MaplePrimes Questions

Hi all,

By solving cubic equation in maple (version 17), I got

restart

``

-0.363700352e-2*y^3-.4041941000*y^2+3.397775673*y-2.377540486 = 0

-0.363700352e-2*y^3-.4041941000*y^2+3.397775673*y-2.377540486 = 0

(1)

"(->)"

[[y = .7709248124], [y = 7.123944371], [y = -119.0286907]]

(2)

``

Now I want to find these roots through the formula.

 

I solve it generally in Maple.. 

 

``# Suppose

A*y^3+B*y^2+C*y+E = 0

A*y^3+B*y^2+C*y+E = 0

(3)

NULL

A := -0.363700352e-2:

B := -.4041941000:

C := 3.397775673:

E := -2.377540486:

``

A*y^3+B*y^2+C*y+E = 0

 

A*y^3+B*y^2+C*y+E = 0

(4)

``

y1 := (1/6)*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3)/A-(2/3)*(3*A*C-B^2)/(A*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3))-(1/3)*B/A

-45.82526955*(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3)-36.74197467/(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3)-37.04460717

(5)

"(=)"

-119.0286907-0.1e-8*I

(6)

y2 := y = -(1/12)*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3)/A+(1/3)*(3*A*C-B^2)/(A*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3))-(1/3)*B/A+(1/2*I)*sqrt(3)*((1/6)*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3)/A+(2/3)*(3*A*C-B^2)/(A*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3)))

y = 22.91263477*(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3)+18.37098733/(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3)-37.04460717+((1/2)*I)*3^(1/2)*(-45.82526955*(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3)+36.74197467/(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3))

(7)

"(=)"

y = .770924807+0.1772050808e-7*I

(8)

y3 := y = -(1/12)*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3)/A+(1/3)*(3*A*C-B^2)/(A*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3))-(1/3)*B/A-(1/2*I)*sqrt(3)*((1/6)*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3)/A+(2/3)*(3*A*C-B^2)/(A*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3)))

y = 22.91263477*(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3)+18.37098733/(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3)-37.04460717-((1/2)*I)*3^(1/2)*(-45.82526955*(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3)+36.74197467/(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3))

(9)

"(=)"

y = 7.123944373-0.1692050808e-7*I

(10)

``


y1, y2, y3 formulas are computed by Maple by solving it for general formula.
But, now I got answers in real and imaginery parts, i.e

 

y1 = -119.0286907-1.*10^(-9)*I

y2 = .770924807+1.772050808*10^(-8)*I

y3 = 7.123944373-1.692050808*10^(-8)*I

 

Why, is it so?

 

 

I want answers in simple forum directly only by using these formulas. As i have to show the proof!

Thanks in advance

 

Download qstn.mw

computer a Gröbner basis for <f_[1] = x^2*y - 2*y*z + 1, f_[2] = x*y^2-z^2+ 2*x,  f_[3] = y^2*z - x^2+ 5 > belong to Q[x,y,z], using ≺= <_grlex with x≺y≺z. compare your output to the Gröbner basis the Maple computers with a different order.

I have no idea where to start with this problem.

I know how to create arrays, but I want to assign characteristics to each position in the array; the array being a population with each member having a set of characteistics like height, weight etc. I want to be able to have some of the characteristics able to change with time, and some remain constant (those that change with time will be defined by generic equations)

I have tried looking on maplesoft for answers, and the help within maple 16, but have been unable to make any progress.

 

Sorry if the question is not specific enough.

 

Thanks in advance x

Please I need programme to solve this nonlinear couple ode with values of k_1 from 1.5 to 2.5 and eta from 0.0 to 2.0 real_work_3.mw Thanks for your help.

When I check the length of the optimal tour found by TravelingSalesman (GraphTheory package), it's different from the given result. What goes wrong?

See attached file.

``

restart: with(GraphTheory):

G := GRAPHLN(undirected,weighted,[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,

14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25],Array(1..25, [{17, 19},{10, 22

},{10, 14, 23},{6, 12, 14},{6, 7, 19},{4, 5},{5, 13, 15, 16},{12, 13, 14, 15},

{20, 25},{2, 3},{22, 25},{4, 8, 13},{7, 8, 12},{3, 4, 8},{7, 8, 21, 23},{7, 17

, 18},{1, 16, 18, 19},{16, 17, 25},{1, 5, 17},{9, 21, 22},{15, 20, 24},{2, 11,

20, 24},{3, 15, 24},{21, 22, 23},{9, 11, 18}]),`GRAPHLN/table/2`,Matrix(25, 25

, {(12, 13) = 137, (14, 4) = 920, (3, 14) = 902, (5, 6) = 561, (17, 18) = 443,

(22, 11) = 670, (16, 17) = 573, (19, 17) = 330, (18, 17) = 280, (10, 2) = 1630

, (16, 18) = 727, (23, 15) = 760, (17, 1) = 900, (4, 6) = 1216, (16, 7) = 600,

(14, 8) = 260, (12, 4) = 580, (1, 19) = 665, (4, 12) = 733, (19, 5) = 750, (8,

14) = 368, (11, 25) = 1366, (24, 22) = 300, (17, 19) = 495, (21, 15) = 930, (6

, 4) = 1110, (11, 22) = 1049, (12, 8) = 100, (15, 21) = 995, (17, 16) = 520, (

1, 17) = 866, (15, 23) = 833, (5, 19) = 930, (9, 20) = 184, (19, 1) = 630, (7,

15) = 598, (13, 8) = 110, (24, 21) = 250, (3, 10) = 471, (24, 23) = 550, (2,

10) = 1682, (13, 12) = 80, (8, 12) = 202, (21, 24) = 287, (23, 3) = 590, (15,

8) = 410, (14, 3) = 800, (23, 24) = 688, (7, 13) = 526, (8, 15) = 477, (20, 21

) = 245, (2, 22) = 547, (15, 7) = 990, (22, 20) = 420, (10, 3) = 300, (4, 14)

= 933, (5, 7) = 690, (18, 25) = 328, (25, 18) = 270, (21, 20) = 130, (25, 9) =

240, (7, 16) = 406, (20, 9) = 140, (6, 5) = 380, (8, 13) = 236, (20, 22) = 452

, (22, 2) = 500, (9, 25) = 227, (13, 7) = 640, (7, 5) = 670, (25, 11) = 1640,

(3, 23) = 518, (22, 24) = 495, (18, 16) = 700}, storage = sparse));

GRAPHLN(undirected, weighted, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], Array(%id = 4487072130), `GRAPHLN/table/2`, Matrix(%id = 4488755818))

(1)

P:=TravelingSalesman(G);

15471, [1, 19, 5, 6, 4, 14, 3, 10, 2, 22, 11, 25, 9, 20, 21, 24, 23, 15, 8, 12, 13, 7, 16, 18, 17, 1]

(2)

add(GetEdgeWeight(G,{P[2][i],P[2][i+1]}),i=1..nops(P[2])-1);

16570

(3)

 

 

``


Download traveling_salesman_e.mw

I came to know that Chrome no longer supports MathML. Will this be an issue with Maple T.A.9/9.5? Should I require my students to switch to Firefox instread? 

Hi all,

We're programming with Maple objects, and would like to have a Maple object that is appliable (i.e. acts as an operator).  We're really after partial differential operator (PDO) objects, but I give a simpler example below.  The problem is this: the ?ModuleApply proc needs to be non-static (so that each object has its own ?ModuleApply), and it may want to refer to the object instance, via ?thismodule.  Code like this works great when it is typed at the command line or read in from .mpl file, but it barfs as soon as saved to a .mla.  Why is that?  And is there an easy fix / workaround?

 

Here is an example worksheet, that creates a basic "compute mod p" object

BugThismoduleMLA.mw

The issue seems to be that, for code typed at command line, ?thismodule is resolved when I would expect, i.e. in the instance object; but saving to the .mla seems to cause ?thismodule to be resolved then-and-there, which means it resolves to the prototype object.  For this particular case there is an easy workaround, but we really want to refer to ?thismodule if possible.  Is there a way to do that?

BTW I'm running Maple 17.02 (sorry don't have access to 18 yet).

Thanks,
Ian and Tracy

One annoying feature in using document mode that I found is this. As I hit the return key to execute one command and automatically jump to the command below it (a feature that I like), but after few returns, I find myself at the bottom edge of the window, with the cursor pointing at the last command in the window.

Now when hitting return, the current command is execuated, and the next command below it appears, and it is also at the bottom edge of the window.  The cursor is from now on, always sitting at the bottom edge of the window, and I am not able to fully see the rest of the command and what is below it any more.

What would be better, is to try to keep the window centered, so that as I hit a return, the actual cursor remains in the middle of the window, and the window itself scrolls up. This way the command I am about to evaluate, and anything below it, remain in full view.

What I end up doing now, is when I get to the bottom of the window, is to manually scroll the window down using the mouse, so that now the cursor is up higher, and I can see more the commands which I am about to evaluate, then I repeate this process.

Is there  a way to configure Maple to try to keep the window centered? it is really very annoying to have to keep adjusting the window every few returns, and when one has 100 commands to evaluate, one by one (since I want to see the result before I go to the next command), this process gets tiring.

(does Maple do any usability studies and evaluation on its user interface by any independent outside group?)

 

HI.

I need your remarks in this problem.

I have ode. diff(y(x),x)=f(x,y);  x in [0,a]; h:=a/(2*N); stepsize.

When the the true solution is not Known, we can test the rate of convergence, of numerical solution. The Numerical solution generated when the stepsize is 2*h denoted by y_i^(2h) and the numerical solution with step size h will be denoted by y_i^(h).

 

if we define the epsilon(h):=sqrt (  1/(N+1)*add(  (y_i^(2h) -y_(2i)^(h) )^2, i=0..N));

 If we useForward Euler ( it's Known that the golbal error isof order 1 and local error of order 2) in the case when the exact solution is know.

But, If we use epsilon(h), and for the same method can some one know the order of Error =h^?????.

Thank you.

restart;
g:=0.88641:
e:=2.53128:
eq:=tan(g)= e*sin(f)/(1+e*cos(f)):
fsolve(eq,f);

gives  1.19749

What command/option do I need to get both solutions like with Mathematica:

g = 0.886461;
e = 2.53128;
eq = Tan[g] == (e Sin[f])/(1 + e Cos[f]);
NSolve[eq, f]

  (*   {{f -> -2.56623}, {f -> 1.19756}} *)

thanks

I took a calculus 1 class in 2002, so i have many maple worksheets i would like to view on my new dell venue 8 pro. can the player read the .mws ext ?  Donald Altringer

ps. I have maple 8 on my laptop but not on th tablet and i don't  have a way of installing it

 

Hi!

I have the following function:

and I want to calculate it for a certain set of r, theta and t, but when I use subs, the theta variable is also subsituted int the integral's parameters and I get the folllowing result:

I really don't understand why it does that given that there is no issue for the r variable...

 

Thanks in advance for your help!

P-S: please forgive my poor English : I'm a French student...

 

Florent

 

Dear all

 

Please I need your help to simplify by the coefficient a in this Matrix

I have The matrix A defined by  A:=Matrix(2,2, [[a,a],[3*a,4*a]]);

I want with maple transform A to  A:=a*Matrix(2,2, [[1,1],[3,4]]);

Thanks for your Help.

 

I try to solve these two nonlinear odes, but no desire outcome. Please helpreal_work1.mwreal_work1.mw  or real_work1.mw

 

Dear all,

Thanks for your answer. I have a simple question:

Let A be a Matrix, X[1] and X[2] two vectors.

I have this equation:  X[2]= X[1]+ A*X[1]+A*X[2];  Using Maple how can I  writte X[2] =P*X[1]; where P is a matrix to be founded.

Here, P:=(Id-A)^(-1)*A; But how using maple.

 

 

 

 

 

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