Maple 2017 Questions and Posts

These are Posts and Questions associated with the product, Maple 2017

Maple gives me poor accuracy for simple arithmetic problems.

My calculator gives me 0.7 and 0.9 respectively.

I guess I could do evalf(convert(2.59/3.7,fraction)) = 0.7000000000

but this seems excessive.

Sup Brainiacs

I found this "solved" problem for backing rectangular items efficiently. The first example (without rotation of items).

https://www.researchgate.net/file.PostFileLoader.html?id=59938b635b49527571134c33&assetKey=AS%3A527790252490752%401502846410852

I think I have the constraints the same as the text, but I get different solutions. my questions are at the end of the worksheet. Thanks

I 2D_BP.mw

How does one look through the Maple 2017 help for a code structure. I have been looking for how to construct a While loop and I am not able to find any example that implements while loop nor the code structure for it.

Any help is appreciated.

Hello,

how could I force Maple to solve this pde

pdsolve(y*(diff(f(x, y, z, w), x))-x*(diff(f(x, y, z, w), y))+w*(diff(f(x, y, z, w), z))-z*(diff(f(x, y, z, w), w)) = 0)

When I hit enter, it happens nothing.

Here are two inocent Vectors.

V1 := Vector[row]([`+`, 1, 2]);

_rtable[18446744074366295326]

(1)

V2 := Vector[row]([1, `+`, 2]);

_rtable[18446744074366288110]

(2)

lprint(V1);

Vector[row](3, {1 = `+`, 2 = 1, 3 = 2}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

 

 

The questions:

 

1.  Try to guess the Maple's answer for:

 

V1, V2;

 

2. Try to explain.

 


Download v1v2.mw

Hi...  I use the "solve" command to solve an algebraic  system. Sometimes, the solution is given using some unknowns as parameters.

A toy example: x+y+z=1,x-y+3z=7 gives x=-2z+4,y=z-3 as a function of the parameter z (in the RHS).

Can I obtain directly (without going through the block-by-block solution) the set of parameters used in the given solution?

Thanks in advance.

I have many expressions in a worksheet like this:

latex(%, "equations.tex", append = true)

I should have defined a file name like this:

fname := "C:/home/MyStuff/Economics/MICRO NOTES/equations.tex"

And then replaced the first expression throughit the worksheet by:

latex(%, fname, append = true)

To acheive this I open the Find/Replace dialogue as in picture below:

This does not work. Instead of replacing with fname the result is "fname" .  Is there any way of doing what I want?

Maple gives the integral's face instead of giving a number as the numerical integration, no matter what command for the numerical integration I use. Does any one know what the problem is?

T2start := -5.036645000*10^9*(x[5]^2+.2725890432*x[5]+.3732640349)*x[5]/(5.036645000*10^9*x[5]^2+1.27004241*10^8*x[5]+5.3714241*10^7); 
T2end := -5.036645000*10^9*(x[5]^2+.2871403962*x[5]+.3945934083)*x[5]/(5.036645000*10^9*x[5]^2+1.27004241*10^8*x[5]+5.3714241*10^7);
J := (25183225000000*x[5]^4+(-100732900000000*T[2]+73827142410000)*x[5]^3+(-112645777230000*T[2]+662242877289)*x[5]^2-2398770574578*T[2]*x[5]-393671672289*T[2])/(10000000*x[5]^2+14658000*x[5]);
int(abs(J), [T[2] = T2start .. T2end, x[5] = 0 .. infinity], numeric);

I also used the following.

evalf(Int(abs(J), [T[2] = T2start .. T2end, x[5] = 0 .. infinity]));

The result was same.

Or when I use

evalf(Int(abs(J), [T[2] = T2start .. T2end, x[5] = 0 .. infinity], method = _MonteCarlo));

It gives an error saying:

Error, (in evalf/int) invalid arguments

When I tried to execute one of my opened worksheets, the "execute the entire worksheet button" became unactive for the others. I am pretty sure there was an option to execute multiple worksheets in Maple 14. Did the developers remove that in newer versions?

Let us consider

sol1 := dsolve({diff(y(x), x) = solve((1/2)*(diff(y(x), x))^2 = (1-ln(y(x)^2))*y(x)^2, diff(y(x), x))[1], 
y(0) = 1}, numeric);
sol1 := proc(x_rkf45) ... end proc

The problem under consideration has the symbolic solution:

sol2 := dsolve({diff(y(x), x) = solve((1/2)*(diff(y(x), x))^2 = (1-ln(y(x)^2))*y(x)^2, diff(y(x), x))[1], 
y(0) = 1});

sol2 := y(x) = exp(x*sqrt(2)-x^2)

Let us compare the plots of sol1 and sol2 (which should coincide):

A := plots:-odeplot(sol1, x = 0 .. 1, color = navy, style = point):
B := plot(rhs(sol2), x = 0 .. 1, color = red):
plots:-display([A, B]);

The plots differ after approximately 0.707. Bug_in_dsolve_numeric.mw

Edit. The title and one of the tags.

evalf(Int(x*(1-2*x^(3/10))^(10./3),x=0..1));  # Crashes Maple

Note that:

int(x*(1-2*x^(3/10))^(10./3),x=0..1);
int(x*(1-2*x^(3/10))^(10/3),x=0..1);

are OK.

(Windows 7, Maple 2017.3, 64 bit)

Application to generate vector exercises using very easy to use patterns. These exercises are for sum of vectors in calculations of magnitude, direction, graph and projections. Basically to evaluate our students on the board and thus not lose the results. For university professors and engineering students.

Generator_of_exercises_with_vectors.mw

Lenin Araujo Castillo

Ambassador of Maple

This is my first time in this forum, so I hope I use the correct conventions. If not please notice me. 

  1. When a light body orbits a heavy body under the influence of gravity (e.g. a planet around the Sun), Newton’s laws show that the orbit is restricted to a two-dimensional plane and is given by the differential equation

    d2/d(φ)2(1/r(φ)) + 1/r(φ) = GM/h2

    Here, (r, φ) is the path of the light body in polar coordinates, M is the mass of the heavy body, G is the gravitational constant, and h is a constant related to the angular velocity of the light body (h = r2φ ̇). The heavy body can be considered to be approximately stationary and located at the origin.

    Use Maple to solve this differential equation numerically, taking M = 1, G = 1, h = 1 with initial conditions

    r(0)=2/3, r′(0)=dr/dφ (0) = 0

    Using polar coordinates, create a plot of the orbit (r(φ), φ) for
    0 ≤ φ < 2π. You should observe a perfect ellipse.

  2. Since I am not a frequent maple user, I hope somebody can help me here

Hi.... I'd want to numerically solve a system of  n  polynomial equations of degree 2 with respect to n unknowns. It seems to me that there is a software in Maple (which deals only with the equations of degree 2) that solves this problem. I cannot find it anymore. Do you know it ? Thanks in advance.

For a numerical integration in Maple, one only adds evalf(...) to the integration commend. Now my question is that is it also the case for the multi-integration? Also consider that the multi-integration of the Maple doen't give any answer for some examples. So I think putting evalf around them, doesn't help. How can someone compute a numerical approximation of a multi-integration by Maple? Is there any prepared commend or package for it?

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