(u(x, t), t, s) = x*(s^2+2)/s^3-laplace(u(x, t)*(diff(u(x, t), x)), t, s)

(4)

lap1 := lap/s^alpha

laplace(u(x, t), t, s) = (x*(s^2+2)/s^3-laplace(u(x, t)*(diff(u(x, t), x)), t, s))/s^alpha

(5)

NULL

lap2 := invlaplace(lap1, s, t)

u(x, t) = -invlaplace(s^(-alpha)*laplace(u(x, t)*(diff(u(x, t), x)), t, s), s, t)+x*(invlaplace(s^(-1-alpha), s, t)+2*invlaplace(s^(-3-alpha), s, t))

(6)

NULL

lap3 := u(x, t) = t^alpha*x/GAMMA(alpha+1)+2*x*t^(alpha+2)/GAMMA(alpha+3)-invlaplace(laplace(u(x, t)*(diff(u(x, t), x)), t, s)/s^alpha, s, t)

u(x, t) = t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha)-invlaplace(laplace(u(x, t)*(diff(u(x, t), x)), t, s)/s^alpha, s, t)

(7)

NULL

NULL

NULL

NULL

``

(8)

u[1](x, t) = -invlaplace(laplace(u[0](x, t)*(diff(u[0](x, t), x)), t, s)/s^alpha, s, t)

u[1](x, t) = -invlaplace(laplace(u[0](x, t)*(diff(u[0](x, t), x)), t, s)/s^alpha, s, t)

(9)

"u[0](x,t):=(t^alpha x)/(GAMMA(1+alpha))+(2 x t^(alpha+2))/(GAMMA(3+alpha))"

proc (x, t) options operator, arrow, function_assign; t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha) end proc

(10)

n := N

N

(11)

k := K

K

(12)

f := proc (u) options operator, arrow; u*(diff(u, x)) end proc

proc (u) options operator, arrow; u*(diff(u, x)) end proc

(13)

for j from 0 to 3 do A[j] := subs(lambda = 0, (diff(f(seq(sum(lambda^i*u[i](x, t), i = 0 .. 20), m = 1 .. 2)), [`$`(lambda, j)]))/factorial(j)) end do

(t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha))*(t^alpha/GAMMA(1+alpha)+2*t^(alpha+2)/GAMMA(3+alpha))

 

u[1](x, t)*(t^alpha/GAMMA(1+alpha)+2*t^(alpha+2)/GAMMA(3+alpha))+(t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha))*(diff(u[1](x, t), x))

 

u[2](x, t)*(t^alpha/GAMMA(1+alpha)+2*t^(alpha+2)/GAMMA(3+alpha))+u[1](x, t)*(diff(u[1](x, t), x))+(t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha))*(diff(u[2](x, t), x))

 

u[3](x, t)*(t^alpha/GAMMA(1+alpha)+2*t^(alpha+2)/GAMMA(3+alpha))+u[2](x, t)*(diff(u[1](x, t), x))+u[1](x, t)*(diff(u[2](x, t), x))+(t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha))*(diff(u[3](x, t), x))

(14)

S1 := u[1](x, t) = -invlaplace((t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha))*(t^alpha/GAMMA(1+alpha)+2*t^(alpha+2)/GAMMA(3+alpha))/s^alpha, s, t)

u[1](x, t) = -x*(t^alpha)^2*invlaplace(s^(-alpha), s, t)*(1/GAMMA(1+alpha)^2+4*t^2/(GAMMA(3+alpha)*GAMMA(1+alpha))+4*t^4/GAMMA(3+alpha)^2)

(15)

NULL

NULL

u[1](x, t) = x*GAMMA(2*alpha+1)*t^(3*alpha)/(GAMMA(1+alpha)^2*GAMMA(3*alpha+1))-4*x*GAMMA(2*alpha+3)*t^(3*alpha+2)/(GAMMA(1+alpha)*GAMMA(3+alpha)*GAMMA(3*alpha+3))-4*`xΓ`(2*alpha+5)/(GAMMA(3+alpha)^2*GAMMA(3*alpha+3))

u[1](x, t) = x*GAMMA(2*alpha+1)*t^(3*alpha)/(GAMMA(1+alpha)^2*GAMMA(3*alpha+1))-4*x*GAMMA(2*alpha+3)*t^(3*alpha+2)/(GAMMA(1+alpha)*GAMMA(3+alpha)*GAMMA(3*alpha+3))-4*`xΓ`(2*alpha+5)/(GAMMA(3+alpha)^2*GAMMA(3*alpha+3))

(16)

NULL

u[2](x, t) = -invlaplace(laplace(u[1](x, t)*(diff(u(x, t), x)), t, s)/s^alpha, s, t)

NULL

NULL


for get definition use this pdf for fractional derivation

[Copyrighted material removed by moderator - see https://doi.org/10.4236/am.2018.94032]

Download solving_example_1.mw

I just installed the 15-day trial for the new Maple 2024.  It looks like Maple 2024 has the same problem as Maple 2023 in that it will not maintain a connection to MapleCloud.  I can sign in to MapleCloud no problem but as soon as I close the window, it forgets my password and I have to log back in each time I want to access MapleCloud.  Is there a way for Maple 2023 or Maple 2024 to remember my Maplesoft password so I do not have to log back in every time I want to access MapleCloud?

Dear all,

I am trying to minimize this polynomial function G on [0,1]x[0,1]:

Maple 2022 seems unable to find the (approximate) minimum. Even adding _EnvExplicit:=true, as suggested here on a previous post, does not fix the issue.

Any suggestion?

Thanks, Nicola

restart:

_EnvExplicit:=true:

G := (x, y) -> ((-1)*38.87*y^4 + 39.7800000000000*y^3 + (-1)*6.76000000000000*y^2 + 10.4000000000000*y - 3.90000000000000)*x^4 + (39.78*y^4 + (-1)*40.4600000000000*y^3 + 6.80000000000000*y^2 + (-1)*10.2000000000000*y + 3.40000000000000)*x^3 + ((-1)*6.76*y^4 + 6.80000000000000*y^3 + (-1)*1.12000000000000*y^2 + 1.60000000000000*y - 0.400000000000000)*x^2 + (10.4*y^4 + (-1)*10.2000000000000*y^3 + 1.60000000000000*y^2 + (-1)*2.00000000000000*y)*x + 1. + (-1)*3.9*y^4 + (-1)*0.4*y^2 + 3.4*y^3

proc (x, y) options operator, arrow; (-38.87*y^4+39.7800000000000*y^3-6.76000000000000*y^2+10.4000000000000*y-3.90000000000000)*x^4+(39.78*y^4-40.4600000000000*y^3+6.80000000000000*y^2-10.2000000000000*y+3.40000000000000)*x^3+(-6.76*y^4+6.80000000000000*y^3-1.12000000000000*y^2+1.60000000000000*y-.400000000000000)*x^2+(10.4*y^4-10.2000000000000*y^3+1.60000000000000*y^2-2.00000000000000*y)*x+1.-3.9*y^4-.4*y^2+3.4*y^3 end proc

(1)

minimize(G(x,y),x=0..1,y=0..1)

 

NULL

Download Untitled.mw

I would like to calculate the following quantity: 

 

Where F is the SU(2) field strength tensor given by:

The gauge field V (in my code A) is defined as

 

where rj is the unit vector in spherical coordinates.

I tried to calculate it with maple, however, the result is not correct. I should get a scalar function, but my result still contains dependencies on x,y,z. And I really don't know why. I have defined the gauge field in (11) and the field strength tensor in (14). I could imagine that SumOverRepeatedIndices() in (16) does not work as I think (For each a = (1,2,3) I would like a summation over mu and nu). Greek letters are my spacetime indices and lowercase letters are my space indices. Do I perhaps have to use SU(2) indices instead of the space indices? But how exactly does a SU(2) index differ from a space index?    

restart

with(Physics)

__________________________________________________________________

(1)

with(Vectors)NULL

Setup(spacetimeindices = greek, spaceindices = lowercaselatin, su2indices = uppercaselatin, signature = `+++-`, coordinates = spherical)

[coordinatesystems = {X}, signature = `+ + + -`, spaceindices = lowercaselatin, spacetimeindices = greek, su2indices = uppercaselatin]

(2)

Setup(realobjects = {g, diff(x, x), diff(y(x), x), diff(z(x), x), f__A(X[1])})

[realobjects = {g, phi, r, rho, theta, x, `x'`, y, `y'`, z, `z'`, f__A(r)}]

(3)

"x'(r,theta,phi)  :=  r * sin(theta) * cos(phi)"

proc (r, theta, phi) options operator, arrow, function_assign; Physics:-`*`(r, sin(theta), cos(phi)) end proc

(4)

"y'(r,theta,phi) := r * sin(theta) * sin(phi)"

proc (r, theta, phi) options operator, arrow, function_assign; Physics:-`*`(r, sin(theta), sin(phi)) end proc

(5)

"z'(r,theta,phi)  := r * cos(theta)"

proc (r, theta, phi) options operator, arrow, function_assign; Physics:-`*`(r, cos(theta)) end proc

(6)

 

This ist my unit vector:

Define(R[a] = [(diff(x, x))/r, (diff(y(x), x))/r, (diff(z(x), x))/r]) 

{Physics:-Dgamma[mu], Physics:-Psigma[mu], R[a], Physics:-d_[mu], Physics:-g_[mu, nu], Physics:-gamma_[a, b], Physics:-LeviCivita[alpha, beta, mu, nu], Physics:-SpaceTimeVector[mu](X)}

(7)

R[definition]

R[a] = [`x'`/r, `y'`/r, `z'`/r]

(8)

Parse:-ConvertTo1D, "first argument to _Inert_ASSIGN must be assignable"

r^2

(9)

"Define(A[mu,~a] =(1-`f__A`(X[1]) )/(g*X[1])*LeviCivita[a, mu,j,4]* R[j] )  "

{A[mu, `~a`], Physics:-Dgamma[mu], F[mu, nu, a], Physics:-Psigma[mu], R[a], Physics:-d_[mu], Physics:-g_[mu, nu], Physics:-gamma_[a, b], Physics:-LeviCivita[alpha, beta, mu, nu], Physics:-SpaceTimeVector[mu](X)}

(10)

A[definition]

A[mu, `~a`] = (1-f__A(r))*Physics:-LeviCivita[4, a, j, mu]*R[j]/(g*r)

(11)

A[]

A[mu, a] = Matrix(%id = 36893489989479580364)

(12)

Define(F[mu, nu, a] = d_[nu](A[mu, a])-d_[mu](A[nu, a])+LeviCivita[a, b, c, 4]*A[mu, `~b`]*A[nu, `~c`])

{A[i, `~a`], Physics:-Dgamma[mu], F[mu, nu, a], Physics:-Psigma[mu], R[a], Physics:-d_[mu], Physics:-g_[mu, nu], Physics:-gamma_[a, b], Physics:-LeviCivita[alpha, beta, mu, nu], Physics:-SpaceTimeVector[mu](X)}

(13)

F[definition]

F[mu, nu, a] = -Physics:-d_[nu](A[a, mu], [X])+Physics:-d_[mu](A[a, nu], [X])-Physics:-LeviCivita[4, a, b, c]*A[mu, `~b`]*A[nu, `~c`]

(14)

simplify(F[])

F[mu, nu, a] = _rtable[36893489989585113204]

(15)

"-1/(4)Simplify(SumOverRepeatedIndices(F[mu,nu,a]*F[~mu,~nu,a])); "

-(1/4)*((2*(-1+f__A(r))*`z'`*r*g-(diff(f__A(r), r))*`z'`*r^2*g-(-1+f__A(r))^2*`z'`*`x'`)^2+4*(-1+f__A(r))^4*`y'`^2*`z'`^2+((diff(f__A(r), r))*`x'`*r^2*g+2*(1-f__A(r))*`x'`*r*g+(1-f__A(r))*(-1+f__A(r))*`z'`^2)^2+((diff(f__A(r), r))*`y'`*r^2*g+2*(1-f__A(r))*`y'`*r*g+(-1+f__A(r))^2*`y'`*`x'`)^2+(2*(-1+f__A(r))*`x'`*r*g-(diff(f__A(r), r))*`x'`*r^2*g-(-1+f__A(r))*(1-f__A(r))*`y'`^2)^2+(-2*(-1+f__A(r))*`z'`*r*g+(diff(f__A(r), r))*`z'`*r^2*g+(-1+f__A(r))^2*`z'`*`x'`)^2+(-(diff(f__A(r), r))*`x'`*r^2*g-2*(1-f__A(r))*`x'`*r*g-(1-f__A(r))*(-1+f__A(r))*`z'`^2)^2+2*(-1+f__A(r))^4*`x'`^4+2*(-1+f__A(r))^4*`y'`^2*`x'`^2+2*(-1+f__A(r))^4*`z'`^2*`x'`^2+(-(diff(f__A(r), r))*`y'`*r^2*g-2*(1-f__A(r))*`y'`*r*g-(-1+f__A(r))^2*`y'`*`x'`)^2+(-2*(-1+f__A(r))*`x'`*r*g+(diff(f__A(r), r))*`x'`*r^2*g+(-1+f__A(r))*(1-f__A(r))*`y'`^2)^2)/(r^8*g^4)

(16)

L__FST := simplify(-(1/4)*((2*(-1+f__A(r))*`z'`*r*g-(diff(f__A(r), r))*`z'`*r^2*g-(-1+f__A(r))^2*`z'`*`x'`)^2+4*(-1+f__A(r))^4*`y'`^2*`z'`^2+((diff(f__A(r), r))*`x'`*r^2*g+2*(1-f__A(r))*`x'`*r*g+(1-f__A(r))*(-1+f__A(r))*`z'`^2)^2+((diff(f__A(r), r))*`y'`*r^2*g+2*(1-f__A(r))*`y'`*r*g+(-1+f__A(r))^2*`y'`*`x'`)^2+(2*(-1+f__A(r))*`x'`*r*g-(diff(f__A(r), r))*`x'`*r^2*g-(-1+f__A(r))*(1-f__A(r))*`y'`^2)^2+(-2*(-1+f__A(r))*`z'`*r*g+(diff(f__A(r), r))*`z'`*r^2*g+(-1+f__A(r))^2*`z'`*`x'`)^2+(-(diff(f__A(r), r))*`x'`*r^2*g-2*(1-f__A(r))*`x'`*r*g-(1-f__A(r))*(-1+f__A(r))*`z'`^2)^2+2*(-1+f__A(r))^4*`x'`^4+2*(-1+f__A(r))^4*`y'`^2*`x'`^2+2*(-1+f__A(r))^4*`z'`^2*`x'`^2+(-(diff(f__A(r), r))*`y'`*r^2*g-2*(1-f__A(r))*`y'`*r*g-(-1+f__A(r))^2*`y'`*`x'`)^2+(-2*(-1+f__A(r))*`x'`*r*g+(diff(f__A(r), r))*`x'`*r^2*g+(-1+f__A(r))*(1-f__A(r))*`y'`^2)^2)/(r^8*g^4))

(-g^2*r^4*(`x'`^2+(1/2)*`y'`^2+(1/2)*`z'`^2)*(diff(f__A(r), r))^2+4*g^2*r^3*(`x'`^2+(1/2)*`y'`^2+(1/2)*`z'`^2)*(-1+f__A(r))*(diff(f__A(r), r))-4*((1/8)*(`x'`^2+`y'`^2+`z'`^2)^2*f__A(r)^2-(1/4)*(`x'`^2+`y'`^2+`z'`^2)^2*f__A(r)+(1/8)*`x'`^4+(g^2*r^2+(1/4)*`y'`^2+(1/4)*`z'`^2)*`x'`^2+(1/2)*(g^2*r^2+(1/4)*`y'`^2+(1/4)*`z'`^2)*(`y'`^2+`z'`^2))*(-1+f__A(r))^2)/(r^8*g^4)

(17)

 

Download SU(2)-field-strength-tensor_.mw

Hi

i use other code for equation too when i use allvalues(Root(...)) it is more near but question is this why not satisfy the ode equation this is my equation this parameter are find for this ODe why not satisfy otherwise my equestions must be wrong!

restart

with(PDEtools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

with(DEtools)

``

with(LinearAlgebra)

with(sumtools)

eq0 := 2*beta*g[1]^3*r[0]^3+2*p^2*sigma*g[1]*r[0]^3 = 0

eq1 := 6*beta*g[1]^3*r[0]^2*r[1]+3*p^2*sigma*g[1]*r[0]^2*r[1]+6*beta*f[0]*g[1]^2*r[0]^2 = 0

eq2 := 6*beta*g[1]^3*r[0]^2*r[2]+6*beta*g[1]^3*r[0]*r[1]^2+2*p^2*sigma*g[1]*r[0]^2*r[2]+p^2*sigma*g[1]*r[0]*r[1]^2+12*beta*f[0]*g[1]^2*r[0]*r[1]+6*beta*f[1]*g[1]^2*r[0]^2+6*beta*f[0]^2*g[1]*r[0]-k^2*sigma*g[1]*r[0]-2*w*g[1]*r[0] = 0

eq3 := 12*beta*g[1]^3*r[0]*r[1]*r[2]+2*beta*g[1]^3*r[1]^3+2*p^2*sigma*g[1]*r[0]*r[1]*r[2]+12*beta*f[0]*g[1]^2*r[0]*r[2]+6*beta*f[0]*g[1]^2*r[1]^2+12*beta*f[1]*g[1]^2*r[0]*r[1]+p^2*sigma*f[1]*r[0]*r[1]+6*beta*f[0]^2*g[1]*r[1]+12*beta*f[0]*f[1]*g[1]*r[0]-k^2*sigma*g[1]*r[1]+2*beta*f[0]^3-k^2*sigma*f[0]-2*w*g[1]*r[1]-2*w*f[0] = 0

eq4 := 6*beta*g[1]^3*r[0]*r[2]^2+6*beta*g[1]^3*r[1]^2*r[2]+2*p^2*sigma*g[1]*r[0]*r[2]^2+p^2*sigma*g[1]*r[1]^2*r[2]+12*beta*f[0]*g[1]^2*r[1]*r[2]+12*beta*f[1]*g[1]^2*r[0]*r[2]+6*beta*f[1]*g[1]^2*r[1]^2+2*p^2*sigma*f[1]*r[0]*r[2]+p^2*sigma*f[1]*r[1]^2+6*beta*f[0]^2*g[1]*r[2]+12*beta*f[0]*f[1]*g[1]*r[1]+6*beta*f[1]^2*g[1]*r[0]-k^2*sigma*g[1]*r[2]+6*beta*f[0]^2*f[1]-k^2*sigma*f[1]-2*w*g[1]*r[2]-2*w*f[1] = 0

eq5 := 6*beta*g[1]^3*r[1]*r[2]^2+3*p^2*sigma*g[1]*r[1]*r[2]^2+6*beta*f[0]*g[1]^2*r[2]^2+12*beta*f[1]*g[1]^2*r[1]*r[2]+3*p^2*sigma*f[1]*r[1]*r[2]+12*beta*f[0]*f[1]*g[1]*r[2]+6*beta*f[1]^2*g[1]*r[1]+6*beta*f[0]*f[1]^2 = 0

eq6 := 2*beta*g[1]^3*r[2]^3+2*p^2*sigma*g[1]*r[2]^3+6*beta*f[1]*g[1]^2*r[2]^2+2*p^2*sigma*f[1]*r[2]^2+6*beta*f[1]^2*g[1]*r[2]+2*beta*f[1]^3 = 0

NULL

NULL

COEFFS := solve({eq0, eq1, eq2, eq3, eq4, eq5, eq6}, {p, f[0], f[1], g[1]}, explicit)

NULL

ode := 2*beta*U(xi)^3+(-k^2*sigma-2*w)*U(xi)+(diff(diff(U(xi), xi), xi))*p^2*sigma = 0

2*beta*U(xi)^3+(-k^2*sigma-2*w)*U(xi)+(diff(diff(U(xi), xi), xi))*p^2*sigma = 0

(2)

P := f[0]+sum(f[i]*R(xi)^i, i = 1 .. 1)+sum(g[i]*((diff(R(xi), xi))/R(xi))^i, i = 1 .. 1)

f[0]+f[1]*R(xi)+g[1]*(diff(R(xi), xi))/R(xi)

(3)

case1 := {p = -sqrt(2)*sqrt(sigma*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))/(sigma*(4*r[0]*r[2]-r[1]^2)), f[0] = -(k^2*sigma+2*w)*r[1]/sqrt(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w)), f[1] = -(2*(k^2*sigma+2*w))*r[2]/sqrt(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w)), g[1] = -sqrt(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))/(beta*(4*r[0]*r[2]-r[1]^2))}

{p = -2^(1/2)*(sigma*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2)/(sigma*(4*r[0]*r[2]-r[1]^2)), f[0] = -(k^2*sigma+2*w)*r[1]/(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2), f[1] = -2*(k^2*sigma+2*w)*r[2]/(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2), g[1] = -(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2)/(beta*(4*r[0]*r[2]-r[1]^2))}

(4)

NULL

``

(5)

K := diff(R(xi), xi) = r[0]+r[1]*R(xi)+r[2]*R(xi)^2

diff(R(xi), xi) = r[0]+r[1]*R(xi)+r[2]*R(xi)^2

(6)

S1 := subs(K, P)

f[0]+f[1]*R(xi)+g[1]*(r[0]+r[1]*R(xi)+r[2]*R(xi)^2)/R(xi)

(7)

NULL

C1 := subs(case1, S1)

-(k^2*sigma+2*w)*r[1]/(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2)-2*(k^2*sigma+2*w)*r[2]*R(xi)/(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2)-(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2)*(r[0]+r[1]*R(xi)+r[2]*R(xi)^2)/(beta*(4*r[0]*r[2]-r[1]^2)*R(xi))

(8)

f := U(xi) = C1

U(xi) = -(k^2*sigma+2*w)*r[1]/(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2)-2*(k^2*sigma+2*w)*r[2]*R(xi)/(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2)-(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2)*(r[0]+r[1]*R(xi)+r[2]*R(xi)^2)/(beta*(4*r[0]*r[2]-r[1]^2)*R(xi))

(9)

NULL

SO := subs(case1, ode)

2*beta*U(xi)^3+(-k^2*sigma-2*w)*U(xi)+2*(diff(diff(U(xi), xi), xi))*(k^2*sigma+2*w)/(4*r[0]*r[2]-r[1]^2) = 0

(10)

NULL

odetest(f, SO)


same_equation_different_parameter.mw

display([plottools[arc]([op(coordinates(Omega))], r, t .. t + Pi/2, color = red, t4), plottools[arc]([op(coordinates(Omega))], r, t + Pi .. t + (3*Pi)/2, color = coral, t4), plottools[arc]([op(coordinates(Omega))], r, t - Pi/2 .. t, color = cyan, t4), plottools[arc]([op(coordinates(Omega))], r, t + Pi/2 .. t + Pi, color = green, t4)],
draw([Cir(color = blue, t4), cir(color = grey, t4), sT(color = black, t4), XXp(color = black, l3), YYp(color = black, l3), L1(color = black, l3), L2(color = black, l3), N1(color = blue, symbol = solidcircle, symbolsize = 15), N2(color = blue, symbol = solidcircle, symbolsize = 15), N3(color = blue, symbol = solidcircle, symbolsize = 15), M1(color = blue, symbol = solidcircle, symbolsize = 15)]), axes = none, view = [-30 .. 10, -10 .. 10], size = [800, 800])::
plots:-animate(Proc, [t], t = 0 .. 2*Pi, frames = 30).;

why the instruction concerning the arcs is not resected ? Thank you.

I liked the recent question from user goebeld and especially the answer from Rouben Rostamian.
I admit, I didn’t even realize that Maple had VariationalCalculus procedures.
But what if the red and green  points are on the surface x1^4 + x2^4 + x3^4 -1 = 0
Points coordinates (-0.759835685700000, -0.759835685700000, 0.759835685700000) and
 (0.759835685700000, 0.759835685700000, -0.759835685700000).

Where will the shortest distance between these points on a given surface be? Taking into account symmetry, of course.

I have a thirder order ODE with non polynomial coefficients and I naively thought to try dsolve for fun to see what happens and Maple returned DESol with a second order differential equation and an arbitrary coefficient. I know Maple outputs DESol when it cannot find a solution similar to RootOf but the arbitrary constant is what is throwing me off. 

I am unsure how to interpret this, if a particular solution is found I could reduce the order and see how I could get with the second order ODE but maple doesn't produce a particular solution when I run that command. 

DESol_Question.mw

What is the problem with the integral below when I use a variable n?

with(Units:-Simple)

V__1 := Unit('m'^3) = Units:-Unit(m^3)NULL

V__2 := 2*Unit('m'^3) = 2*Units:-Unit(m^3)NULL

int(1/V, V = V__1 .. V__2)

ln(2)

(1)

`assuming`([int(n/V, V = n*Unit('m'^3) .. m*Unit('m'^3))], [n > 0, m > 0])

-ln(n)*n+ln(m)*n

(2)

NULL

Download Units_Int.mw

Dear all, is there a maple call to calculate the space curve connecting two points of a 3d plane?

e.g. the plane is defined by: f(x,y) = -x^2/9 + y^2/4

The two points are: P = (1,2,0), Q=(1,-1,0)

Searched: space curve laying on 3d plane connecting the two points.

Thanks

restart

with(PDEtools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

with(DEtools)

NULL

with(DifferentialAlgebra)

"with(Student[ODEs][Solve]): "

with(IntegrationTools)

with(inttrans)

with(PDEtools)

with(Physics)

with(PolynomialTools)

with(RootFinding)

with(SolveTools)

with(LinearAlgebra)

with(sumtools)

pde := I*(diff(psi(x, t), t))+alpha*(diff(psi(x, t), `$`(x, 2)))+(beta[3]*abs(psi(x, t))+beta[4]*abs(psi(x, t))^2)*psi(x, t)+gamma*(diff(abs(psi(x, t))^2, `$`(x, 2)))*psi(x, t)/abs(psi(x, t)) = 0

case1 := {k = k, lambda = sqrt(-1/(18*alpha*beta[4]+18*gamma*beta[4]))*beta[3], w = -(9*alpha*k^2*beta[4]+2*beta[3]^2)/(9*beta[4]), A[0] = -beta[3]/(3*beta[4]), A[1] = beta[3]/(3*beta[4]), B[1] = 0}

" psi(x,t):=U(xi)*exp(I*(-k*x+w*t+theta))"

proc (x, t) options operator, arrow, function_assign; U(xi)*exp(I*(-k*x+w*t+theta)) end proc

(2)

" U(xi):=-(beta[3] (cosh(xi)-sinh(xi)))/(3 beta[4] cosh(xi))"

proc (xi) options operator, arrow, function_assign; -(1/3)*beta[3]*(cosh(xi)-sinh(xi))/(beta[4]*cosh(xi)) end proc

(3)

convert(U(xi), trig)

-(1/3)*beta[3]*(cosh(xi)-sinh(xi))/(beta[4]*cosh(xi))

(4)

xi := sqrt(-1/(18*alpha*beta[4]+18*gamma*beta[4]))*beta[3]*(2*alpha*kt+x)

(-1/(18*alpha*beta[4]+18*gamma*beta[4]))^(1/2)*beta[3]*(2*alpha*kt+x)

(5)

S := psi(x, t)

-(1/3)*beta[3]*(cosh((-1/(18*alpha*beta[4]+18*gamma*beta[4]))^(1/2)*beta[3]*(2*alpha*kt+x))-sinh((-1/(18*alpha*beta[4]+18*gamma*beta[4]))^(1/2)*beta[3]*(2*alpha*kt+x)))*exp(I*(-k*x+t*w+theta))/(beta[4]*cosh((-1/(18*alpha*beta[4]+18*gamma*beta[4]))^(1/2)*beta[3]*(2*alpha*kt+x)))

(6)

solution := subs(case1, S)

-(1/3)*beta[3]*(cosh((-1/(18*alpha*beta[4]+18*gamma*beta[4]))^(1/2)*beta[3]*(2*alpha*kt+x))-sinh((-1/(18*alpha*beta[4]+18*gamma*beta[4]))^(1/2)*beta[3]*(2*alpha*kt+x)))*exp(I*(-k*x-(1/9)*(9*alpha*k^2*beta[4]+2*beta[3]^2)*t/beta[4]+theta))/(beta[4]*cosh((-1/(18*alpha*beta[4]+18*gamma*beta[4]))^(1/2)*beta[3]*(2*alpha*kt+x)))

(7)

pdetest(psi(x, t) = -beta[3]*(cosh(sqrt(-1/(18*alpha*beta[4]+18*gamma*beta[4]))*beta[3]*(2*alpha*k+x))-sinh(sqrt(-1/(18*alpha*beta[4]+18*gamma*beta[4]))*beta[3]*(2*alpha*k+x)))*exp(I*(-k*x-(9*alpha*k^2*beta[4]+2*beta[3]^2)*t/(9*beta[4])+theta))/(3*beta[4]*cosh(sqrt(-1/(18*alpha*beta[4]+18*gamma*beta[4]))*beta[3]*(2*alpha*k+x)))*exp(I*(-k*x-(9*alpha*k^2*beta[4]+2*beta[3]^2)*t/(9*beta[4])+theta)), pde)

Error, (in pdetest) unable to determine the indeterminate function

 

NULL

 

 

 

 

Download pde-solve.mw

Dear all, in the example below I create a matrix(3x2) and each element contains a vector. How can I avoid the double brackets of the matrix elements or eliminate the double brackets?

Thanks for help

restart;
with(PolynomialTools);
with(RootFinding);
with(SolveTools);
with(LinearAlgebra);
NULL;
NULL;
E1 := (-alpha*k^2*A[1] - alpha*k^2*B[1] + 3*A[0]^2*A[1]*beta[4] + 3*A[0]^2*B[1]*beta[4] + A[1]^3*beta[4] + 3*A[1]^2*B[1]*beta[4] + 3*A[1]*B[1]^2*beta[4] + B[1]^3*beta[4] + 2*A[0]*A[1]*beta[3] + 2*A[0]*B[1]*beta[3] - w*A[1] - w*B[1])*cosh(xi)^6 + (-alpha*k^2*A[0] + A[0]^3*beta[4] + 3*A[0]*A[1]^2*beta[4] + 6*A[0]*A[1]*B[1]*beta[4] + 3*A[0]*B[1]^2*beta[4] + A[0]^2*beta[3] + A[1]^2*beta[3] + 2*A[1]*B[1]*beta[3] + B[1]^2*beta[3] - w*A[0])*sinh(xi)*cosh(xi)^5 + (2*alpha*k^2*A[1] + alpha*k^2*B[1] - 2*alpha*lambda^2*A[1] + 2*alpha*lambda^2*B[1] - 2*gamma*lambda^2*A[1] + 2*gamma*lambda^2*B[1] - 6*A[0]^2*A[1]*beta[4] - 3*A[0]^2*B[1]*beta[4] - 3*A[1]^3*beta[4] - 6*A[1]^2*B[1]*beta[4] - 3*A[1]*B[1]^2*beta[4] - 4*A[0]*A[1]*beta[3] - 2*A[0]*B[1]*beta[3] + 2*w*A[1] + w*B[1])*cosh(xi)^4 + (alpha*k^2*A[0] - A[0]^3*beta[4] - 6*A[0]*A[1]^2*beta[4] - 6*A[0]*A[1]*B[1]*beta[4] - A[0]^2*beta[3] - 2*A[1]^2*beta[3] - 2*A[1]*B[1]*beta[3] + w*A[0])*sinh(xi)*cosh(xi)^3 + (-alpha*k^2*A[1] + 4*alpha*lambda^2*A[1] + 4*gamma*lambda^2*A[1] + 3*A[0]^2*A[1]*beta[4] + 3*A[1]^3*beta[4] + 3*A[1]^2*B[1]*beta[4] + 2*A[0]*A[1]*beta[3] - w*A[1])*cosh(xi)^2 + (3*A[0]*A[1]^2*beta[4] + A[1]^2*beta[3])*sinh(xi)*cosh(xi) - 2*alpha*lambda^2*A[1] - 2*gamma*lambda^2*A[1] - A[1]^3*beta[4] = 0;
N := 6;
for i from 0 to N do
    equ[1][i] := coeff(E1, {cosh(xi)^i, sinh(xi)^i}, i) = 0;
end do;
             //        2               2     
equ[1][0] := \\-alpha k  A[1] - alpha k  B[1]

           2                      2                    3        
   + 3 A[0]  A[1] beta[4] + 3 A[0]  B[1] beta[4] + A[1]  beta[4]

           2                           2               3        
   + 3 A[1]  B[1] beta[4] + 3 A[1] B[1]  beta[4] + B[1]  beta[4]

                                                                \ 
   + 2 A[0] A[1] beta[3] + 2 A[0] B[1] beta[3] - w A[1] - w B[1]/ 

          6   /        2            3        
  cosh(xi)  + \-alpha k  A[0] + A[0]  beta[4]

                2                                   
   + 3 A[0] A[1]  beta[4] + 6 A[0] A[1] B[1] beta[4]

                2               2               2        
   + 3 A[0] B[1]  beta[4] + A[0]  beta[3] + A[1]  beta[3]

                               2                 \          
   + 2 A[1] B[1] beta[3] + B[1]  beta[3] - w A[0]/ sinh(xi) 

          5   /         2               2     
  cosh(xi)  + \2 alpha k  A[1] + alpha k  B[1]

                   2                      2     
   - 2 alpha lambda  A[1] + 2 alpha lambda  B[1]

                   2                      2     
   - 2 gamma lambda  A[1] + 2 gamma lambda  B[1]

           2                      2             
   - 6 A[0]  A[1] beta[4] - 3 A[0]  B[1] beta[4]

           3                 2             
   - 3 A[1]  beta[4] - 6 A[1]  B[1] beta[4]

                2                              
   - 3 A[1] B[1]  beta[4] - 4 A[0] A[1] beta[3]

                                            \         4   /      
   - 2 A[0] B[1] beta[3] + 2 w A[1] + w B[1]/ cosh(xi)  + \alpha 

   2            3                      2        
  k  A[0] - A[0]  beta[4] - 6 A[0] A[1]  beta[4]

                                    2                 2        
   - 6 A[0] A[1] B[1] beta[4] - A[0]  beta[3] - 2 A[1]  beta[3]

                                 \                  3   /
   - 2 A[1] B[1] beta[3] + w A[0]/ sinh(xi) cosh(xi)  + \
        2                      2                      2     
-alpha k  A[1] + 4 alpha lambda  A[1] + 4 gamma lambda  A[1]

           2                      3        
   + 3 A[0]  A[1] beta[4] + 3 A[1]  beta[4]

           2                                            \ 
   + 3 A[1]  B[1] beta[4] + 2 A[0] A[1] beta[3] - w A[1]/ 

          2
  cosh(xi) 

     /           2               2        \                  
   + \3 A[0] A[1]  beta[4] + A[1]  beta[3]/ sinh(xi) cosh(xi)

                   2                      2            3           
   - 2 alpha lambda  A[1] - 2 gamma lambda  A[1] - A[1]  beta[4] = 

   \    
  0/ = 0


                       equ[1][1] := 0 = 0

                       equ[1][2] := 0 = 0

                       equ[1][3] := 0 = 0

                       equ[1][4] := 0 = 0

                       equ[1][5] := 0 = 0

                       equ[1][6] := 0 = 0

NULL;
NULL;

Download loop_for_coeficent.mw

Is the a print or plot function that can generate from an expression an expression tree

and/or the corresponding expression DAG

 

Taken from ?ProgrammingGuide,Chapter02

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