Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Lang_2_output_as_tswitch_varies.mw

^ in this worksheet I have made a graph of a variable in a simple ODE against time (shown below), at t=150 a switch condition, in the worksheet called tswitch, changes the rates of change of the ODE.

I am thinking about afunction that maps tswitch->solution of the ODE and would like to visualise it as a 3d surface, but couldn't work it out in Maple

 

Hello everyone,

I have a function of 5 variables, A, P, N, k. I want to solve and express as a power series of 'k'

w=F*k+G+H/k+...

and gather the coefficients of each power.

However, the result I obtain in my code differs from the analytical value I found. What am I doing wrong?

Thanks!

collect_mp.mw

Does Maple allow importing HDF5 data files? I checked the docs & cannot find any hint that it does. But before I launch an SCR I thought I'd ask here.

TIA,

M.D.

I've recently changed to maple 2019, from the 2016 version as my license for that product had expired. 
However I find it really frustrating that often upon evaluating an expression I can't convert the units. 

For instance I had a calculation that evaluated to: 

2.114163508*10^7 [kg/s^2]
 

When I try to directly replace the units within maple to instead be [J/m^2] I recieve the following error message: 


"Error, (in  Units:-TestDimensions) 'op(3, i) does not  evaluate to module" 

There is no explanation for this error when I try to look it up. However if I once again manually write the answer: 
2.114163508*10^7 [kg/s^2] and use the replace units function. 
No problem. 
I find this quite annoying and frustrating and I hope you can help.
 

Best regards 

Anders Alexander Wagenblast 

Hello all

I am going to find the diffusion constant in the following equation :

PDE:=diff(C(x,t),t)=d*diff(C(x,t),x,x);

In a way that ,

evalf(Int(C(x,t=specific),x=0..L))/L - m_number(t=specific)=0
 

In other words, It would be an iterative procedure to guess "d" and then find the solution C (something like shooting method). The objective is to find "d" in a way that the average of C (solution of PDE) would be equal to m_number at that specific time.

Also, Since I have 5 specific time and m_number, I will have 5 different d. So, I need to use least square method or other optimization technique find one finalized d value.

I have uploaded my code.

inverse_numerical_diffusion.mw

I am not good at using Proc command and  I think the error of my code is because of that.

Would you help me to find out my problem in the code and any new idea for solviong this equaltion would be greatly appreciated.

Thank you for your kind attentions in advance

Amir

 

 

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.

expr:=1/(y^3+1)^(2/3);

1/(y^3+1)^(2/3)

int(expr,y)

y*hypergeom([1/3, 2/3], [4/3], -y^3)

simplify(%)

(2/9)*y*Pi*3^(1/2)*LegendreP(-1/3, -1/3, (-y^3+1)/(y^3+1))/((-y^3)^(1/6)*(y^3+1)^(1/3)*GAMMA(2/3))

 


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
 

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 := `assuming`([dsolve({bc, de}, {omega, y(x)})], [a > 0, b > a])

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)}

(1)

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

Oliveira


 

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?

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