Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I would like to factor an algebraic expression that contains exponentials.
Maple spits it back unfactored. Did I enter it wrong?

factor(exp(4*y) + 2*exp(2*y) + 1);

Good afternoon everybody,

I am a beginer user in maple and I am having problems to plot a system of differential equations. My code is

----------------------

restart; with(VectorCalculus); with(LinearAlgebra); with(DEtools);
> p := 2*u*x*y^2; q := (x-1)/x;
> doth := simplify(-(sqrt(6)*x^3*(y-1)^2+u*((3+sqrt(6))*x^3*(y-1)^2+3*y^2-9*x*y^2+3*x^2*(y^2+2*y-1)))/p); ddotphi := simplify((y-1)*(sqrt(6)*x*y^2*(x-1)+u*(3*y^2-(6+sqrt(6))*x*y^2+x^2*((3+sqrt(6))*y^2+6*y-3)))/p);

>ode1 := diff(x(t), t) = x(t)*(1-x(t))*doth-x(t)^2*ddotphi/sqrt(6); ode2 := diff(y(t), t) = y(t)*(y(t)-1)*doth; ode3 := diff(u(t), t) = sqrt(3/2)*u(t)*(1+u(t))*q;

>DEplot3d([ode1, ode2, ode3], [x(t), y(t), u(t)], t = -2 .. 2, x = 0 .. 1, y = 0 .. 1, u = -1 .. 0, [[x(0) = .9, y(0) = .25, u(0) = -.95], [x(0) = .9, y(0) = .25, u(0) = -.5], [x(0) = .85, y(0) = .2, u(0) = -.15], [x(0) = .25, y(0) = .5, u(0) = -.5], [x(0) = .7, y(0) = .5, u(0) = -.6]], linecolor = [red, green, black, navy, maroon], thickness = 2, axes = boxed, labels = [x(t), y(t), u(t)], arrows = medium, stepsize = 0.1e-1, orientation = [30, 65]);

--------------------------

and the next error appears

Error, (in DEtools/DEplot/direction3d) unable to store 'HFloat(HFloat(undefined))+HFloat(HFloat(undefined))*I' when datatype=float[8]

 

I have no idea what to do, and searching for solutions I have only found things that I dont understand.

 

Thank you very much in advance

I want the legend to be produced to look like the third to last example. https://fr.maplesoft.com/support/help/Maple/view.aspx?path=plots/contourplot 

However, mine keeps coming out like this.

hello how do i solve these equations and what type exactly are they ? so i can find more information

(i dont understand if this is a partial-something)

for the following function

f(y,z)=y*sin(z) + 2*cos(y)

i need to evaluate it at the following point

fy(pi/2,pi)  and  fz(pi/2,pi)

this is the part i dont understand how to do, i keep getting 0 in the equation.

 

thanks for you! and your time

I would like to "run" or execute parts of my code that I put in a same section. Unfortunately, selecting "Execute" when right-clicking on a section does nothing...

For entering system of linear ode's, from textbook, such as this example

I can either use x[1],x[2]  or x__1 and x__2.

Maple dsolve works with both. The Latex generated is also exactly the same Which is x_{1} and x_{2}.

The only minor difference I see is on the screen in the worksheet (I only use 1D), where the subscript looks a little nicer in the case of x[1] vs. x__1

The subscript in the case of x[1] is upright while the one in x__1 is italic. I like the first one more.

Other than this cosmetic difference, Are there are subtle sematic differences between the two forms in terms of computation? I know x[1] create table x. OK.  While x__1 is a separate symbol. No table is created.,

Which would be  a safer/better option to use in this case?   Or is it just a matter of choice?

sys:=[ diff(x[1](t),t)=x[1](t)+x[2](t),diff(x[2](t),t)=x[1](t)+3*x[2](t)];
sys:=[ diff(x__1(t),t)=x__1(t)+x__2(t),diff(x__2(t),t)=x__1(t)+3*x__2(t)];

In some way, using x__1(t) might be a little easier to read on the eye than x[1](t) since there is only one type of paranthesis involved.

ps. I tried to search for __ in Maple help to read more about it, but ?__ do not show it. I am sure __ is in the help under some other name.

How do I insert an empty or null value into a matrix imported from a csv file?  The imported data assumes the value is zero.

For display only purposes, to get the Latex looking better, I replace the constant of integrations Maple using which is _C1, _C2., etc... to c[1],c[2],..... 

This is something I do at the very end of computation, just before I get the Latex of the expression.

The way I do this now, is not good. .And I am asking if there is a better way to do this replacement. In Mathematica, I can do this using a patterm where I tell it to replace  C?  by c[?] where ? means anything.

Is it possible to do something like this in Maple? Here is an example

sol:=dsolve(diff(x(t),t$3) = x(t));

This gives solution as

And just before ask for the Latex of this, I change it to 

This is done using a function. Please see worksheet below.

The problem with the current solution is that I do not know how many _C there are, so I assumed 10 as worst case, which works for my case. But I prefer a more general solution, may be using pattern in the subs command?


 

restart;

replace_all_C:=proc(expr::anything)
local n,N,c;
local new_expr;
local max_count :=10; #worst case, since do not know how many

    new_expr:=expr;
    for n from 1 to max_count do
        N:=convert(n,string);
        new_expr:=subs( :-parse(cat("_C",N))=:-parse(cat("c[",N,"]")),new_expr);
    od:
    return new_expr;
end proc:

sol:=dsolve(diff(x(t),t$3) = x(t));
tmp:=replace_all_C(sol)

x(t) = _C1*exp(t)+_C2*exp(-(1/2)*t)*sin((1/2)*3^(1/2)*t)+_C3*exp(-(1/2)*t)*cos((1/2)*3^(1/2)*t)

x(t) = c[1]*exp(t)+c[2]*exp(-(1/2)*t)*sin((1/2)*3^(1/2)*t)+c[3]*exp(-(1/2)*t)*cos((1/2)*3^(1/2)*t)

 


 

Download q.mw

And now I get the latex of tmp in the above, instead of sol which looks better.

 

 

Can anyone help with plotting the logistic map as a function in Maple

Logistic map x_(n+1)=f(x_n); f(x_n)=r*X(1-x) with the following values:

r=2.0; x(1)=0.3 f=r.*x.*(1-x)

Please help? Thanks.

I created some simple maple 9 code to do some z->w mappings long time ago, on my web page:

https://ingalidakis.com/math/ComplexMaps.html

Upon revising my webpage, I've stumbled upon a page for comformal mappings, by David Bau:

http://davidbau.com/conformal/#exp(z)

Here's the current version of my code in Maple 18:

rrestart;
NULL;
with(plots);
xMax := 1;
yMax := 1;
N := 10;
step := abs(xMax)/N;
GL := proc (x, y) options operator, arrow; x+I*y end proc;
f := sin;
G := {};
for k from -N+1 to N+1 do

G := `union`(G, {complexplot(f(GL(x, (k-1)*step)), x = -xMax .. xMax, color = brown)});

G := `union`(G, {complexplot(f(GL((k-1)*step, y)), y = -yMax .. yMax, color = brown)})

end do;
display(G, scaling = constrained);

The code is pretty simple: I am simply scanning the 1x1 unit square complex grid and create a complex plot of it on the w-plane, by passing it through whatever function is at: f:=x.

Does anyone have any idea why the grid lines on the w-plane do not agree with Bau's grid lines mapping of the w-plane? To try it for exp for example, input "exp(z)" in Bau's home page.

The difference is quite noticeable, especially on exp and log, where the orientation of the w-grid on the left and right half-planes, seem to be opposite of what my code displays.

The reason may be Mathematical, but from what I see from the description on Bau's page, there's no difference on the identity function, so I am clueless.

Many thanks in advance

Any idea why the result of the FirstChild function of the attached file is

_XML_Text("\n  ")

Test.zip

I also miss a more complete example on Maple Help for writing, reading and processing xml files.

restart;

W := proc ()

      global rf;

     rf := add(xx[ii]^2-nn, ii = 1 .. nn);

    return rf ;

   end proc;

Optimization:-Minimize(W(), nn = 1 .. 5, seq(xx[ii] = 1 .. 10, ii = 1 .. nn));


Error, (in W) unable to execute add

 

Please solve

A triangle ABC with fixed B and C vertex is considered in the plane, A being variable so that b+c remains constant and equal to a given length L.
We call P, T, T' the points of contact of the exinscrit circle in the angle B with the sides BC, AB and AC respectively.
Show that P is fixed and is one of the vertex of the ellipse described by point A. What are the locus of T and T'? How to animate the drawing when A move ? Thank you.

Hello! Sorry if this question was already asked, I just can't find my answer and I don't really know how to form the question since I'm new to using Maple. My question is: How can I find a point on a plot I did in Maple? When I use the cursor position(from when I click Probe info) I can never align it right enough for me to not get a decimal answer. For instance, I can't figure out the y-value for when x=2 because the closest I can get to 2 is like 2.1 which isn't exact enough for me. 

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