Unanswered Questions

This page lists MaplePrimes questions that have not yet received an answer

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

Does this happen to you (ChatGPT session):

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 used: 
Y := ssystem("dir C:"); print(Y)
result is

[0,"\" El volumen de la unidad C es OS\n El n£mero de serie del volumen es: 54A9-09DA\n\n Directorio de C:\\Program Files\\Maple 2016"

Windows operating system English version but Maple shows Spanish result
I want result is English. Please help me

Y := ssystem("dir C:"):

[0, " El volumen de la unidad C es OS
 El n£mero de serie del volumen es: 54A9-09DA

 Directorio de C:\Program Files\Maple 2016

21/02/2025  07:53 AM    <DIR>          .
22/02/2025  08:34 AM    <DIR>          ..
21/02/2025  07:50 AM    <DIR>          afm
21/02/2025  07:55 AM    <DIR>          bin.X86_64_WINDOWS
21/02/2025  07:52 AM    <DIR>          data
13/02/2025  07:46 AM    <DIR>          eBookTools
21/02/2025  07:50 AM    <DIR>          etc
02/02/2016  05:05 AM            73,861 EULA.html
21/02/2025  07:52 AM    <DIR>          examples
21/02/2025  07:52 AM    <DIR>          examplesclassic
21/02/2025  07:52 AM    <DIR>          Excel
21/02/2025  07:50 AM    <DIR>          extern
21/02/2025  07:52 AM    <DIR>          Fonts
13/01/2016  06:39 AM           223,499 Install.html
21/02/2025  07:52 AM    <DIR>          java
21/02/2025  07:52 AM    <DIR>          jre
21/02/2025  07:52 AM    <DIR>          lib
21/02/2025  07:55 AM    <DIR>          license
27/01/2011  11:13 PM             6,296 Maple Cloud Terms of Service.html
17/02/2016  02:54 PM         5,490,560 MapleToolbox2016.0WindowsX64Installer.exe
13/02/2025  07:48 AM           317,257 Maple_2016_Install_2025_02_13_08_46_07.log
21/02/2025  07:52 AM           317,834 Maple_2016_Install_2025_02_21_08_47_47.log
21/02/2025  07:50 AM    <DIR>          profiles
21/02/2025  07:52 AM             5,396 readme.txt
21/02/2025  07:52 AM    <DIR>          redist
21/02/2025  07:52 AM    <DIR>          samples
21/02/2025  07:52 AM    <DIR>          uninstall
21/02/2025  07:52 AM    <DIR>          update
13/02/2025  07:46 AM    <DIR>          Users
               7 archivos      6,434,703 bytes
              22 dirs  148,583,636,992 bytes libres"]

(1)

``

Download language_maple.mw

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

 always i try to apply a technique like long wave limit to get my result, but this time when i do i reach zero so the author try to use another method which really i can't reach how they did and some term are dispear and some are remain , it about substituting and apply epsilon go to zero which i don't know how they apply, anyone can figure out how they reach the result, and maybe my letter and paper are not same about small and capital but it is so clear 

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)

_local(gamma)

declare(u(x, y, z, t))

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

(2)

declare(f(x, y, z, t))

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

(3)

NULL

pde := diff(diff(u(x, y, z, t), t)+6*u(x, y, z, t)*(diff(u(x, y, z, t), x))+diff(u(x, y, z, t), `$`(x, 3)), x)-lambda*(diff(u(x, y, z, t), `$`(y, 2)))+diff(alpha*(diff(u(x, y, z, t), x))+beta*(diff(u(x, y, z, t), y))+gamma*(diff(u(x, y, z, t), z)), x)

diff(diff(u(x, y, z, t), t), x)+6*(diff(u(x, y, z, t), x))^2+6*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x))+diff(diff(diff(diff(u(x, y, z, t), x), x), x), x)-lambda*(diff(diff(u(x, y, z, t), y), y))+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+gamma*(diff(diff(u(x, y, z, t), x), z))

(4)

pde_linear, pde_nonlinear := selectremove(proc (term) options operator, arrow; not has((eval(term, u(x, y, z, t) = a*u(x, y, z, t)))/a, a) end proc, expand(pde))

diff(diff(u(x, y, z, t), t), x)+diff(diff(diff(diff(u(x, y, z, t), x), x), x), x)-lambda*(diff(diff(u(x, y, z, t), y), y))+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+gamma*(diff(diff(u(x, y, z, t), x), z)), 6*(diff(u(x, y, z, t), x))^2+6*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x))

(5)

lambda := 1; alpha := 1; beta := 1; gamma := 1

1

 

1

 

1

 

1

(6)

NULL

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

t*w[i]+x*k[i]+y*l[i]+z*r[i]

(7)

NULL

eqw := w[i] = -(k[i]^4+k[i]^2+k[i]*l[i]+k[i]*r[i]-l[i]^2)/k[i]

w[i] = -(k[i]^4+k[i]^2+k[i]*l[i]+k[i]*r[i]-l[i]^2)/k[i]

(8)

NULL

Bij := proc (i, j) options operator, arrow; (3*k[i]^4*k[j]^2-6*k[i]^3*k[j]^3+(3*k[j]^4+l[j]^2)*k[i]^2-2*k[i]*k[j]*l[i]*l[j]+k[j]^2*l[i]^2)/(3*k[i]^4*k[j]^2+6*k[i]^3*k[j]^3+(3*k[j]^4+l[j]^2)*k[i]^2-2*k[i]*k[j]*l[i]*l[j]+k[j]^2*l[i]^2) end proc

proc (i, j) options operator, arrow; (3*k[i]^4*k[j]^2-6*k[i]^3*k[j]^3+(3*k[j]^4+l[j]^2)*k[i]^2-2*k[i]*k[j]*l[i]*l[j]+k[j]^2*l[i]^2)/(3*k[i]^4*k[j]^2+6*k[i]^3*k[j]^3+(3*k[j]^4+l[j]^2)*k[i]^2-2*k[i]*k[j]*l[i]*l[j]+k[j]^2*l[i]^2) end proc

(9)

NULL

eij := (3*k[i]^4*k[j]^2-6*k[i]^3*k[j]^3+(3*k[j]^4+l[j]^2)*k[i]^2-2*k[i]*k[j]*l[i]*l[j]+k[j]^2*l[i]^2)/(3*k[i]^4*k[j]^2+6*k[i]^3*k[j]^3+(3*k[j]^4+l[j]^2)*k[i]^2-2*k[i]*k[j]*l[i]*l[j]+k[j]^2*l[i]^2)

(3*k[i]^4*k[j]^2-6*k[i]^3*k[j]^3+(3*k[j]^4+l[j]^2)*k[i]^2-2*k[i]*k[j]*l[i]*l[j]+k[j]^2*l[i]^2)/(3*k[i]^4*k[j]^2+6*k[i]^3*k[j]^3+(3*k[j]^4+l[j]^2)*k[i]^2-2*k[i]*k[j]*l[i]*l[j]+k[j]^2*l[i]^2)

(10)

eval(eij, k[j] = b*k[i]); series(%, k[i], 3); convert(%, polynom); eval(%, b = k[j]/k[i]); Bij := (%-1)/(k[i]*k[j])

(3*k[i]^6*b^2-6*k[i]^6*b^3+(3*b^4*k[i]^4+l[j]^2)*k[i]^2-2*k[i]^2*b*l[i]*l[j]+b^2*k[i]^2*l[i]^2)/(3*k[i]^6*b^2+6*k[i]^6*b^3+(3*b^4*k[i]^4+l[j]^2)*k[i]^2-2*k[i]^2*b*l[i]*l[j]+b^2*k[i]^2*l[i]^2)

 

series(1+O(k[i]^4),k[i],4)

 

1

 

1

 

0

(11)

NULL


Download transformation.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?

So just like the title illustrates, I found a paper authored by Gary Nicklason in 2022: Autonomous Planar Systems of Riccati Type and in the last section it mentioned about a class of Abel ODE, which belongs to AIA(Abel Inverse Abel) class. It is of First kind and the inverse of it(by swapping variables) is of second kind.

While the first kind is solvable in terms of Airy function, the inverse of it along with its equivalence class is not solvable by the existing dsolve.

I have tested it in my worksheet Nicklason_equation.mw. So is it possible to add this class into the dictionary for solvable Abel ODE, or, maybe there are some bugs within the internal procedure of dsolve, which results in failure for catching the solvable candidates?

I have a system of polynomial equations where the unknowns are real numbers. The set of solutions is infinite (positive-dimensional). How can I compute the real dimension of the solution set (i.e. of a real algebraic variety)?

As it as mentioned in arXiv:2105.10255, this can be done using the RealTriangularize function from the RegularChains package. What is best way of getting the real dimension from the regular_semi_algebraic_system object, which is returned by this function?

Is there a good way to include subscript(s) to a letter within a 'text' command?  Currently I do this by specifying the coordinates, letter, and font for the letter, then specify the coordinates, number and font for the subscript.  However, with this method the letter and subscript can be compressed if the viewing interval is compressed or expanded.  

Is there another way to include letters with a subscript in a text command?

is(Im(x)*x = 0);
                              true

 

Surely, Im(i)*i != 0?

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

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