Maple 16 Questions and Posts

These are Posts and Questions associated with the product, Maple 16

 I am trying to solve 2 equations in maple:

 1/  solve({1<x or x<3 or x>5});

 {x=x}    solution is correct

 2/  solve({1<x or x<3 or x<5});

 {x<5}    solution is wrong

 How do I have solution correct is {x=x} in Maple?

 Please teach me about this.

 Thank you very much!

I think that I am probably making this more complicated than it needs to be, but I'm fairly certain that the way that I am doing this is possible within Maple. 

 

Currently I have this line of code

>implicitplot3d({2*sqrt(2)*x-2*z+sqrt(2) = 0, 2*sqrt(2)*x+2*z-sqrt(2) = 0, 2*sqrt(2)*y-2*z-sqrt(2) = 0, 2*sqrt(2)*y+2*z+sqrt(2) = 0}, x = -2 .. 2, y = -2 .. 2, z = -2 .. 2)

 

So these equations create planes that intersect creating a tetrahedron. The problem I'm running into is that I need to "trim" the extra bits of the planes outside of the tetrahedron. The idea I have right now is constraining each plane by 3 equations which would turn the planes into triangles. I think this will work but I'm not sure how to constrain each individual plane with different equations AND plot them on the same graph. Any direction here would be greatly appreciated. I would prefer to stick with using implicitplot3d and avoid any special plotting tools. 

 

Thanks for any help!

hello everyone!!

I need to plot the function x^3-x^2-x-1, and in the plot I need to calculate de point X that make the function equals to cero (the cutting point with the x axis).

Thanks you!!

I just found that Maple 17 and Maple 16 do not have the option "output=string" in the latex command.

And I need a way to convert the Latex generated to the screen to a string and save it to a variable like I can do with Maple 2017

Here is an example. In current Maple 2017 this works

result_of_int:=int((-5+3*x)^2/(2*x-1)^(7/2),x):
my_latex:= latex(result_of_int,output=string);

But in Maple 16, it gives an error

If I remove the output, then the result is not string.

How to capture the above output which is on the screen and save it as string in a variable?

I do not want to send the output to a file as is. I need to first convert it to a string, and save
it to variable first.

 

 

I have a system of equations that can't be solved analytically, but can be solved using fsolve. I would like to plot the solution for one of the unknowns as a function of a parameter "DV" that is in a few of the equations. There are two issues at hand. First, even if I give DV a numerical value, the solutions are of the form { x = 0.23, y = 4.56 }, a form that plot( ) obviously can't handle directly. Generally I have dealt with this by using the op( ) command to pick out the solution I want; is there a better way?

But even after I have the solution I want, fsolve( ) won't work until I give it a value for DV. Thus a plot( ) command like

   plot(op(2, op(2, fsolve({e1, e2}, {x, y})), DV = -1 .. 1)

fails with an "Error, (in fsolve) DV is in the equation, and is not solved for" error.

There's got to be an esy way to do this!

I found from this forum that to plot a 2D array of points use can be made of the Maple procedure surfdata.
 

Does anyone have suggestions on how to plot contours in (preferrably) Maple 16 or Maple 17?

I tried the following

Output := Array(-10 .. 10, -10 .. 10, proc (i, j) options operator, arrow; i^2+j^2 end proc):
F := proc (x, y) -> x^2+y^2 end proc:
surfdata(Output, color = F, dimension = 2);

but "the option dimension = 2" is a Maple 18 addition.

Ideally, I would like also to be able to plot contours with options found in the procedure
contourplot

Hi, i encountered this, error, and the link to the help page was broken.

Error, (in RootOf) expression independent of _S000100
 

I don't recall ever changing any settings in my copy of Maple 16. But for some reason, I tried to make a plot and it spit out line-printed output rather than a regular plot.

How do I change this back? I have no use for line-printed output.

lineprinted_fail.mw
 

plot([E1(x), E2(x), E3(x)], x = 0 .. 5, title = "Nitrogen Nucleus Second-Order Energy Shifts")


                                                                              
                  Nitrogen Nucleus Second-Order Energy Shifts                 
  |                                                                           
  +                                                                     HHHHH
6e-08                                                               HHHHH     
  +                                                            HHHHHH         
4e-08                                                     HHHHHH              
  +                                                  HHHHHH                   
  +                                           HHHHHHH                         
2e-08                                  HHHHHHHH                               
  +                           HHHHHHHHHH                                      
  +             HHHHHHHHHHHHHHH                                               
  ***************************************************************************
0 +              1    HHHHHHHHHH2HH           3              4              5
  +                               HHHHHHHHH                                   
-2e-08                                    HHHHHHHH                            
  +                                              HHHHHHH                      
-4e-08                                                 HHHHHH                 
  +                                                         HHHHHH            
  +                                                              HHHHH        
-6e-08                                                                HHHHH   
  +                                                                       HHH
                                                                              

 

NULL

``


 

Download lineprinted_fail.mw

 

Hello,

I am solving a simple system of algebraic equations in a "for" loop. I would like to write all the values of solutions to a matrix, but I only get the symbols. Here is my code:

A:=1:E:=0.1:L0:=<5,5,5,5>:m0g:=0.05:u:=<-5/4,-1/4,-3/4,-1/4>:v:=<-1/2,-3/2,1/2,1/2>:w:=<0,1,0,-1>:
Force:=Matrix(m,2);
for i from 1 to m do
 r1||i:=H||i*L0(i)/(A*E)+H||i/m0g*(arcsinh(V_A||i/H||i)+arcsinh((m0g*L0(i)-V_A||i)/H||i))-sqrt(u(i)^2+v(i)^2);
 r2||i:=V_A||i*L0(i)/(A*E)*(m0g*L0(i)/(2*V_A||i)-1)+H||i/m0g*(sqrt(1+((m0g*L0(i)-V_A||i)/H||i)^2)-sqrt(1+(V_A||i/H||i)^2))-abs(w(i));
 rozw||i:=fsolve({r1||i, r2||i}, {H||i,V_A||i},H||i=0..1);Force(i,1):=H||i;Force(i,2):=V_A||i;subs(rozw||i,Force(i,..));
end do:
evalf(Force);

Thanks in advance,

Iza

Let be the number z so that |z+3-2*I| + |z-3-8*I| = 6*sqrt(2). Find min and max of the modulus of z. How can I find min and max of modulus of z with Maple.

Thank for your help!

How to manually switch frames in the DifferentialGeometry package? (Example: Help_Differential geometry_lesson2_exercise 4). Thank you

Maple 16 code

 

N1 := FileTools[Text][CountLines](g)

I encounter an error message

in FileTools:-Text:-CountLines) permission denied

What  went wrong ?  This never happened before

I  re install  Maple 16, the same error persists.

 

Please help

Martin
 


Please help me on this :

restart; with(PDETools), with(plots)

n := .3:

Eq1 := (1-n)*(diff(f(x, y), `$`(y, 3)))+(1+x*cot(x))*f(x, y)*(diff(f(x, y), `$`(y, 2)))-(diff(f(x, y), y))/Da+(diff(f(x, y), y))^2+n*We*(diff(f(x, y), `$`(y, 2)))*(diff(f(x, y), `$`(y, 3)))+sin(x)*(theta(x, y)+phi(x, y))/x = x*((diff(f(x, y), y))*(diff(f(x, y), y, x))+(diff(f(x, y), `$`(y, 2)))*(diff(f(x, y), x))):

Eq2 := (diff(theta(x, y), `$`(y, 2)))/Pr+Nt*(diff(theta(x, y), y))^2/Pr+Nb*(diff(phi(x, y), y))*(diff(theta(x, y), y))/Pr+(1+x*cot(x))*f(x, y)*(diff(theta(x, y), y)) = x*((diff(f(x, y), y))*(diff(theta(x, y), x))+(diff(theta(x, y), y))*(diff(f(x, y), x))):

Eq3 := Nb*(diff(phi(x, y), `$`(y, 2)))/(tau*Pr)+Nt*(diff(theta(x, y), `$`(y, 2)))/(tau*Pr)+(1+x*cot(x))*f(x, y)*(diff(phi(x, y), y)) = x*((diff(f(x, y), y))*(diff(phi(x, y), x))+(diff(phi(x, y), y))*(diff(f(x, y), x))):

ValWe := [0, 5, 10]:

bcs := {Nb*(D[2](phi))(x, 0)+Nt*(D[2](theta))(x, 0) = 0, f(0, y) = ((1/12)*y)^2*(6-8*((1/12)*y)+3*((1/12)*y)^2), f(x, 0) = 0, phi(0, y) = -.5*y, phi(x, 12) = 0, theta(0, y) = (1-(1/12)*y)^2, theta(x, 0) = 1, theta(x, 12) = 0, (D[2](f))(x, 0) = Da^(1/2)*(D[2, 2](f))(x, 0)+Da*(D[2, 2, 2](f))(x, 0), (D[2](f))(x, 12) = 0}:

pdsys := {Eq1, Eq2, Eq3}:

p1 := ans[1]:-plot(theta(x, y), x = 1, color = blue):

plots[display]({p1, p2, p3})

 

``


 

Download untitle_2_(1).mw

Download 2222222222222222222.mw

 

> restart; 
> A[0] := 10^(-3); a := 10^5;
> sys := diff(R(theta), theta) = A[0]*exp(2*mu(theta))*sin(theta)/(2*a), R(theta) = 2*exp(-2*mu(theta))*(1-(diff(mu(theta), `$`(theta, 2)))-cot(theta)*(diff(mu(theta), theta)));
> cond := R(0) = 10^(-5), mu(0) = 118.92, (D(mu))(0) = 0;
> F := dsolve({cond, sys}, [R(theta), mu(theta)], numeric);
> with(plots);
> odeplot(F, [theta, R(theta)], 0 .. 3.14, color = black, thickness = 3, linestyle = 4)
> odeplot(F, [theta, mu(theta)], 0 .. 3.14, color = blue, thickness = 3, linestyle = 1)

After last two lines maple writes:

Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

And gives me empty plots. I can't figure out where an error can be. Some things I noticed:

Maple doesn't calculate the system before and after zero. If I change the range from 0..3.14 to -10..10 or to 0.00001..0.00001, it gives me 2 errors for 1 plot.

Also if I change the condition mu(0) = 118.92 to mu(0) = 1 or mu(0) = 50 or mu(0) = 80, it works. After ~80 it gives an error. I can't imagine where could appear a division by 0 or some other mistake.

I have been trying to find a solution for the equation below. Is there a non numerical explicit solution?
 

restart

with(DEtools)

[AreSimilar, Closure, DEnormal, DEplot, DEplot3d, DEplot_polygon, DFactor, DFactorLCLM, DFactorsols, Dchangevar, Desingularize, FunctionDecomposition, GCRD, Gosper, Heunsols, Homomorphisms, IVPsol, IsHyperexponential, LCLM, MeijerGsols, MultiplicativeDecomposition, ODEInvariants, PDEchangecoords, PolynomialNormalForm, RationalCanonicalForm, ReduceHyperexp, RiemannPsols, Xchange, Xcommutator, Xgauge, Zeilberger, abelsol, adjoint, autonomous, bernoullisol, buildsol, buildsym, canoni, caseplot, casesplit, checkrank, chinisol, clairautsol, constcoeffsols, convertAlg, convertsys, dalembertsol, dcoeffs, de2diffop, dfieldplot, diff_table, diffop2de, dperiodic_sols, dpolyform, dsubs, eigenring, endomorphism_charpoly, equinv, eta_k, eulersols, exactsol, expsols, exterior_power, firint, firtest, formal_sol, gen_exp, generate_ic, genhomosol, gensys, hamilton_eqs, hypergeomsols, hyperode, indicialeq, infgen, initialdata, integrate_sols, intfactor, invariants, kovacicsols, leftdivision, liesol, line_int, linearsol, matrixDE, matrix_riccati, maxdimsystems, moser_reduce, muchange, mult, mutest, newton_polygon, normalG2, ode_int_y, ode_y1, odeadvisor, odepde, parametricsol, particularsol, phaseportrait, poincare, polysols, power_equivalent, rational_equivalent, ratsols, redode, reduceOrder, reduce_order, regular_parts, regularsp, remove_RootOf, riccati_system, riccatisol, rifread, rifsimp, rightdivision, rtaylor, separablesol, singularities, solve_group, super_reduce, symgen, symmetric_power, symmetric_product, symtest, transinv, translate, untranslate, varparam, zoom]

(1)

``

sol := (JacobiCN((1/10)*sqrt(5)*sqrt(2)*t, (1/3)*sqrt(3))*sqrt(5)+2*sqrt(2))/(JacobiCN((1/10)*sqrt(5)*sqrt(2)*t, (1/3)*sqrt(3))*sqrt(5)+5*sqrt(2))

(JacobiCN((1/10)*5^(1/2)*2^(1/2)*t, (1/3)*3^(1/2))*5^(1/2)+2*2^(1/2))/(JacobiCN((1/10)*5^(1/2)*2^(1/2)*t, (1/3)*3^(1/2))*5^(1/2)+5*2^(1/2))

(2)

sol1 := diff(psi(t), t) = sol

diff(psi(t), t) = (JacobiCN((1/10)*5^(1/2)*2^(1/2)*t, (1/3)*3^(1/2))*5^(1/2)+2*2^(1/2))/(JacobiCN((1/10)*5^(1/2)*2^(1/2)*t, (1/3)*3^(1/2))*5^(1/2)+5*2^(1/2))

(3)

odeadvisor(sol1, psi(t))

[_quadrature]

(4)

sol2 := dsolve({sol1, psi(0) = 0})

psi(t) = Int((JacobiCN((1/10)*_z1*10^(1/2), (1/3)*3^(1/2))*5^(1/2)+2*2^(1/2))/(JacobiCN((1/10)*_z1*10^(1/2), (1/3)*3^(1/2))*5^(1/2)+5*2^(1/2)), _z1 = 0 .. t)

(5)

``

``

sol3 := convert(sol, parfrac)

1-(3/5)*2^(1/2)*5^(1/2)/(JacobiCN((1/10)*5^(1/2)*2^(1/2)*t, (1/3)*3^(1/2))+2^(1/2)*5^(1/2))

(6)

sol4 := diff(psi(t), t) = sol3

diff(psi(t), t) = 1-(3/5)*2^(1/2)*5^(1/2)/(JacobiCN((1/10)*5^(1/2)*2^(1/2)*t, (1/3)*3^(1/2))+2^(1/2)*5^(1/2))

(7)

dsolve({sol4, psi(0) = 0})

psi(t) = Int(-(3/5)*10^(1/2)/(JacobiCN((1/10)*_z1*10^(1/2), (1/3)*3^(1/2))+10^(1/2)), _z1 = 0 .. t)+t

(8)

sol5 := diff(psi(t), t) = 3*sqrt(2)*sqrt(5)/(5*(JacobiCN((1/10)*sqrt(5)*sqrt(2)*t, (1/3)*sqrt(3))+sqrt(5)*sqrt(2)))

diff(psi(t), t) = 3*2^(1/2)*5^(1/2)/(5*2^(1/2)*5^(1/2)+5*JacobiCN((1/10)*5^(1/2)*2^(1/2)*t, (1/3)*3^(1/2)))

(9)

odeadvisor(sol5)

[_quadrature]

(10)

dsolve({sol5})

{psi(t) = Int((3/5)*10^(1/2)/(JacobiCN((1/10)*t*10^(1/2), (1/3)*3^(1/2))+10^(1/2)), t)+_C1}

(11)

``


 

Download Jacobi_Diff_eqn_Mapleprime_post.mw

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