Maple 2018 Questions and Posts

These are Posts and Questions associated with the product, Maple 2018

Hello. I have the equations written into the arrays. I want to combine them into a common system and solve it. I gave a simple example of what I need. How do I perform this operation?


T1 := array(1 .. 2);

array( 1 .. 2, [ ] )


x = 1


y = 2


T2 := array(1 .. 2);

array( 1 .. 2, [ ] )


z = 3


r = x+y+z


solve({T1, T2}, {r, x, y, z});




restart; with(Student[LinearAlgebra]); A := Matrix([[2, 3, -4], [0, -4, 2], [1, -1, 5]]); for i to 3 do for j to 3 do print((-1)^(i+j)*Minor(A, i, j)) end do end do; How to code to get that is egal to Adjoint(A)? Thank you.
An ellipse of focus F1 and F2 is considered in which the focal length F1F2=2c is equal to the length 2b of the short axis; the length of the long axis is 2a. M being any point of this ellipse, calculate the lengths MF1=x and MF2=y according to a and angle F1MF2 = alpha. What is the maximum value of alpha? Thank you for your help.

I want to vary t from -15 to -7 and from 7 to 15 how to write the Explore command?
example : Explore(Fig(t), t=-15..-7 and t=7..15); which does't work.  Thank you.

Hi guys

I want to solve the following non-linear differential equation but by using dsolve(), the computer cannot solve it, so please guide me.

Q:=2*diff(a(t), t, t)*a(t)^3 - 3*diff(a(t), t)^4 + diff(a(t), t)^2*a(t)^2

with the best regards

eqell := expand((x+(1/2)*R1-(1/2)*R)^2/a^2+y^2/b^2-1); geometry:-ellipse(ell, eqell, [x, y]); detail(ell); ellipse: hint: unable to determine if 1/(1/2*R+1/2*R1)^2*(1/(-8*R^3*R1+14*R^2*R1^2-3*R*R1^3)*R^2+2/(-8*R^3*R1+14*R^2*R1^2-3*R*R1^3)*R1*R+1/(-8*R^3*R1+14*R^2*R1^2-3*R*R1^3)*R1^2) is zero Error, (in geometry:-ellipse) the given polynomial/equation is not an algebraic representation of a ellipse. How to manage this error ? Thank you.


I want to define an orthonormal tetrad basis of my choice in a spacetime having a metric given in some system of coordinates. My problem is that Maple automatically proposes an orthonormal metric but this is not the one that suits my requirements. So, I would like to specify the tetrad basis manually. As an example, I am trying to reproduce the calculations in sections 6 and 7 of the article . Here, the metric $g$ is given by the line element $ds^2 = - (c(t,r)^2 - v(t,r)^2) dt^2 + 2 v(t,r) dr dt + dr^2 + r^2 (d\theta^2 + sin(\theta)^2 d\phi^2)$ in $(t, r, \theta, \phi)$ coordinates. My chosen signature is (- + + +). Let, us adopt the convention used by Maple and denote spacetime indices by Greek alphabets and tetrad indices by lowercase Latin letters. Now, I would like to define a tetrad $e_a = (V, S, \Theta, \Phi)$ (as in section 7 of the article referred to above) where:

V^\mu = \frac{1}{c\sqrt{1-\beta(t,r)^2}}[1, - (v + c \beta), 0, 0] \\

S^\mu = \frac{1}{c\sqrt{1-\beta^2}}[-\beta, c + v \beta, 0, 0] \\

\Theta^\mu = [0,0,1,0]

\Phi^\mu = [0,0,0,1].

Here, $|\beta(t,r)| < 1$. I do not know how I may specify this in my worksheet. This may come of use somewhere later. Now, with this choice of the tetrad, we know that $g(e_a, e_b) = \eta_{ab}$ with $\eta$ being the Minkowski metric in spherical coordinates. After defining this tetrad basis, I finally want to calculate Einstein tensor, components of energy-momentum tensr etc. I have problem with constructing this orthonormal tetrad basis myself. It would be great if you could help me with this.


An additional curiosity: when we work with multiple tetrad bases, is it possible to denote the the tetrad indices by hatted tetrad labels themselves, as in $\eta_{\hat V, \hat \Theta}$?


Thank you.



[`*`, `.`, Annihilation, AntiCommutator, Antisymmetrize, Assume, Bra, Bracket, Cactus, Check, Christoffel, Coefficients, Commutator, CompactDisplay, Coordinates, Creation, D_, Dagger, Decompose, Define, Dgamma, Einstein, EnergyMomentum, Expand, ExteriorDerivative, Factor, FeynmanDiagrams, Fundiff, Geodesics, GrassmannParity, Gtaylor, Intc, Inverse, Ket, KillingVectors, KroneckerDelta, LeviCivita, Library, LieBracket, LieDerivative, Normal, Parameters, PerformOnAnticommutativeSystem, Projector, Psigma, Redefine, Ricci, Riemann, Setup, Simplify, SpaceTimeVector, StandardModel, SubstituteTensor, SubstituteTensorIndices, SumOverRepeatedIndices, Symmetrize, TensorArray, Tetrads, ThreePlusOne, ToFieldComponents, ToSuperfields, Trace, TransformCoordinates, Vectors, Weyl, `^`, dAlembertian, d_, diff, g_, gamma_]


Setup(signature = `-+++`, coordinates = (X = [t, r, theta, phi]))

`* Partial match of  'coordinates' against keyword 'coordinatesystems'`


`Default differentiation variables for d_, D_ and dAlembertian are: `*{X = (t, r, theta, phi)}


`Systems of spacetime Coordinates are: `*{X = (t, r, theta, phi)}


[coordinatesystems = {X}, signature = `- + + +`]


Setup(g_=-(c(t,r)^2 - v(t,r)^2)*dt^2 + 2*v(t,r)*dt*dr + dr^2 + r^2*dtheta^2 + r^2*sin(theta)^2*dphi^2)

[metric = {(1, 1) = -c(t, r)^2+v(t, r)^2, (1, 2) = v(t, r), (2, 2) = 1, (3, 3) = r^2, (4, 4) = r^2*sin(theta)^2}]


PDETools:-declare(c(t, r), v(t, r))

` c`(t, r)*`will now be displayed as`*c


` v`(t, r)*`will now be displayed as`*v



`Setting lowercaselatin_ah letters to represent tetrad indices `


0, "%1 is not a command in the %2 package", Tetrads, Physics


0, "%1 is not a command in the %2 package", Tetrads, Physics


[IsTetrad, NullTetrad, OrthonormalTetrad, PetrovType, SegreType, TransformTetrad, e_, eta_, gamma_, l_, lambda_, m_, mb_, n_]



Physics:-Tetrads:-e_[a, mu] = Matrix(%id = 18446744078438692614)







Hi guys,

I am trying to determine the first 5 eigen frequencies of a bending beam with rotational and translational spring supports. This is done by setting the determinant of the coefficient matrix equal to zero. I use RootFInder -> Analytic to find the first 5 roots between 0.001 and 0.1. After I substitute the roots back in to the equation they do not give me a zero value.

Can someone see where this goes wrong?


Be an ellipse E of center O, of foci F, F1, of major axis AA1 (OA=a, OF=c), M a point of E, m its projection on AA1, T and N the points where the tangent and the normal in M cut AA1 respectively. How to establish the formulas: NF=c/a*MF; Om*OT=a² ; ON=c²/a²*Om ? Thank you.

A triangle ABC with fixed B and C vertex is considered in the plane, A being variable so that b+c remains constant and equal to a given length L.
We call P, T, T' the points of contact of the exinscrit circle in the angle B with the sides BC, AB and AC respectively.
Show that P is fixed and is one of the vertex of the ellipse described by point A. What are the locus of T and T'? How to animate the drawing when A move ? Thank you.

In the plane, an ABC triangle is considered for the vertices B and C are fixed, A being variable so that b +c remains constant and equal to a given length l. (b=distance(A,C), (c=distance(A,B)
How to show that the product tan(B/2=*tan(C/2) remains constant ?


Good day to all.

I have a data set consisting of 12 points in the x-y plane. These points form a periodic pattern and I was wondering if it is possible to obtain a curve that is a best-fit for these points. I have reason to expect that this pattern will repeat for successive points (i.e. points 13, 14, ..., 30).

Does anyone know of a way to obtain a function that can represent this behavior?

Thanks for reading!


Whoever designed Maple's user-interface thinks very differently from me. How can I insert a 2nd section into Chapter 1? There's no space between the end of Section 1 and the end of Chapter 1 for me to put the cursor, so where should I put the cursor, and what should I do?

What do I need to do to the "2 + 3" in the attached Document in order to make it evaluate? I know about F5 to switch between Text and Math modes, but that's not enough to get me where I want to be. The "2 + 3" is already in Math mode, but that's not enough to get it to evaluate.

The Document:

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