Maple 2018 Questions and Posts

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

In the two examples below (in the second example, the range for the roots is simply expanded), we see bugs in both examples (Maple 2018.2). I wonder if these errors are fixed in Maple 2020?
 

restart;

solve({log[1/3](2*sin(x)^2-3*cos(2*x)+6)=-2,x>=-7*Pi/2,x<=-2*Pi}, explicit, allsolutions); # Example 1 - strange error message
solve({log[1/3](2*sin(x)^2-3*cos(2*x)+6)=-2,x>=-4*Pi,x<=-2*Pi}, explicit, allsolutions);  # Example 2 - two roots missing

Error, (in assume) contradictory assumptions

 

{x = -(11/3)*Pi}, {x = -(10/3)*Pi}

(1)

plot(log[1/3](2*sin(x)^2-3*cos(2*x)+6)+2, x=-7*Pi/2..-2*Pi);
plot(log[1/3](2*sin(x)^2-3*cos(2*x)+6)+2, x=-4*Pi..-2*Pi);

 

 

Student:-Calculus1:-Roots(log[1/3](2*sin(x)^2-3*cos(2*x)+6)=-2, x=-7*Pi/2..-2*Pi);  # OK
Student:-Calculus1:-Roots(log[1/3](2*sin(x)^2-3*cos(2*x)+6)=-2, x=-4*Pi..-2*Pi);  # OK

[-(10/3)*Pi, -(8/3)*Pi, -(7/3)*Pi]

 

[-(11/3)*Pi, -(10/3)*Pi, -(8/3)*Pi, -(7/3)*Pi]

(2)

 


I am glad that  Student:-Calculus1:-Roots  command successfully handles both examples.

 

Download bugs-in-solve.mw

At the moment t=0, we place a body at 100 ° C in a room at 25°C; we designate by q(t) the temperature at the moment t. The differential equation is.q'(t)+k*(q(t)-25)=t, with k cooling coefficient equal to 2.
Determine the solution that checks the initial condition.
What is the body temperature after 30 minutes.
After how long the temperature drops to 50°C. Thank you for the help.

Eq=z"(t)+3z'(t)+2z(t)=24*(exp(-3t)-exp(-4t)) how to find the gereral solution of this equation. Thank you.

 

Hello,

 

I have a problem with PDE coupled that I don't know how to solve in the maple.

Are there some analitical/numerical methods to solve the problem?

 

Any help will be usefull!!

 

 

Hi,

The evalDG command included in the LieAlgebras via the DifferentialGeometry package allows summations such as evalDG(e1+e2) where e1 and e2 are two generators of a given Lie algebra.

Now, let L be a list of such summations, e.g.,

L= [e1+a*e3,2*e2+b*e4,e1+3*e5]

where a and b are symbols for variable names in the real domain.
Then, while the code

evalDG(add(eval(cat(e,i)),i=1..n));

works fine (n be a given integer), the code

evalDG(add(eval(L[i]),i=1..n));

does not, and an error message results due to an "invalid subscript selector".

What is the right code to realize this summation?

Thanks.

Jaqr

Hi everybody,

This is my code:

assume(0 < a, 0 < L, a < L);

M := piecewise(0 <= x and x < a, P*x*(L-a)/L, a <= x and x < L, P*a*(L-x)/L);
ode := diff(y(x), `$`(x, 2)) = M/(E*I__0);
ic := y(0) = 0, y(L) = 0;
sol := factor(dsolve([ode, ic], y(x))); assign(sol); y1 := y(x);

I have two questions:

1) How to plot y1?

I would like to plot y1, but in the plot can to specify a values of a, L, P, E and I.

2) How can I find a maximun and minimun value of y1?

I tried to use maximize and minimize commands but really I don't know if I used them correctly.

Thank you.

 

 

Hi, my problem is the next differential equation:

In maple. I used this code to solved it, but throws this error:

dsolve({diff(y(x), x, x) = -P*x/(I*E), eval(y(x), x = L) = 0, eval((D(y))(x), x = L) = 0});
Error, (in dsolve) found differentiated functions with same name but depending on different arguments in the given DE system: {y(L), y(x)}

What is the problem with my code? How can solve my ODE with tis boundary conditions? 

 

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?

restart

T1 := array(1 .. 2);

array( 1 .. 2, [ ] )

 

x = 1

 

y = 2

(1)

T2 := array(1 .. 2);

array( 1 .. 2, [ ] )

 

z = 3

 

r = x+y+z

(2)

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

``


 

Download 4.mw

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.

Hello,

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 https://arxiv.org/abs/gr-qc/0510083 . 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.
 

restart

with(Physics)

[`*`, `.`, 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_]

(1)

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 = `- + + +`]

(2)

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}]

(3)

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

(4)

with(Tetrads)

`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_]

(5)

e_[]

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

(6)

``


 

Download dynBH.mw

 


 

 

 

Natural_frequency_No_Foundation_Mass.mw

Natural_frequency_No_Foundation_Mass.pdf

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?

 

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