Maple 2016 Questions and Posts

These are Posts and Questions associated with the product, Maple 2016

I have not been using Maple for the last couple of years because I have Maple installed on my big and heavy laptop. Such laptop forces me to sit at a desk when I work which I dont like. This has resulted in that I have only (for the most part) used my ipad for the last couple of years hence dropping my laptop and Maple. The problem with such approach has been that is more difficult to write scientific papers because you cant run a full version of word on the ipad hence you cant use a citation manager. There does not exist an app on the ipad that offer one. This leads to a lot of extra work!

I have therefore now bought a Microsoft Surface Pro 4 which is a tablet (like the ipad) but its a not a "toy" tablet like the ipad or android tablets because it has Windows 10 Pro (64-bit) which means that you can run full versions of pc software like word 2016 and Maple. The version of Surface Pro 4 I bought has an Intel Core m3-6Y30 processor with 2 cores, 4GB RAM, 128 GB of storage, no fan and a processor base frequency of 0.9 GHz. The m3-6Y30 processor has something called dynamic frequency scaling which means (as I understand it) that the processor can go up to 2.2 GHz when it is under heavy load. Since Maple recommend that you have a system with a cpu with at least 1 GHz to run Maple 2016 I am not anticipating any problems here.

http://www.maplesoft.com/products/system_requirements.aspx

However, I am not completly sure if maplesoft means that the base frequency needs to be 1 Ghz or not? Since my tablet has not been delivered yet I cant comment on how Maple runs on it but as I said I am not anticipating any problems.

Now to my question: When will Maple 2017 come out? Since it is already 2017 I dont want to buy an old version of Maple now that I want to update my Maple software.

I can't find in the Linear Algebra package the command for creating the duplication matrix.

The duplication matrix is the n * n rows and n * ( n + 1 ) / 2 columns that transforms vech(A)
to vec(A) where A is a symmetric n by n matrix (Magnus & Neudecker).

If it not yet in Maple itself, has someone already made a proc for it?

Harry Garst

 

I want  to find the parametrs that verify the below inequalities at the same time:

beta*(v+u)>phi*(alpha+lamda+u+delta)

phi>beta

beta> (alpha+lamda+u+delta)

phi* (alpha+lamda+u+delta)>beta*(u+v+alpha),

question : find the values of u,v,delta,lamda,phi,beta,alpha such as all these parameters are in the intervall ]0,1]

can anyone help me ?

 

hi

why this equation does not any answer?

thanks

s-s.mw
 

restart

``

eq:={-J*g[1]*(diff(w(x), x, x, x, x, x, x))+J*c[1]*(diff(w(x), x, x, x, x))+A*g[113113]*(diff(w(x), x, x, x, x))+(beta[11]*A*0)*`ΔT`*(diff(w(x), x, x))+2*b*f[1133]*(Pi/L)^2*(d[33]*lambda[3]*`ΔT`*L/mu[33]-2*f[1133]*a*Pi/L-P[3]*`ΔT`*L)*sin(Pi*x/L)*sinh(h*Pi/(2*L))/(2*cosh(h*Pi/(2*L))*(-a33+d[33]^2/mu[33])) = 0, w(0) = 0, w(L) = 0, (D(w))(0) = 0, (D(w))(L) = 0, ((D@@3)(w))(0) = 0, ((D@@3)(w))(L) = 0}

{-J*g[1]*(diff(diff(diff(diff(diff(diff(w(x), x), x), x), x), x), x))+J*c[1]*(diff(diff(diff(diff(w(x), x), x), x), x))+A*g[113113]*(diff(diff(diff(diff(w(x), x), x), x), x))+b*f[1133]*Pi^2*(d[33]*lambda[3]*`ΔT`*L/mu[33]-2*f[1133]*a*Pi/L-P[3]*`ΔT`*L)*sin(Pi*x/L)*sinh((1/2)*h*Pi/L)/(L^2*cosh((1/2)*h*Pi/L)*(-a33+d[33]^2/mu[33])) = 0, w(0) = 0, w(L) = 0, (D(w))(0) = 0, (D(w))(L) = 0, ((D@@3)(w))(0) = 0, ((D@@3)(w))(L) = 0}

(1)

dsolve(eq, w(x))

``


 

Download s-s.mw

 

Graphical Programming with MapleSim in Vector Mechanics to Structures 2D

At the present time before constructing or starting to develop a mechanical structures project it is necessary to model it using graphic programming; In this opportunity and used MapleSim as a computational tool belonging to the company Maplesoft. The modern approach to modeling and simulation makes the fabrication of complex designs easy to solve. We will cover some examples taken from the engineering being implemented in Maplesim with insertion of physical objects; To be seen in real time through video output; Then integrates with Maple to analyze the equations and data through the static and dynamic behavior of the fabricated. Solved methods of physical block components include functionality for many domains: rotational and translational mechanics, multi-body dynamics, logic, and structural blocks; With techniques like: Drag-and-Drop Physical Modeling Environment and Create Custom Components Directly From Their Equations, thus the systems that would take hours or days to build from equations; In principle they can be created in a fraction of time using MapleSim, so it can incorporate significantly more complex graphical algorithms. In MapleSim, I use the revolutionary multibody technology that perfectly combines advanced multi-domain modeling tools to provide all the functionality you need in one environment.

FAST_UNT_2017.pdf

Lenin Araujo Castillo

Ambassador Maple - Perú

 

 

Let:

f:=x->1/sqrt(2*Pi)*exp(-x^2/2);

I.e. f is a standard Gaussian PDF.

Then (in Maple 2016.1):

Int(convert(f(x)*f(y)*x*x*abs(x+y),piecewise,x),x=-infinity..infinity,y=-infinity..infinity):
evalf(%);

Returns:

1.692568751

However (again in Maple 2016.1):

int(convert(f(x)*f(y)*x*x*abs(x+y),piecewise,x),x=-infinity..infinity,y=-infinity..infinity):
evalf(%);

Returns:

-0.5641895835

This is clearly incorrect, as the integral of a positive function must be positive.

This also seems to be a problem in which ever version of Maple is used behind the scenes on this forum.

int(convert(1/sqrt(2*Pi)*exp(-x^2/2)*1/sqrt(2*Pi)*exp(-y^2/2)*x*x*abs(x+y),piecewise,x),x=-infinity..infinity,y=-infinity..infinity)

gives:

int(convert(1/sqrt(2*Pi)*exp(-x^2/2)*1/sqrt(2*Pi)*exp(-y^2/2)*x*x*abs(x+y),piecewise,x),x=-infinity..infinity,y=-infinity..infinity)

It is suggested  

hypergeom([1/3, 2/3], [3/2], (27/4)*z^2*(1-z)) = 1/z

if z > 1. Here is my try to prove that with Maple:


 

a := `assuming`([convert(hypergeom([1/3, 2/3], [3/2], (27/4)*z^2*(1-z)), elementary)], [z > 1])

-(1/((1/2)*(27*z^3-27*z^2+4)^(1/2)+(3/2)*z*(3*z-3)^(1/2))^(1/3)-1/((1/2)*(27*z^3-27*z^2+4)^(1/2)-(3/2)*z*(3*z-3)^(1/2))^(1/3))/(z*(3*z-3)^(1/2))

(1)

b := `assuming`([simplify(a, symbolic)], [z >= 1])

2*(-(12*(3*z+1)^(1/2)*z-12*z*(3*z-3)^(1/2)-8*(3*z+1)^(1/2))^(1/3)+(12*(3*z+1)^(1/2)*z+12*z*(3*z-3)^(1/2)-8*(3*z+1)^(1/2))^(1/3))/((3*z-3)^(1/2)*(12*(3*z+1)^(1/2)*z+12*z*(3*z-3)^(1/2)-8*(3*z+1)^(1/2))^(1/3)*(12*(3*z+1)^(1/2)*z-12*z*(3*z-3)^(1/2)-8*(3*z+1)^(1/2))^(1/3)*z)

(2)

plot(1/b, z = 1 .. 10)

 

simplify(diff(1/b, z), symbolic)

-48*(((3*z-2)*(3*z+1)^(1/2)+z*(3*z-3)^(1/2))*((12*z-8)*(3*z+1)^(1/2)-12*z*(3*z-3)^(1/2))^(1/3)+((12*z-8)*(3*z+1)^(1/2)+12*z*(3*z-3)^(1/2))^(1/3)*((-3*z+2)*(3*z+1)^(1/2)+z*(3*z-3)^(1/2)))/((3*z+1)^(1/2)*(3*z-3)^(1/2)*((12*z-8)*(3*z+1)^(1/2)+12*z*(3*z-3)^(1/2))^(2/3)*((12*z-8)*(3*z+1)^(1/2)-12*z*(3*z-3)^(1/2))^(2/3)*(((12*z-8)*(3*z+1)^(1/2)-12*z*(3*z-3)^(1/2))^(1/3)-((12*z-8)*(3*z+1)^(1/2)+12*z*(3*z-3)^(1/2))^(1/3))^2)

(3)

``


 

Download simplification.mw

I want to get solutions of this system ,can anyone help me ?solutions.mw

Can someone help me with this:

reverse_eng.mw

happy new year!

Friends in Maple

I have a Vehicle Routing Problem I wish to cast as a integer model. VRP is a kind of TSP and knapsack problem hybrid  I would be grateful if someone can finish it. answers included. This isn't homework BTW.

VRP_IP.mw

I use maple 12 on my dual core laptop and i plan to buy maple 2016 and an 8 core system to get advandage of multiple processors. 

Does maple 2016 functions get advandage of multiprocessor systems or it will be the same as having one processor?

Here is one that the students generated which caused confusion. 

a := 0.76;
eq1 := 2*cot(a*sqrt(2*E)) = (2*E-5.4)/(sqrt(E*(5.4-E));
solve(eq1, E)

And the results are: 0., 4.411954070, 2.423743792

The problem is with the second answer because it does not exist. If we plot the LHS and the RHS of eq1 vs E where E=0..5.4

plot([2*cot(0.76*sqrt(2*E)), (2*E-5.4)/sqrt(E*(5.4-E))], E=0..5.4, -3..3)

And it gets more interesting, if we calculate:

solve(evalf(eq1), E)

The answers are: 0., 2.423743793, 14.33807304+27.39159712*I

where the 3rd answer is again incorrect.

Finally, if a = 0.8 or larger, the incorrect answers disappear. 

Note - fsolve does handle this problem correctly. And despite my attempts to remind them to use fsolve, they see the solve command as the universal truth. Apparently this will be another teaching moment for next year.

So any thoughts about why this happens and why there is a difference in the outcomes between 0.76 and 0.8 for the value of a?

 

hi .how i can fsolve 8 equations, in which obtained from

for k from 2 to m do eq1[k_] end do

AND

for k from 2 to m do eq2[k_] end do  and so on........

And gain unknown functions as f3[2], f4[4],....

thanks?

fdm-maple.mw
 

 

 ############################Define some parameters

 

 
restart; Digits := 15; n := 1; m := 3; len := 1; h := len/m; nn := m+1
 ############################Define some equation

eq1[k_] := -3.0*h*(-f2[k]*f1[k-1]+f2[k]*f1[k+1]+f1[k]*(-f2[k+1]+f2[k-1]))*f4[k]^2+((-8.0*f1[k]+4.0*f1[k-1]+4.0*f1[k+1])*f3[k]+(-f1[k+1]+f1[k-1])*(-f3[k+1]+f3[k-1]))*f4[k]-f3[k]*(-f1[k+1]+f1[k-1])*(-f4[k+1]+f4[k-1]):

 

 

 

 

                                     ######################################  APPLY BOUNDARY CONDITIONS


f2[0] := f2[2];

1.0

(1)


``for k from 2 to m do eq1[k_] end do

-1.00000000000000*(-f1[2]*f2[3]+f1[3]*(-f2[4]+f2[2]))*f4[3]^2+((-8.0*f1[3]+4.0*f1[2])*f3[3]+f1[2]*(-f3[4]+f3[2]))*f4[3]-f3[3]*f1[2]*(-f4[4]+f4[2])

(2)

for k from 2 to m do eq2[k_] end do

(-4.16666666666667*f2[2]^2+(50.0000000000000*f2[3]+8.33333333333333*f2[4])*f2[2]-100.000000000000*f2[3]^2+50.0000000000000*f2[3]*f2[4]-4.16666666666667*f2[4]^2+1/27)*f4[3]^2+((f2[2]-1.*f2[4]-.5*f2[3])*f3[3]+(-50.*f3[2]+50.*f3[4])*f2[2]+(-50.*f3[2]+50.*f3[4])*f2[4]+(100.*f3[2]-100.*f3[4])*f2[3])*f4[3]+((50.*f4[2]-50.*f4[4])*f2[2]+(50.*f4[2]-50.0*f4[4])*f2[4]+(-100.0*f4[2]+100.*f4[4])*f2[3])*f3[3]

(3)

for k from 2 to m do eq3[k_] end do

-0.123456790123457e-1*f4[3]^3*f3[3]+((1/27)*(.5*f2[2]-.5*f2[4])*f3[3]-0.277777777777778e-1*f2[3]*f3[2]+0.277777777777778e-1*f2[3]*f3[4])*f4[3]^2+(-.222222222222222*f3[3]^2+((1/9)*f3[2]+(1/9)*f3[4]+4.*f2[3]^2+(-4.*f2[2]-4.*f2[4])*f2[3]+f2[2]^2+2.*f2[4]*f2[2]+f2[4]^2)*f3[3]+0.277777777777778e-1*f3[2]^2-0.555555555555556e-1*f3[2]*f3[4]+0.277777777777778e-1*f3[4]^2)*f4[3]+(1/9)*((-.25*f4[2]+.25*f4[4])*f3[2]+(.25*f4[2]-.25*f4[4])*f3[4])*f3[3]

(4)

for k from 2 to m do eq4[k_] end do

-0.493827160493827e-1*f4[3]^4-(1/27)*(-f2[4]+f2[2])*f4[3]^3+(.111111111111111*f2[3]*(f4[4]-f4[2])-.888888888888889*f3[3]+16.0*(f2[3]-.500000000000000*f2[2]-.500000000000000*f2[4])^2)*f4[3]^2+.444444444444444*((f3[3]+.250000000000000*f3[2]-.250000000000000*f3[4])*f4[2]+f4[4]*(f3[3]-.250000000000000*f3[2]+.250000000000000*f3[4]))*f4[3]-(1/9)*f3[3]*(f4[4]-f4[2])^2

(5)

``


 

Download fdm-maple.mw

 

hi.

how i can dsolve this differential equations?

thanks

ich.mw
 

restart; Digits := 50; dsol1 := dsolve({diff(F(eta), eta, eta, eta)+.5*H(eta)*((diff(F(eta), eta))^2+F(eta)*(diff(F(eta), eta, eta)))/G(eta)^2+2*(diff(G(eta), eta))*(diff(F(eta), eta, eta))/G(eta)-(diff(H(eta), eta))*(diff(F(eta), eta, eta))/H(eta) = 0, diff(G(eta), eta, eta)+H(eta)*((diff(F(eta), eta))*G(eta)+.5*F(eta)*(diff(eta, eta)))/G(eta)^2+2*(diff(G(eta), eta))^2/G(eta)-((diff(H(eta), eta))*(diff(H(eta), eta)))/H(eta)+(diff(F(eta), eta, eta))^2-(H(eta)/G(eta))^2 = 0, diff(H(eta), eta, eta)+(.5*1.3)*H(eta)*(5*(diff(F(eta), eta))*H(eta)+F(eta)*(diff(H(eta), eta)))/G(eta)^2+2*(diff(G(eta), eta))*(diff(H(eta), eta))/G(eta)-(diff(H(eta), eta))^2/H(eta)+(1.3*1.44)*H(eta)*(diff(F(eta), eta, eta))/G(eta)-(1.3*1.92)*(H(eta)/G(eta))^3 = 0, F(0) = 0, G(0) = 0, H(0) = 0, (D(F))(0) = 1, (D(F))(1) = 0, (D(G))(0) = 0, (D(H))(0) = 0}, 'maxmesh' = 900, numeric, output = listprocedure, method = bvp[middefer], abserr = 0.1e-2); fy := eval(F(eta), dsol1)

Error, invalid input: eval received dsol1, which is not valid for its 2nd argument, eqns

 

 

NULL


 

Download ich.mw

 

In the test package below I want the the Value of Clr to be "B" when the package is loaded. How do I achieve that?
 

restart

mylibdir := cat(kernelopts(homedir), kernelopts(dirsep), "maple", kernelopts(dirsep), "toolbox", kernelopts(dirsep), "personal", kernelopts(dirsep), "lib")

"C:\Users\Ronan.Ronan-PC\maple\toolbox\personal\lib"

(1)

``

libname := mylibdir, libname

"C:\Users\Ronan.Ronan-PC\maple\toolbox\personal\lib", "C:\Program Files\Maple 2016\lib", "C:\Users\Ronan.Ronan-PC\maple\toolbox\personal\lib"

(2)

``

``

``

"RTest:=module()  option package;  export  Sums;    global Clr;  Clr:=B;  Sums:=proc(p1,p2,c:=Clr)  if c=B or c=b  then    p1+p2  elif c=G or c=g then  p1-p2  elif c=R or c=r  then      if p2 =0 then "Not Valid"       else ( p1)/(p2)        end if  else "Error"  end if  end proc;    end module; "

_m655171968

(3)

``

savelib('RTest')

restart

``

with(RTest)

[Sums]

(4)

"At This point I want the value of Clr to be automaticially   B"

Sums(2, 3)

"Error"

(5)

RTest:-Sums(2, 3, b)

5

(6)

``

RTest:-Sums(2, 3, r)

2/3

(7)

RTest:-Sums(2, 3, g)

-1

(8)

Clr := g

g

(9)

RTest:-Sums(2, 3)

-1

(10)

RTest:-Sums(2, 3, b)

5

(11)

RTest:-Sums(2, 3)

-1

(12)

RTest:-Sums(2, 0, r)

"Not Valid"

(13)

``


 

Download Module_Test_global_Var.mw

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