Maple 2017 Questions and Posts

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

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?

I have a code in Maple that solves a system of polynomial equations (18 equations, 18 variables) using the command 'RootFinding[Isolate]' (it takes to Maple about 40 minutes to find all the solutions to the equations). Is it possible to see the implementation of the Isolate command? if not, is there any other open source code that implements the equivalent to Isolate command and also able to solve such equations? (I'm talking about the  numeric solutions. not symbolic).

I already tried to use the command 'solve_poly_system' in python (sympy package) which is open source. but the function didn't return a solution after a very long time (and I used a system of 9 equations and 9 variables which were much simpler than the equations Maple was able to solve using Isolate command).

I'm attaching the equations Maple solved using Isolate command. and also the equivalent in python with the simpler equations (that it wasn't able to solve).

solving_18_polynomial_equations.mw

trying_to_solve_polynomial_equations_python.txt

I'd appreciate any idea of how to use open source code that produces the same results as the code in Maple (if it's possible).

Thanks

 

Hey everyone
 

I am trying to create a procedure, which includes a part, where a function is plotted. I want to be able to declare the range of the plot within the procedure parameters as x=range - example when executing: procedureName(function,x=range). I have isolated a small part of the procedure and the different approaches I have tried:

For simplicity's sake let's call the procedure test.

test:=proc(function,{x::range:=0..1})

#I would then like to be able to plot the following:

plot(function,'x'=x);

end proc:
 

However, the single quotes do not prevent x from being evaluated within the procedure, and there interprets the second argument of 'plot' as 0..1=0..1. Another approach I tried was the following:

 

test:=proc(function,{x::range:=0..1})

local xRange:=x;

unassign('x');

plot(function,x=xRange);

end proc:

 

However, I run into the same problem as above - the elements within the single quotes are still evaluted within the procedure. A workaround would be to simply rename the range parameter, for example:

 

test:=proc(function,{xInr::range:=0..1})

plot(function,x=xInr);

end proc:

 

I would really like to be able use x as the parameter, though.

 

Thanks in advance!

Here is my code:

with(DEtools): with(plots): with(linearAlgebra):

DE1 := diff(y(x), x) = d^3*y(x)/dx^3+3*d^2*y(x)/dx^2+4*d*y(x)/dx+12*y(x);

DEplot(DE1, [y(x), x = 0 .. 5][[y(0) = -3, (D(y))(0) = 0, ((D^(2)(y))(0) = 0, ((D^(3)(y))(0)]]);

I get the Error message: Error, (in DEtools/DEplot) called with too few arguments

Any help would be greatly appreciated, thanks.

My question is within the worksheet.

assignation.mw

In the context of homework, there are some calculations that I do through Maple, and others that I do mostly by hand, and just show my work with Maple's engine that is great at rendering special mathematical formats (like matrices, for example).

I would like to show something like that:

 

It's pretty easy to make the matrices, right now my line looks like this:

 

But I would like to refrain for executing the "+" operator and the multiplication by x6 and x7, to have the output like in the first picture. If I disable all execution and take the statement as plain text, then obviously I will not get the correctly rendered matrices.

Is there a way, like an escape character, to prevent specific operations from being executed in one line in particular?

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