Maple 2019 Questions and Posts

These are Posts and Questions associated with the product, Maple 2019

I am trying to compute the rank of the Commutator Matrix of a Lie algebra. That is, I wish to construct a matrix version of the multiplication table for a given matrix Lie algebra, and then compute the rank of this matrix.



with(DifferentialGeometry); with(LieAlgebras)



M := [Matrix([[1, 0], [0, 0]]), Matrix([[0, 0], [0, 1]]), Matrix([[0, 1], [0, 0]])]

[Matrix(%id = 18446744078224010646), Matrix(%id = 18446744078224010766), Matrix(%id = 18446744078224003190)]


L := LieAlgebraData(M, Alg1)

_DG([["LieAlgebra", Alg1, [3, table( [ ] )]], [[[1, 3, 3], 1], [[2, 3, 3], -1]]])




`Lie algebra: Alg1`


T := MultiplicationTable("LieTable")

Matrix(%id = 18446744078223968366)








I have the above, but I run into two issues:

1. It doesn't have matrix format, so Rank is undefined (I have tried convert(T,matrix) to no avail),

2. I need to be able to remove the first and second rows and columns from T (because these rows/columns are occupied by the Lie algebra's basis elements, and separating lines, respectively).


I believe that if I can convert T into a matrix somehow, I can simply use SubMatrix to remove the things I don't want, and then Rank should work.


Any help would be greatly appreciated!


P.S. Thanks to dharr1338 for the suggestion of including the worksheet, I'm very new to Maple and MaplePrimes, so I appreciate the patience.

MacDude posted a worksheet for creating help files using the makehelp command that I found very useful.  However, his worksheet created a table of contents that organized the command help pages under a single folder.  I wanted to create a help file table of contents with the commands organized into sub-folders under the main application folder. ie. Package Name,Folder Name, command. The help page for makehelp is not very informative; in particular the example that shows (purportedly) how to override the existing help pages with your own help file is very misleading.  Also, the description of the parameters to the browser option of the makehelp command is too vague. I needed an error message to tell me that the browser option expects parameters in the form List(Name,String).  In the end, I was able to get a folder/sub-folder structure using a structure [`Folder Name`,`Subfolder Name`,"Command"].  Sub-folders are sorted alphabetically. If anyone has a need, the attached worksheet shows how I created the table of contents structure.

I have loaded a series of worksheets into a help file using the makehelp command and installed in my toolbox package. Except for one of them, the worksheets appear in the help browser as worksheets instead of help files. Whenever I select one of them, it opens in maple as a worksheet. I would like to control whether a given help file opens as a worksheet or opens as a help.  I have read the helptools help and the help page for makehelp, but have been unable to identify the setting that determines which mode the help file operates in. Please advise what I am missing here.

How do I write this in logical notation in Maple? Is it even possible?

Show logical notation that expresses the following statement: If one dice shows an even number of spots and the second dice shows an odd number of spots, then the total for the pair is less than or equal to 9.


I solved these equations numerically but I need to solve it by Runge-Kutta fourth order Method. Kindly help me in the coding of the same.


N1 :=1:N2 :=1: N3 :=0.1 :R := -1:
EQ:={(1+N1)*diff(f(x),x$4)-N1*diff(g(x),x$2)-R*(-diff(f(x),x)*diff(f(x),x$2)+f(x)*diff(f(x),x$3))=0, N2*diff(g(x),x$2)+N1*(diff(f(x),x$2)-2*g(x))-N3*R*(f(x)*diff(g(x),x)-diff(f(x),x)*g(x))=0}:

IC:={D(D(f))(0)=0, D(f)(1)=0,f(0)=0,f(1)=1,g(0)=0,  g(1)=0}:

sol:= dsolve(EQ union IC, numeric,output=Array([0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1])):

I want to show the animation of the polar equation r=cos(2theta) be plotted from theta=0 to 2pi

I have a simple matrix, 11 rows x 3 columns, with header row.  <<

I multiply column 1 and 2 to get <<0.,0.031,0.218,0.657,1.084,1.095,0.654,0.217>>

Now, I just want to add up these elements, but 'sum' doesn't work 'Sum' doesn't work either. Is there a simpel way to do this?

m1 := `<|>`(`<,>`("# girls", 0, 1, 2, 3, 4, 5, 6, 7, 8), `<,>`("P(x)", 0.4e-2, 0.31e-1, .109, .219, .271, .219, .109, 0.31e-1, 0.4e-2), `<,>`("x*P(x)", 0, 0, 0, 0, 0, 0, 0, 0, 0))

Matrix(%id = 18446745635438952446)


m1[2 .. 9, 3] := `~`[`*`](m1[2 .. 9, 1], m1[2 .. 9, 2])

Vector[column](%id = 18446745635417541318)



Vector[column](%id = 18446745635493441398)



Error, (in LinearAlgebra:-Multiply) invalid arguments




Download Untitled_(3).mw

I want to shade the area where the two polar curves overlap. The first curve is r=2 and the other curve is r=2(1-cos(theta)). How do I do this?

I want to find the surface area of this parametric curve revolving around the x-axis. I was able to plot the 2D rendering but I want to show the plot so that I can see the surface area. I suspect that would be the 3D rendering.

x=cos(t), y=2+sin(t), 0<=t<=2pi, x-axis


It seems that plottools:-extrude doesn't support the "style" option: no error returned, just the extusion being always of surface style.
Am I correct ?

The solver seems to have a problem with some sets of boundary conditions. (See attached worksheet.)

Is there a way to get this numerical solution?

[differentiation of f and greek letter xi in bracket]


I am trying to find q(t) from this 

ode1:=-diff(q(t), t) - 1.851851852*10^(-7)*q(t)*(2.042885233*10^10 - 3.517396152*10^18*(0.00001474262739*cos((1000*sqrt(1122)*t)/33) + 0.00001474262739*sin((1000*sqrt(1122)*t)/33))^2) + 9.259259260*10^(-7);

with initial condition

ics := q(0) = 2.45*10^(-12)



but I cannot get the full solution. Is there any way I could find q(t)?



This is the source:





I am having equation y(x) in 5 variable c1, c2, A, R and x.

I am not able to plot graph in x and y(x) for A=1, c1 = 2.3, c2 = 2.4 and R=0,2 5,9.

Range of x: -1..1

Caption :graph of y(x) at different value of R.

Legend: R=0, R=1, R=2, R=3.

my equation is


"y(x):=0.0000148809523809523809 A^3 R^2 x^10-0.000334821428571428572 A^3 R^2 x^8+0.00156250000000000000 A^3 R^2 x^7+0.000133928571428571429 A^3 R^2 x^6-0.00312500000000000000 A^2 R^2 x^7+0.00156250000000000000 A^3 R^2 x^5-0.0156250000000000000 A^3 R^2 x^4-0.00312500000000000000 A^2 R^2 x^5-0.00625000000000000000 A^2 R x^6+0.00647321428571428572 A^3 R^2 x^3+0.0625000000000000000 A^2 R^2 x^4-0.0129464285714285714 A^2 R^2 x^3-0.0625000000000000000 A R^2 x^4+0.0625000000000000000 A c1 c2 x^4+0.125000000000000000 A^2 R x^3-0.00319293058132343847 A^3 R^2+0.00803571428571428571 A^2 R x^2-0.250000000000000000 A R x^3+0.0125000000000000000 A^2 R^2-0.00178571428571428571 A^2 R-0.0125000000000000000 A R^2+0.0125000000000000000 A c1 c2-0.750000000000000000 A x^2+0.500000000000000001 (0.0380078849721706865 A^3 R^2-0.150000000000000000 A^2 R^2+0.150000000000000000 A R^2-0.150000000000000000 A c1 c2) x^2+0.750000000000000000 A+1.00000000000000000 (-0.00959821428571428571 A^3 R^2+0.0191964285714285714 A^2 R^2) x+1.00000000000000000 (-0.125000000000000000 A^2 R+0.250000000000000000 A R) x:"







pde := diff(w(x, t), x $ 4) + diff(w(x, t), t $ 2)/c^2 = 0;

diff(diff(diff(diff(w(x, t), x), x), x), x)+(diff(diff(w(x, t), t), t))/c^2 = 0


test1 := w(x, t) = W(x)*cos(omega*t); pde1 := expand((eval(pde, test1))/cos(omega*t))

w(x, t) = W(x)*cos(omega*t)


diff(diff(diff(diff(W(x), x), x), x), x)-W(x)*omega^2/c^2 = 0


ode := algsubs(omega^2/c^2 = alpha^4, pde1); sol := dsolve(ode); sol := convert(sol, trig)

-W(x)*alpha^4+diff(diff(diff(diff(W(x), x), x), x), x) = 0


W(x) = _C1*exp(-alpha*x)+_C2*exp(alpha*x)+_C3*sin(alpha*x)+_C4*cos(alpha*x)


W(x) = _C1*(cosh(alpha*x)-sinh(alpha*x))+_C2*(cosh(alpha*x)+sinh(alpha*x))+_C3*sin(alpha*x)+_C4*cos(alpha*x)


L_collection := [indets(sol, specfunc({cos, cosh, sin, sinh}))[]]

[cos(alpha*x), cosh(alpha*x), sin(alpha*x), sinh(alpha*x)]



temp := collect(sol, [sinh, cosh, sin, cos])

W(x) = (-_C1+_C2)*sinh(alpha*x)+(_C1+_C2)*cosh(alpha*x)+_C3*sin(alpha*x)+_C4*cos(alpha*x)


CL := [coeffs(rhs(temp), L_collection)]NULL

[-_C1+_C2, _C1+_C2, _C3, _C4]


R:=[seq(cat(_D,i)=CL[i], i=1..nops(CL))]

[_D1 = -_C1+_C2, _D2 = _C1+_C2, _D3 = _C3, _D4 = _C4]


MX:= subs((rhs=lhs)~(R), temp);

W(x) = _D1*sinh(alpha*x)+_D2*cosh(alpha*x)+_D3*sin(alpha*x)+_D4*cos(alpha*x)


boundary_condition_1 := simplify(rhs(eval(diff(MX, `$`(x, 1)), x = 0))/alpha = 0)

_D1+_D3 = 0


boundary_condition_2 := simplify(rhs(eval(MX, x = 0)) = 0)

_D2+_D4 = 0


boundary_condition_3 := simplify(rhs(eval(diff(MX, `$`(x, 1)), x = L))/alpha = 0)

cosh(alpha*L)*_D1+sinh(alpha*L)*_D2+cos(alpha*L)*_D3-sin(alpha*L)*_D4 = 0


boundary_condition_4 := simplify(rhs(eval(MX, x = L)) = 0)

_D1*sinh(alpha*L)+_D2*cosh(alpha*L)+_D3*sin(alpha*L)+_D4*cos(alpha*L) = 0


boundary_condition_solve := solve([boundary_condition_1, boundary_condition_2, boundary_condition_3, boundary_condition_4]); MX := eval(MX, boundary_condition_solve)

Warning, solutions may have been lost


{L = L, _D1 = -_D3, _D2 = -_D4, _D3 = _D3, _D4 = _D4, alpha = 0}, {L = 0, _D1 = -_D3, _D2 = -_D4, _D3 = _D3, _D4 = _D4, alpha = alpha}, {L = L, _D1 = 0, _D2 = 0, _D3 = 0, _D4 = 0, alpha = alpha}


Error, invalid input: eval received ({L = L, _D1 = -_D3, _D2 = -_D4, _D3 = _D3, _D4 = _D4, alpha = 0}, {L = 0, _D1 = -_D3, _D2 = -_D4, _D3 = _D3, _D4 = _D4, alpha = alpha}, {L = L, _D1 = 0, _D2 = 0, _D3 = 0, _D4 = 0, alpha = alpha}), which is not valid for its 2nd argument, eqns





I have tried to solve these 4 equations to get the characteristic equation and finally the solution of the PDE.  But it shows some error. Can you please help with this issue?

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