Maple 2015 Questions and Posts

These are Posts and Questions associated with the product, Maple 2015

I'm looking at Maple as a possible alternative to Mathcad (which I've been using for years, but is now very jaded compared to other options like Maple and Mathematica).  I'm a civil engineer and for what I do, one of the better features of Mathcad is the way it handles units.  For example, if I specify an angle in degrees (say phi=30 degrees) and then ask for sin(phi), I get 0.5.  At face value, I though Maple would do the same kind of thing.  However, this doesn't appear to be the case (see attached worksheet).  The only workaround that I can see is to specify the angle in degrees (but without assigning ) and then multiply the specified value by pi/180 (to convert to radians) before passing it to the sin function.  Which is all a bit messy and not at all an attractive solution.

Am I misunderstanding the way units work in Maple and is there a clean way of specifying angles in degrees (which is what engineers work with) and using these values directy in trig functions?

Thanks in anticipation,

Ian

I am very new to Maple and am wondering how i would install a package. The package I am trying to install is located at

http://math.rutgers.edu/~russell2/papers/IdentityFinder 

I am using Maple 2015 on windows 8. Any advice would be useful

Hi everyone!

I use two "ArrayTools:-Copy" commands to copy elements from Vector A to Vector B.

restart;
A := LinearAlgebra:-RandomVector(10); A := convert(A, Vector[row]);
B := Vector[row](10); ArrayTools:-Copy(2, A, 1, B, 1); ArrayTools:-Copy(2, A, 7, B, 7); B;

My question is: Could I obtain the same result using only one command?

P.S. I tried to use "ArrayTools:-BlockCopy", but didn't get correct result.

 

I want to retrieve all the commands input by user in a maple document saved on disk. How this can be done? DocumentTools:-Retrieve permits to receive only the labeled expressions but not the input commands.

Maple function plot allows to build a linear plot for two vectors, when one vector contains X coordinates, another -- Y coordinates (similar to plot below):

Is it possible to build such a plot for several Y-vectors like this:

12

 

Some of the Rotation Coefficients are not calculating properly.

Question_about_Ricci_Rotation_Coefficients.mw

 

 

Hello,

 

I wonder if it is possible to create standalone executables in Maple that would run in a  computer without Maple. Also if it is possible can we do that with Matlab code in it too?  

 

Matlab does not allow to create standalone executable is you use symbolic toolbox and I want to find a solution for that. What I will need to take second derivatives and get the coefficients of polynomials. 

hi, the equations read as 

eq:=[2*x-0.2e-1*y-2.04*sqrt(-v^2+1)*v, 2*y-0.2e-1*x-2.16*sqrt(-u^2+1)*u, 2*u+2.16*u^2*y/sqrt(-u^2+1)-2.16*sqrt(-u^2+1)*y, 2*v+2.04*v^2*x/sqrt(-v^2+1)-2.04*sqrt(-v^2+1)*x] ;

i do as follows using DirectSearch package v.2

i find the solutions not the same,some time the results not much difference,but another,sols1 have one solution,sols2 have three solutions.in some time,some solutions are lost,the result show  me  random.may i have run the command serveral times? regards.

Why does Maple 2015 solve this very simple system incorrectly?

solve({abs(a-b)=0, sqrt(2*b+c)=0, c^2-c+1/4=0});

              

 

With Maple 12 no problem:

solve({abs(a-b)=0, sqrt(2*b+c)=0, c^2-c+1/4=0});

              

 

 

With this application we can meet safety characteristics of a relationship and simple or compound functions. Made with maple 2015.

Relaciones_y_Funciones.mw

(in spanish)

L.AraujoC.

I have been trying to fit a function to experimental data. To do this i was using

.

The data is of the type

.

When I use initialvalues, I get a result, that fits the data well, but is clearly not the desired minimum. Maple delivers g always bigger than 10000 which is nowhere near -7, where it has to be for physical reasons. When using parameterranges I get the error

Warning, no iterations performed as initial point satisfies first-order conditions.

He stopps computing and simply prints out my initialvalues or the first value that is in the parameterrange with a huge RSS.

How can I use initialvalues and parameterranges together for my data?

I would like to create a variable name that consists of a greek letter and an english letter. For example, δx.   If I type

>delta = 5;

Maple displays the output as δ = 5

However, I would like to have variable names that are output as δx.

Is there a way to do this in worksheet mode? I tried cat(delta,x) but that just gave me deltax.

 

Thanks for your help,

Harish

Hello. Earlier, I asked about it, (see http://www.mapleprimes.com/questions/203573-How-To-Do-Simple-Operations-On-Tensors). However, not all I was able to understand. Below I will give a try, and maybe you'll show me where I'm wrong.

Also, I'm interested in how you can determine the components of the tensor in a different coordinate system connected with the original in any conversion. Thank for your help.

restart; with(Physics); with(DifferentialGeometry)

ds := Physics:-`^`(dx__1, 2)+Physics:-`^`(dx__2, 2)+Physics:-`^`(dx__3, 2)

dx__1^2+dx__2^2+dx__3^2

(1)

Physics:-Setup(coordinates = (X = [x__1, x__2, x__3]), dimension = 3, metric = ds, quiet)

[coordinatesystems = {X}, dimension = 3, metric = {(1, 1) = 1, (2, 2) = 1, (3, 3) = 1}]

(2)

g_[]

g_[mu, nu] = (Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 2) = 1, (2, 3) = 0, (3, 3) = 1}, storage = triangular[upper], shape = [symmetric]))

(3)

``

u__1 := Physics:-`*`(Physics:-`*`(P, Physics:-`^`(Physics:-`*`(Physics:-`*`(4, Pi), G), -1)), Physics:-`*`(x__3, Physics:-`*`(x__1, Physics:-`^`(Physics:-`^`(r, 3), -1)))-Physics:-`*`(Physics:-`*`(1-Physics:-`*`(2, nu), x__1), Physics:-`^`(Physics:-`*`(r, r+x__3), -1))):u__2 := Physics:-`*`(Physics:-`*`(P, Physics:-`^`(Physics:-`*`(Physics:-`*`(4, Pi), G), -1)), Physics:-`*`(x__2, Physics:-`*`(x__3, Physics:-`^`(Physics:-`^`(r, 3), -1)))-Physics:-`*`(Physics:-`*`(1-Physics:-`*`(2, nu), x__2), Physics:-`^`(Physics:-`*`(r, r+x__3), -1))):u__3 := Physics:-`*`(Physics:-`*`(P, Physics:-`^`(Physics:-`*`(Physics:-`*`(4, Pi), G), -1)), Physics:-`*`(Physics:-`*`(2, 1-nu), Physics:-`^`(r, -1))+Physics:-`*`(Physics:-`^`(x__3, 2), Physics:-`^`(Physics:-`^`(r, 3), -1))):

`e__1,1` := diff(u__1, x__1):`e__2,2` := diff(u__2, x__2):`e__3,3` := diff(u__3, x__3):

`e__1,2` := Physics:-`*`(Physics:-`^`(2, -1), diff(u__1, x__2)+diff(u__2, x__1)):`e__1,3` := Physics:-`*`(Physics:-`^`(2, -1), diff(u__1, x__3)+diff(u__3, x__1)):`e__2,3` := Physics:-`*`(Physics:-`^`(2, -1), diff(u__2, x__3)+diff(u__3, x__2)):

`e__2,1` := `e__1,2`:

`e__3,1` := `e__1,3`:

`e__3,2` := `e__2,3`:

  E := matrix(3, 3, proc (i, j) options operator, arrow; e[i, j] end proc)

Matrix(3, 3, {(1, 1) = e[1, 1], (1, 2) = e[1, 2], (1, 3) = e[1, 3], (2, 1) = e[2, 1], (2, 2) = e[2, 2], (2, 3) = e[2, 3], (3, 1) = e[3, 1], (3, 2) = e[3, 2], (3, 3) = e[3, 3]})

(4)

Physics:-Define(E[i, j])

{gamma[mu], E[i, j], sigma[mu], Physics:-d_[mu], Physics:-g_[mu, nu], delta[mu, nu], epsilon[alpha, mu, nu], Physics:-SpaceTimeVector[mu](X)}

(5)

Physics:-TensorArray(%)

{E[i, j], Array(1..3, 1..3, 1..3, {(1, 1, 1) = 0, (1, 1, 2) = 0, (1, 1, 3) = 0, (1, 2, 1) = 0, (1, 2, 2) = 0, (1, 2, 3) = 0, (1, 3, 1) = 0, (1, 3, 2) = 0, (1, 3, 3) = 0, (2, 1, 1) = 0, (2, 1, 2) = 0, (2, 1, 3) = 0, (2, 2, 1) = 0, (2, 2, 2) = 0, (2, 2, 3) = 0, (2, 3, 1) = 1, (2, 3, 2) = 1, (2, 3, 3) = 1, (3, 1, 1) = 0, (3, 1, 2) = 0, (3, 1, 3) = 0, (3, 2, 1) = -1, (3, 2, 2) = -1, (3, 2, 3) = -1, (3, 3, 1) = 0, (3, 3, 2) = 0, (3, 3, 3) = 0}), Array(1..3, {(1) = x__1, (2) = x__2, (3) = x__3}), Array(1..3, {(1) = Physics:-Psigma[1], (2) = Physics:-Psigma[2], (3) = Physics:-Psigma[3]}), Array(1..3, {(1) = Physics:-d_[1], (2) = Physics:-d_[2], (3) = Physics:-d_[3]}), Array(1..3, {(1) = Physics:-Dgamma[1], (2) = Physics:-Dgamma[2], (3) = Physics:-Dgamma[3]}), Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1}), Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1})}

(6)

``

Physics:-Setup(dimension)

[dimension = 3]

(7)

NULL

Physics:-Define(E[i, j], query)

[E, [0, 0, 0], 0]

(8)

DifferentialGeometry:-DGsetup([y__1, y__2, y__3], M):

Phi1 := DifferentialGeometry:-Transformation(N, M, [y__1 = Physics:-`*`(Physics:-`^`(sqrt(6), -1), x__1)+Physics:-`*`(Physics:-`*`(2, Physics:-`^`(sqrt(6), -1)), x__2)+Physics:-`*`(Physics:-`^`(sqrt(6), -1), x__3), y__2 = Physics:-`*`(Physics:-`^`(sqrt(2), -1), x__1)-Physics:-`*`(Physics:-`^`(sqrt(3), -1), x__2)+Physics:-`*`(Physics:-`^`(sqrt(3), -1), x__3), y__3 = Physics:-`*`(Physics:-`^`(sqrt(2), -1), x__1)-Physics:-`*`(Physics:-`^`(sqrt(2), -1), x__3)]):

NULL

 

Download 1.mw

Another application for the study of rational numbers in operations, generating fraction, etc.

 

Numeros_Racionales.mw

(in spanish)

 

Atte.

L.AraujoC.


restart; with(Physics); with(Tetrads); with(PDETools)

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

(1)

coords := zetabar, zeta, v, u

zetabar, zeta, v, u

(2)

X = [coords]

X = [zetabar, zeta, v, u]

(3)

ds2 := Physics:-`*`(Physics:-`*`(2, dzeta), dzetabar)+Physics:-`*`(Physics:-`*`(2, du), dv)+Physics:-`*`(Physics:-`*`(2, H(coords)), Physics:-`^`(du+Physics:-`*`(Ybar(coords), dzeta)+Physics:-`*`(Y(coords), dzetabar)-Physics:-`*`(Physics:-`*`(Y(coords), Ybar(coords)), dv), 2))

2*dzeta*dzetabar+2*du*dv+2*H(zetabar, zeta, v, u)*(du+Ybar(zetabar, zeta, v, u)*dzeta+Y(zetabar, zeta, v, u)*dzetabar-Y(zetabar, zeta, v, u)*Ybar(zetabar, zeta, v, u)*dv)^2

(4)

PDEtools:-declare(ds2)

Ybar(zetabar, zeta, v, u)*`will now be displayed as`*Ybar

(5)

vierbien := Matrix([[1, 0, -Ybar(coords), 0], [0, 1, -Y(coords), 0], [Physics:-`*`(H(coords), Y(coords)), Physics:-`*`(H(coords), Ybar(coords)), 1-Physics:-`*`(Physics:-`*`(H(coords), Y(coords)), Ybar(coords)), H(coords)], [Y(coords), Ybar(coords), -Physics:-`*`(Y(coords), Ybar(coords)), 1]])

vierbien := Matrix(4, 4, {(1, 1) = 1, (1, 2) = 0, (1, 3) = -Ybar(zetabar, Zeta, v, u), (1, 4) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = -Y(zetabar, Zeta, v, u), (2, 4) = 0, (3, 1) = H(zetabar, Zeta, v, u)*Y(zetabar, Zeta, v, u), (3, 2) = H(zetabar, Zeta, v, u)*Ybar(zetabar, Zeta, v, u), (3, 3) = 1-H(zetabar, Zeta, v, u)*Y(zetabar, Zeta, v, u)*Ybar(zetabar, Zeta, v, u), (3, 4) = H(zetabar, Zeta, v, u), (4, 1) = Y(zetabar, Zeta, v, u), (4, 2) = Ybar(zetabar, Zeta, v, u), (4, 3) = -Y(zetabar, Zeta, v, u)*Ybar(zetabar, Zeta, v, u), (4, 4) = 1})

(6)

``

Physics:-Setup(coordinatesystem = (X = [zetabar, zeta, v, u]), metric = ds2, tetrad = vierbien, mathematicalnotation = true, automaticsimplification = true, signature = "+++-")

RicciT := proc (a, b) options operator, arrow; Physics:-SumOverRepeatedIndices(Ricci[mu, nu]*e_[a, `~mu`]*e_[b, `~nu`]) end proc

proc (a, b) options operator, arrow; Physics:-SumOverRepeatedIndices(Physics:-`*`(Physics:-`*`(Physics:-Ricci[mu, nu], Physics:-Tetrads:-e_[a, `~mu`]), Physics:-Tetrads:-e_[b, `~nu`])) end proc

(7)

SlashD := proc (f, a) options operator, arrow; Physics:-SumOverRepeatedIndices(Physics:-D_[mu](f)*e_[a, `~mu`]) end proc

proc (f, a) options operator, arrow; Physics:-SumOverRepeatedIndices(Physics:-`*`(Physics:-D_[mu](f), Physics:-Tetrads:-e_[a, `~mu`])) end proc

(8)

SlashD(H(X), 4) = H(X)[4]

(diff(H(X), zetabar))*Ybar(X)+(diff(H(X), zeta))*Y(X)+diff(H(X), v)-(diff(H(X), u))*Y(X)*Ybar(X) = H(X)[4]

(9)

Gamma := proc (a, b, c) options operator, arrow; -gamma_[a, b, c] end proc

proc (a, b, c) options operator, arrow; Physics:-`*`(Physics:-Tetrads:-gamma_[a, b, c], -1) end proc

(10)

Gamma(1, 4, 4) = 0

-(diff(Ybar(X), u))*Y(X)*Ybar(X)+Y(X)*(diff(Ybar(X), zeta))+Ybar(X)*(diff(Ybar(X), zetabar))+diff(Ybar(X), v) = 0

(11)

``

Gamma(2, 4, 4) = 0

-(diff(Y(X), u))*Y(X)*Ybar(X)+Y(X)*(diff(Y(X), zeta))+(diff(Y(X), zetabar))*Ybar(X)+diff(Y(X), v) = 0

(12)

``

Gamma(3, 4, 4) = 0

0 = 0

(13)

``

Gamma(4, 4, 4) = 0

0 = 0

(14)

Gamma(4, 1, 1) = 0

-(diff(Ybar(X), zeta))+(diff(Ybar(X), u))*Ybar(X) = 0

(15)

``

Gamma(4, 2, 2) = 0

-(diff(Y(X), zetabar))+(diff(Y(X), u))*Y(X) = 0

(16)

NULL

shearconditions := {-(diff(Y(X), zetabar))+(diff(Y(X), u))*Y(X) = 0, -(diff(Ybar(X), zeta))+(diff(Ybar(X), u))*Ybar(X) = 0, -(diff(Y(X), u))*Y(X)*Ybar(X)+Y(X)*(diff(Y(X), zeta))+(diff(Y(X), zetabar))*Ybar(X)+diff(Y(X), v) = 0, -(diff(Ybar(X), u))*Y(X)*Ybar(X)+Y(X)*(diff(Ybar(X), zeta))+Ybar(X)*(diff(Ybar(X), zetabar))+diff(Ybar(X), v) = 0}

{-(diff(Y(X), zetabar))+(diff(Y(X), u))*Y(X) = 0, -(diff(Ybar(X), zeta))+(diff(Ybar(X), u))*Ybar(X) = 0, -(diff(Y(X), u))*Y(X)*Ybar(X)+Y(X)*(diff(Y(X), zeta))+(diff(Y(X), zetabar))*Ybar(X)+diff(Y(X), v) = 0, -(diff(Ybar(X), u))*Y(X)*Ybar(X)+Y(X)*(diff(Ybar(X), zeta))+Ybar(X)*(diff(Ybar(X), zetabar))+diff(Ybar(X), v) = 0}

(17)

simplify(RicciT(1, 2), shearconditions) = 0

H(X)*(diff(diff(Y(X), zeta), zetabar))*Ybar(X)-H(X)*Ybar(X)*Y(X)*(diff(diff(Ybar(X), u), zetabar))-H(X)*Ybar(X)^2*(diff(diff(Y(X), u), zetabar))-H(X)*Y(X)^2*(diff(diff(Ybar(X), u), zeta))-2*H(X)*Y(X)*Ybar(X)*(diff(diff(Y(X), u), zeta))+H(X)*Y(X)^2*Ybar(X)*(diff(diff(Ybar(X), u), u))-H(X)*Y(X)*(diff(diff(Ybar(X), u), v))+H(X)*Y(X)*Ybar(X)^2*(diff(diff(Y(X), u), u))-H(X)*(diff(diff(Y(X), u), v))*Ybar(X)+H(X)*(diff(Ybar(X), zetabar))^2+(-3*H(X)*Y(X)*(diff(Ybar(X), u))-(diff(H(X), u))*Y(X)*Ybar(X)+(diff(H(X), zeta))*Y(X)+(diff(H(X), zetabar))*Ybar(X)+diff(H(X), v))*(diff(Ybar(X), zetabar))+H(X)*(diff(Y(X), zeta))^2+(-4*H(X)*(diff(Y(X), u))*Ybar(X)-(diff(H(X), u))*Y(X)*Ybar(X)+(diff(H(X), zeta))*Y(X)+(diff(H(X), zetabar))*Ybar(X)+diff(H(X), v))*(diff(Y(X), zeta))+2*H(X)*Y(X)^2*(diff(Ybar(X), u))^2-Y(X)*((diff(H(X), zetabar))*Ybar(X)+(diff(H(X), zeta))*Y(X)+diff(H(X), v)-(diff(H(X), u))*Y(X)*Ybar(X))*(diff(Ybar(X), u))+2*(H(X)*(diff(Y(X), u))*Ybar(X)+(1/2)*(diff(H(X), u))*Y(X)*Ybar(X)-(1/2)*(diff(H(X), zeta))*Y(X)-(1/2)*(diff(H(X), zetabar))*Ybar(X)-(1/2)*(diff(H(X), v)))*(diff(Y(X), u))*Ybar(X) = 0

(18)

0 = 0

0 = 0

(19)

The values in the paraenthesis  should substitute H[4]. This sequence works in Maple 18 but not in Maple 2015

 

NULL


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