Hello!

I recently began learning how to 3D print with maple using the "Export & .stl " command together.

I was wondering if anyone knew how to increase the surface thickness for parametric plots and implicit plots. My hope would be to increase the "extrusion level" so to say.

I came across:

https://www.mapleprimes.com/questions/134103-Plotting-3d-Surfaces-With-A-Thickness

But I am not sure how to extend this idea to a parametric surface or an implict surface.

One more quick tidbit is that I will be trying to print several surfaces arising in differential geometry and algebraic geometry. Severel of these surfaces are open and or have singularities that I would like to "smooth out."

I would love to hear any ideas and thanks!

How to get correct result this equation
restart; with(Student:-MultivariateCalculus);
A := [0, 0, 0];
B := [c, 0, 0];
S := [x, 0, z];
solve([Distance(S, A) = a, Distance(S, B) = b], [x, z]) assuming and(a > 0, b > 0, c > 0);

The integral of y = Dirac(phi-m), in which phi is a continuously variable quantity and m is a positive integer, from -infinity to infinity yields 1 as an answer.   The analogous integral of y² yields no answer.  Is it possible that the latter integral has some mathematical meaning that might yield an answer?

I have Differential equation sytems as follow:

r := 10^(-2);k := 10^12;c1 := 5*10^(-11);c2 := 10^(-13);mu := 8;lambda := 4.16;a := 2*10^3;q := 300;s0 := 3*10^5;d := 10^(-3);rho := 10^(-12);gama := 10^2;delta := 10^4;b := 5*10^6;

eq1 := {N(0) = 2*10^10, P(0) = 5*10^7, Q(0) = 0, diff(N(t), t) = r*N(t)*(1 - N(t)/k) - c1*N(t)*P(t) - mu*N(t)*Q(t)/(a + Q(t)), diff(P(t), t) = s(t) + s0 - d*P(t) + rho*N(t)*P(t)/(gama + N(t)) - c2*N(t)*P(t) - delta*P(t)*Q(t)/(b + Q(t)), diff(Q(t), t) = q(t) - lambda*Q(t)}. I replace I with P.

N(t):The number of cancer cells; P(t): The number of immune cells (Healthy T-Lymphocuyes); Q(t): The amount of chemotherapeutic agent in bloodstream; q(t): Source terms standing for chemotherapy.

My question is how to get the first two figures below based on these information: q_infinity means constant chemotherapy infusion, while s_infinity means constant immunotherpy.

I got the plot for Q(t) as follow:

Please anyone has any suggestions to help. Thank you very much.

This is may be a philosophical question. But sometimes Maple suprises me when telling it to "simplify" expression. As in this example.

For me, the original result is "simpler". (Not only smaller leaf count, but it has one special function, vs. two: Legendre and Gamma). But may be Maple considers hypergeom always more "complex" than any other?

That is why I use simplify(expr,size) because I am scared of simplify without any option, as I have little idea how it decides which is simpler.

Any thoughts from the experts on how Maple decided to simplify something when no option is used? What kinds of rules it uses to decide how to transform the expression?

Maple 2019.1

Download simplify.mw

In the DE solution below I cannot convert the RootOf function to radicals.
macro(solve = allvalues@solve);
_EnvExplicit := true;
de := x^4*diff(y(x), x $ 2) + omega^2*y(x) = 0;
bc := y(a) = 0, y(b) = 0, D(y)(a) = 1;
dsol := (dsolve({bc, de}, {omega, y(x)}) assuming (0 < a, a < b));
convert(dsol, radical);
{omega = RootOf(tan(_Z)*_Z*b*_C2 - sin(-2*_B5*Pi + 2*Pi*_Z10 + 2*_B5*arccos(_Z*b*_C2/a) - arccos(_Z*b*_C2/a))*a)*b, y(x) = x*(-cos(RootOf(tan(_Z)*_Z*b*_C2 - sin(-2*_B5*Pi + 2*Pi*_Z10 + 2*_B5*arccos(_Z*b*_C2/a) - arccos(_Z*b*_C2/a))*a)*b/x)*sin(-2*_B5*Pi + 2*Pi*_Z10 + 2*_B5*arccos(RootOf(tan(_Z)*_Z*b*_C2 - sin(-2*_B5*Pi + 2*Pi*_Z10 + 2*_B5*arccos(_Z*b*_C2/a) - arccos(_Z*b*_C2/a))*a)*b*_C2/a) - arccos(RootOf(tan(_Z)*_Z*b*_C2 - sin(-2*_B5*Pi + 2*Pi*_Z10 + 2*_B5*arccos(_Z*b*_C2/a) - arccos(_Z*b*_C2/a))*a)*b*_C2/a))*a/(RootOf(tan(_Z)*_Z*b*_C2 - sin(-2*_B5*Pi + 2*Pi*_Z10 + 2*_B5*arccos(_Z*b*_C2/a) - arccos(_Z*b*_C2/a))*a)*b) + sin(RootOf(tan(_Z)*_Z*b*_C2 - sin(-2*_B5*Pi + 2*Pi*_Z10 + 2*_B5*arccos(_Z*b*_C2/a) - arccos(_Z*b*_C2/a))*a)*b/x)*_C2)}

Does anyone know how to convert the above expression to radicals?
I'm grateful.
Oliveira
RootOf_to_radical.mw
 

Download RootOf_to_radical.mw

I have just made a bar graph in Visualising_numerous_derivatives_of_the_L2_model.mw

and i would like to set it to be logscaled, but could not find an option in the documentation, or a way of using a logplot to get similar functionality

The video component is going to save me alot of hassle in that I was previously building external java applications for audio visual analysis purposes, with the downside of course being that I didnt have maple code at my disposal. 

I read in the manual for the video component that I can provide a HTTP address for which a video is located, which would mean i could probably stream an IP camera, but I can I use the localhost IP address with some sort of extension that directs to the I/O of a webcamera connected to my local machine?

Hi all, how to write description, suggestions for method (procedure) like image below. I tried searching for a solution but can't. Thank you very much

Is there extendable combinatorics experiment architect system design

such as new method can combine or use with old method and find relationship between them , these kind of big data system design in combinatorics experiment design?

Hi

I have made a worksheet showing how a variable, from an ode varies with time 

I would like to make similar graphs for y',y'',y''' etc and i couldn't think of how to do it.

Additionally I wanted to plot a bar graph of  y^(i)(1000)-lim(t approaches 1000 from below of y) any ideas oin how to do that?

thanks

I am playing around with certain "simple" integrals, and came across this strange behavior in Maple. Maple is able to integrate sin(x)^(1/2)*cos(x)^3, but not sin(x)^(1/3)*cos(x)^3. Any idea why?

trig_integral.mw
 

I am not able to understand why this ODE is quadrature. It is first order ODE of second degree. Solving for y'(x) gives two ODE's. Only one of these two ODE's is quadrature and the second is Abel.

So  why and how did odesdvisor come to conclusion that it is  quadrature? Did it pick the first ODE that comes from solving for y'(x)?

Note that from help, quadrature is ODE (for first order) is one which
the ODE is of first order and the right hand sides below depend only on x or y(x)

And the above definition only applied here for one of the 2 ODE's embeded inside this first order ODE of second degree. So I am just trying to understand the logic behind this result of odeadvisor

Download why_only_quadrature.mw

btw, the above is just one example. I have many more. below show one more such example

Download why_only_quadrature_2.mw

Maple 2019.1

I gave up. Spend 40 minutes trying everything and can't figure the right syntax. 

I need to use indets to obtain all occurrences of specific function in expression. Such as sin() or cos() or ln(), etc...

The indets commands has the form indets(expression, type).

But what is the type of ln ? It is of function type. But this picks up all other functions in the expression. I tried specfun and could not make it work. For example

expr:=x+sin(x)+ln(y)+10+ln(x+y)^2;

I want  to obtain  {ln(y),ln(x+y)^2}

I tried

indets(expr,function); 
indets(expr,specfun(ln));

and many more. Since indets needs a name of a type in the second argument, then what is the type name for ln or sin or cos, etc... I can't use indential, it did not work, since it is not a symbol I am looking for. I could use patmatch, but I am trying to learn indets for all these things.

Do I need to use subsindets for this? I still do not know how to use subsindets.

Maple 2019.1

hi i did this in maple and i get an error when i try to solve the system of equation  :

restart;
with(Student[VectorCalculus]);
with(PDEtools);with(plots);

h_f := 300;
h_a := 1000;
T_f := 1500 + 273;
T_a := 30 + 273;
k_r := 15;
k_s := 70;
Ra := 5;
Rf := 6.05;
Rc := 6;