Maple 2024 Questions and Posts

These are Posts and Questions associated with the product, Maple 2024

I tried the following procedure in a worksheet; Maple did not like it and claimed there was an error. However, I cannot even copy this to a Maple prompt; it jumps to another type of region. Any ideas? If I retype the command there is no problem with an error.

It reminds me of Maple 2 and the letter t which sometimes had to be retyped to get Maple to respond-a very strange bug which was eliminated years ago.

Hey guys, 

 

I try to solve big systems of polynomial equations and inequalities. Therefore I use the command SemiAlgebraic. In the moment I take those result and want to go on calculating with them. Sadly it turns out, that solve has some problems with RootOf expressions. It doesnt find a solution (althoug the graph shows that there is one) and gives the warning solution may have been lost. So now I though I might just aks SemiAlgebraic to give me solutions without RootOf expressions. For example you can write {x = RootOf(_Z^2 - y)+1, 1 < y, y < 2} as {x=t+1, y=t^2,1<t<2^0.5 . This might be easier to work with for solve. 

So my question is: Is there any way I can tell SemiAlgebraic precisely in what form the solution should be? 
Since the websites are down Im not able to do a first own research on this problem. So thank you in advance. 

Regards

Felix

I have a student who has a problem when closing and opening a Maple file.

It seems as if Maple turns math fields into text, but still execute when using ! or !!!

The dark red part is written in a text field, but Maple still executes

If I try to write in a math field and executes, closes Maple and opens again, this does not happen, so it is not the file that is the problem.  The student is running 2024.2 version.

Can anyone explain the problem and how to solve it.

 

I am unable to add a comment or the file. I have tried several times, without any luck

I occasionally find myself inexplicably in a region of my worksheet that does not respond to my editing, fe.g., I cannot erae or I cannot copy. I recently typed a command-there was an error of some form and I tried unsuccessfully to edit it. Then I tried to copy the code and enter it at a prompt. It refused to enter it at the prompt but copied it below the prompt in a strnge region that I do not understand. When I retyped the command at a prompt it worked fine. I do not understand th dead regions that pop up mysteriously. (I am using Maple 2024 on a Mac) The page is too long to copy but I could upload it if given directions.

this function i have is so long and my parameter are twenty they are two much when i make a change in explore i the change is so slow and i can't see some of this parameter how act to figure when i change becuase the placement of parameters i want some of parameter being in right  and some of them being in right  and figure be in the middle for see them together can we do something like that?

figure.mw

Hi everyone,

I'm trying to compute the cohomology group of some Lie algebras using the LieAlgebra package, but it appears that the Cohomology command doesn't provide the correct basis for the higher dimensional cohomology group, instead repeating up to the correct dimension only one element.

For example, with the following Lie algebra

L1:=_DG([["LieAlgebra", Alg1, [6]], [[[1, 3, 2], 1], [[1, 2, 3], -1], [[4, 6, 5], 1], [[4, 5, 6], -1]]])
DGSetup(L1)

the command

C := RelativeChains([])

does provide the correct k-forms on Alg1, but then

H := Cohomology(C)
provides
[[theta4,theta1],[theta1 &w theta4, theta1 &w theta4, theta1 &w theta4],[theta1 &w theta2 &w theta3,theta1 &w theta2 &w theta3,theta1 &w theta2 &w theta3,theta1 &w theta2 &w theta3], [theta1 &w theta2 &w theta3 &w theta4,theta1 &w theta2 &w theta3 &w theta4,theta1 &w theta2 &w theta3 &w theta4],[theta1 &w theta2 &w theta3 &w theta4 &w theta5 &w theta6, theta1 &w theta2 &w theta3 &w theta4 &w theta5 &w theta6], [theta1 &w theta2 &w theta3 &w theta4 &w theta5 &w theta6]

A similar thing does happen for the examples provided in the online help (e.g. example 1 from https://de.maplesoft.com/support/help/Maple/view.aspx?path=DifferentialGeometry/LieAlgebras/Cohomology). Is the command broken?

Any help is really appreciated.

restart

with(PDEtools)

undeclare(prime, quiet); declare(u(x, y, z, t), quiet); declare(f(x, y, z, t), quiet)

``

(1)

thetai := k[i]*(t*w[i]+y*l[i]+z*r[i]+x)

eqw := w[i] = (-1+sqrt(-4*beta*mu*l[i]-4*delta*mu*r[i]-4*mu*k[i]^2-4*alpha*mu+1))/(2*mu)

Bij := proc (i, j) options operator, arrow; -24*mu/(sqrt(1+(-4*beta*l[j]-4*delta*r[j]-4*alpha)*mu)*sqrt(1+(-4*beta*l[i]-4*delta*r[i]-4*alpha)*mu)-1+((2*r[i]+2*r[j])*delta+(2*l[i]+2*l[j])*beta+4*alpha)*mu) end proc

NULL

theta1 := normal(eval(eval(thetai, eqw), i = 1)); theta2 := normal(eval(eval(thetai, eqw), i = 2))

eqf := f(x, y, z, t) = theta1*theta2+Bij(1, 2)

eqfcomplex := collect(evalc(eval(eval(eqf, l[2] = conjugate(l[1])), l[1] = a+I*b)), t)

eq17 := u(x, y, z, t) = 2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^2; equ := simplify(eval(eq17, eqfcomplex))

So we want to find a substitution that removes the time dependence from u. One way is to find the maximum and see how it moves. Here, the first solution gives what we want.

ans := solve({diff(rhs(equ), x), diff(rhs(equ), y), diff(rhs(equ), z)}, {x, y, z}, explicit)

 

NULL

Download hfz.mw

i need the result for (eqt33) but i can reach the result there is any  other way for finding? i need to plot 3D of that function but without have the function how i can do explore on it

w1.mw

I would like to generate a brief description of the object Iterator:-Product but I get the following error:  

Describe(Iterator:-Product);

object Product :: Class<<36893490916968945900>>:

    ModuleApply( )

    ModuleCopy( self::_Product, proto::_Product, 
Error, (in Describe) `proto` does not evaluate to a module

How do I get rid of this message? 

i did try but i don't know the result is not come out? also i am not sure to put equation in eq1 in pde or linear part?

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

undeclare(prime)

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

(1)

declare(u(x, y, t))

u(x, y, t)*`will now be displayed as`*u

(2)

declare(f(x, y, t))

f(x, y, t)*`will now be displayed as`*f

(3)

pde := diff(u(x, y, t), t, y)+diff(u(x, y, t), `$`(x, 3), y)-3*(diff(u(x, y, t), x))*(diff(u(x, y, t), x, y))-3*(diff(u(x, y, t), `$`(x, 2)))*(diff(u(x, y, t), y))+alpha*(diff(u(x, y, t), x, y))+beta*(diff(u(x, y, t), `$`(x, 2)))

diff(diff(u(x, y, t), t), y)+diff(diff(diff(diff(u(x, y, t), x), x), x), y)-3*(diff(u(x, y, t), x))*(diff(diff(u(x, y, t), x), y))-3*(diff(diff(u(x, y, t), x), x))*(diff(u(x, y, t), y))+alpha*(diff(diff(u(x, y, t), x), y))+beta*(diff(diff(u(x, y, t), x), x))

(4)

pde_nonlinear, pde_linear := selectremove(proc (term) options operator, arrow; has((eval(term, u(x, y, t) = a*u(x, y, t)))/a, a) end proc, pde)

-3*(diff(u(x, y, t), x))*(diff(diff(u(x, y, t), x), y))-3*(diff(diff(u(x, y, t), x), x))*(diff(u(x, y, t), y)), diff(diff(u(x, y, t), t), y)+diff(diff(diff(diff(u(x, y, t), x), x), x), y)+alpha*(diff(diff(u(x, y, t), x), y))+beta*(diff(diff(u(x, y, t), x), x))

(5)

eq := u(x, y, t) = -2*(diff(ln(f(x, y, t)), x))

u(x, y, t) = -2*(diff(f(x, y, t), x))/f(x, y, t)

(6)

eq1 := -(1/2)*numer(normal(eval(pde_linear, eq)))

f(x, y, t)^4*(diff(diff(diff(f(x, y, t), x), x), x))*beta+f(x, y, t)^4*(diff(diff(diff(f(x, y, t), x), x), y))*alpha-f(x, y, t)^3*(diff(f(x, y, t), y))*(diff(diff(f(x, y, t), x), x))*alpha-2*f(x, y, t)^3*(diff(diff(f(x, y, t), x), y))*(diff(f(x, y, t), x))*alpha-3*f(x, y, t)^3*(diff(f(x, y, t), x))*(diff(diff(f(x, y, t), x), x))*beta+2*f(x, y, t)^2*(diff(f(x, y, t), y))*(diff(f(x, y, t), x))^2*alpha+2*f(x, y, t)^2*(diff(f(x, y, t), x))^3*beta+(diff(diff(diff(f(x, y, t), t), x), y))*f(x, y, t)^4+(diff(diff(diff(diff(diff(f(x, y, t), x), x), x), x), y))*f(x, y, t)^4-(diff(diff(f(x, y, t), t), x))*(diff(f(x, y, t), y))*f(x, y, t)^3-(diff(diff(diff(diff(f(x, y, t), x), x), x), x))*(diff(f(x, y, t), y))*f(x, y, t)^3-(diff(diff(f(x, y, t), x), y))*(diff(f(x, y, t), t))*f(x, y, t)^3-4*(diff(diff(diff(f(x, y, t), x), x), x))*(diff(diff(f(x, y, t), x), y))*f(x, y, t)^3-(diff(f(x, y, t), x))*(diff(diff(f(x, y, t), t), y))*f(x, y, t)^3-4*(diff(diff(diff(diff(f(x, y, t), x), x), x), y))*(diff(f(x, y, t), x))*f(x, y, t)^3-6*(diff(diff(f(x, y, t), x), x))*(diff(diff(diff(f(x, y, t), x), x), y))*f(x, y, t)^3+2*(diff(f(x, y, t), x))*(diff(f(x, y, t), t))*(diff(f(x, y, t), y))*f(x, y, t)^2+8*(diff(diff(diff(f(x, y, t), x), x), x))*(diff(f(x, y, t), x))*(diff(f(x, y, t), y))*f(x, y, t)^2+6*(diff(diff(f(x, y, t), x), x))^2*(diff(f(x, y, t), y))*f(x, y, t)^2+24*(diff(diff(f(x, y, t), x), x))*(diff(f(x, y, t), x))*(diff(diff(f(x, y, t), x), y))*f(x, y, t)^2+12*(diff(diff(diff(f(x, y, t), x), x), y))*(diff(f(x, y, t), x))^2*f(x, y, t)^2-36*(diff(diff(f(x, y, t), x), x))*(diff(f(x, y, t), x))^2*(diff(f(x, y, t), y))*f(x, y, t)-24*(diff(f(x, y, t), x))^3*(diff(diff(f(x, y, t), x), y))*f(x, y, t)+24*(diff(f(x, y, t), x))^4*(diff(f(x, y, t), y))

(7)

NULL

T := f(x, y, t) = h*a[10]+m^2+n^2+a[9]

T1 := m = t*a[3]+x*a[1]+y*a[2]+a[4]

T2 := n = t*a[7]+x*a[5]+y*a[6]+a[8]

T3 := h = a[10]*exp(t*p[3]+x*p[1]+y*p[2])

L2 := expand(subs({T1, T2, T3}, T))

f(x, y, t) = a[10]^2*exp(p[3]*t)*exp(p[1]*x)*exp(p[2]*y)+t^2*a[3]^2+2*t*x*a[1]*a[3]+2*t*y*a[2]*a[3]+x^2*a[1]^2+2*x*y*a[1]*a[2]+y^2*a[2]^2+2*t*a[3]*a[4]+2*x*a[1]*a[4]+2*y*a[2]*a[4]+a[4]^2+t^2*a[7]^2+2*t*x*a[5]*a[7]+2*t*y*a[6]*a[7]+x^2*a[5]^2+2*x*y*a[5]*a[6]+y^2*a[6]^2+2*t*a[7]*a[8]+2*x*a[5]*a[8]+2*y*a[6]*a[8]+a[8]^2+a[9]

(8)

eq9a := eval(eq1, L2)

indets(%)

{alpha, beta, t, x, y, a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9], a[10], p[1], p[2], p[3], exp(p[1]*x), exp(p[2]*y), exp(p[3]*t)}

(9)

p2b := subs({exp(p[1]*x) = eX, exp(p[2]*y) = eY, exp(p[3]*t) = eT}, eq9a); indets(%)

{alpha, beta, eT, eX, eY, t, x, y, a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9], a[10], p[1], p[2], p[3]}

(10)

p2c := numer(normal(p2b))

eqns := {coeffs(collect(p2c, {eT, eX, eY}, distributed), {eT, eX, eY})}; nops(%)

5

(11)

solve(eqns, {a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9], a[10], p[1], p[2], p[3]})

 

NULL

Download parameters.mw

If I understand right, in the following calling an exception should be raised since the return value of the matching coercion procedure is of course not of type “set”: 

restart;
foo := (x::coerce(set, (y::rtable) -> convert(y, list))) -> x:
foo(<0>);
 = 
                              [0]

Did I miss something?

i try find some part of solution of this kind of pde but i can't get results my openion is maybe this pde is wronge when i defined 

pde.mw

 Can I solve the Tolman-Oppenheimer-Volkoff equation with Maple ?  I'm having trouble with Einstein's equation with the energy tensor as the second member

How apply long wave limit for removing the constant k in such function , i need a general formula 

Limiting process from eq 12 to Bij

restart

NULL

Eq 12.

eij := ((-3*k[i]*(k[i]-k[j])*l[j]+beta)*l[i]^2-(2*(-3*k[j]*(k[i]-k[j])*l[j]*(1/2)+beta))*l[j]*l[i]+beta*l[j]^2)/((-3*k[i]*(k[i]+k[j])*l[j]+beta)*l[i]^2-(2*(3*k[j]*(k[i]+k[j])*l[j]*(1/2)+beta))*l[j]*l[i]+beta*l[j]^2)

((-3*k[i]*(k[i]-k[j])*l[j]+beta)*l[i]^2-2*(-(3/2)*k[j]*(k[i]-k[j])*l[j]+beta)*l[j]*l[i]+beta*l[j]^2)/((-3*k[i]*(k[i]+k[j])*l[j]+beta)*l[i]^2-2*((3/2)*k[j]*(k[i]+k[j])*l[j]+beta)*l[j]*l[i]+beta*l[j]^2)

(1)

eval(eij, k[j] = k[i]); series(%, k[i], 3); convert(%, polynom); eval(%, k[j] = k[i]); Bij := %

(beta*l[i]^2-2*beta*l[i]*l[j]+beta*l[j]^2)/((-6*k[i]^2*l[j]+beta)*l[i]^2-2*(3*k[i]^2*l[j]+beta)*l[j]*l[i]+beta*l[j]^2)

 

series(1+((6*l[i]^2*l[j]+6*l[i]*l[j]^2)/(beta*l[i]^2-2*beta*l[i]*l[j]+beta*l[j]^2))*k[i]^2+O(k[i]^4),k[i],4)

 

1+(6*l[i]^2*l[j]+6*l[i]*l[j]^2)*k[i]^2/(beta*l[i]^2-2*beta*l[i]*l[j]+beta*l[j]^2)

 

1+(6*l[i]^2*l[j]+6*l[i]*l[j]^2)*k[i]^2/(beta*l[i]^2-2*beta*l[i]*l[j]+beta*l[j]^2)

 

1+(6*l[i]^2*l[j]+6*l[i]*l[j]^2)*k[i]^2/(beta*l[i]^2-2*beta*l[i]*l[j]+beta*l[j]^2)

(2)

NULL

NULL

Download b12.mw

I need to find parameter a[12] any one have any vision for finding parameter  , in p2a must contain 3 exponential but we recieve 19 of them which is something i think it is trail function but trail is give me result so must be a way for finding parameter 

a[12]-pde.mw

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