Adding assumptions to variables to simplify integr...

Hello,

I'm new to Maple, but somewhat competent in computer mathematics. Below is some code that I wrote. I start off with f, my original function, and try to simplify it. I tried defining some assumptions as best I could. When I calculate the integral, it gives me an odd range of validity.

I'm wondering if I can further add to my assumptions to make the integral result more concise, i.e. without the piecewise range of validity. All my variables in f and g are already real and positive, so there is no reason one of the expressions should be less than zero.

Thank you in advance for any insight.

 (1)

 (2)

 (3)

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3D Printing and Surface Thickness...

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!

Why does this error appear? "Error, (in DynamicSys...

Hello,

I am trying to define a statespace object. Here my code reads:

 with(DynamicSystems):
 > aSys≔StateSpace(⟨⟨1,2⟩∣∣⟨3,4⟩⟩,⟨⟨2,3⟩⟩,⟨⟨1,0⟩∣∣⟨0,1⟩⟩,⟨⟨0,0⟩⟩):

Error, (in DynamicSystems:-StateSpace) unsupported type of index, t

I do not have any clue what is wrong with my code.

Any help will be really appreciated.

Thanks

How to compare list in a if statement?...

I want to extract lists that are term by term smaller than a fix one.

To be clearer, I want to create something like

if a[i] <= b[i] for all i=1..min(nops(a),nops(b)) then ...

I tried with the forall call, but it doesn't work:

if forall( i=1..min(nops(a),nops(b)),a[i] <= b[i]) then ...

I also tried the assuming call with the is call. It works, but doesnt't give me the result I want:

if is(a[i] <= b[i]) assuming(1 <= i, i <= min(nops(a),nops(b))) then...

Is there a way to have a chain of conditions in a if statement like I am trying to do?

How do I use maple inbuilt numerical methods like ...

1. y''(x)+10y(x)=99sin(x), y(0)=1, y'(0)=11 in the interval [0,100]

the exact solution is y(x)=cos(10x)+sin(10x)+sin(x)

2. y'=z, y(0)=1

z'=-y(x)+x, z(0)=2

the exact solutions are y(x)=cos(x)+sin(x)+x, z(x)=cos(x)-sin(10x)+1

how to find equation of intersection between a pla...

Hi
i need to find equation of intersection between a plane(Z=0)  and 3d curve like below:

plane :  Z=0

curve:

sqrt(G*(2-G))+(1-G)*(arccos(G-1)+(1/5)*Pi)+k*sqrt(G*(2-G))*cos(sqrt((1+k)/k)*arccos(G-1)+(1/5)*Pi)+sqrt(k/(1+k))*(1-G)*k*sin(sqrt((1+k)/k)*arccos(G-1)+(1/5)*Pi)

I ploted Z=0 plane and that curve . it is like this .
i want equation of the pointed curve(curve equation of intersection between Z=  and curve )in bellow  such as k=f(G) .

best regards

How can I animate the flattening of an octohedron?...

The worksheet below animates the flattening of a tetrahedron by expanding one of its faces, namely its triangular base.

I would like to animate the flattening of an octahedron so that it assumes the 2D figure resembling the Morley triangle which is included in the worksheet.

Are there documents on the web explaining the technique for doing so? Is there a Maple worksheet available on the web demonstrating the desired animation?

Flatten_a_tetrahedron.mw

Internal Error in Typesetting invalid object...

Hi, my codes ran smoothly well until I changed some assignment value. It reported invalid object error.

Error, Got internal error in Typesetting:-Parse:-Postprocess : "internal error: invalid object "

Part of the codes are as follows:

""sigma:=0.00002:    m:=5:   n:=4:
Error, Got internal error in Typesetting:-Parse:-Postprocess : "internal error: invalid object "

Could anyone give some hints on what goes wrong here? It seems to be a configuration issue but I completely have no clue..

Thanks a million in advance,

Best,

Jie

how do i solve it ?...

please where is the problem

with(DEtools);

eq1 := (D(x))(t) = -y(t);

eq2 := (D(y))(t) = x(t)+2*x(t)^3-signum(z(t));

eq3 := (D(z))(t) = w(t);

eq4 := (D(w))(t) = -z(t)*(1+6*x(t)^2);

sys := eq1, eq2, eq3, eq4;

ic1 := [x(0) = 0, y(0) = 0, z(0) = cos(1), w(0) = sin(1)];

ic2 := [x(0) = 0, y(0) = 0, z(0) = cos(2.5), w(0) = sin(2.5)];

ic := ic1, ic2;

DEplot([sys], [x(t), y(t), z(t), w(t)], t = 0 .. 10, [ic], stepsize = 0.5e-1, scene = [x(t), y(t)], linecolor = [blue, red]);

sol1:=dsolve({sys,x(0)=0,y(0)=0,z(0)=cos(1),w(0)=sin(1)},{x(t),y(t),z(t),w(t)},type=numeric);

T := 10.0 ; N := 100 ; h := T/N;

xk := 0;

for k from 1 to N do

solk := sol1(k*h);

xknew := subs(solk,x(t));

yknew := subs(solk,y(t));

if xk*xknew<=0 and abs(yknew-6)<0.5 then break fi;

xk := xknew;

od; sol1(k*h);

temps := proc(alpha,eps)

local sol,solk,T,N,h,k,xk,xknew,yknew,t0,t1,tm,x0,x1,xm;

sol := dsolve({sys,x(0)=0,y(0)=0,z(0)=cos(alpha),w(0)=sin(alpha)},{x(t),y(t),z(t),w(t)},type=numeric);

T := 10.0 ; N := 100 ; h := T/N;

xk := 0;

for k from 1 to N do

solk := sol(k*h);

xknew := subs(solk,x(t));

yknew := subs(solk,y(t));

if xk*xknew<=0 and abs(yknew-6)<0.5 then break fi;

xk := xknew;

od;

t0 := (k-1)*h ; t1 := k*h ;

x0 := subs(sol(t0),x(t)) ; x1 := subs(sol(t1),x(t)) ;

while abs(x0-x1)>eps do

tm := (t0+t1)/2;

xm := subs(sol(tm),x(t));

if xm*x0<0 then x1 := xm; t1:=tm;

else x0 := xm; t0:=tm;

fi;

od;

RETURN(t0);

end;

dicho := proc(eps)

local a,b,m,sola,solb,solm,ta,tb,tm,ya,yb,ym;

a := 1 ; b := 2.5 ;

sola := dsolve({sys,x(0)=0,y(0)=0,z(0)=cos(a),w(0)=sin(a)},{x(t),y(t),z(t),w(t)},type=numeric);

solb := dsolve({sys,x(0)=0,y(0)=0,z(0)=cos(b),w(0)=sin(b)},{x(t),y(t),z(t),w(t)},type=numeric);

ta := temps(a,eps) ; tb := temps(b,eps) ;

ya := subs(sola(ta),y(t)) ; yb := subs(solb(tb),y(t)) ;

while abs(yb-ya)>eps do

m := evalf((a+b)/2);

solm := dsolve({sys,x(0)=0,y(0)=0,z(0)=cos(m),w(0)=sin(m)},{x(t),y(t),z(t),w(t)},type=numeric);

tm := temps(m,eps) ;

yb := subs(sol(tm),y(t));

if (ym-6)*(ya-6)<0 then b := m; yb := ym;

else a := m; ya := ym;

fi;

od;

RETURN(a);

end;

dicho(0.01);

2.136718750

temps(2.136718750,0.01);

8.737500000

DEplot([sys], [x(t), y(t), z(t), w(t)], t = 0 .. 8.7375, [[x(0)=0,y(0)=0,z(0)=cos(2.136718750),w(0)=sin(2.136718750)]], stepsize = 0.5e-1, scene = [x(t), y(t)], linecolor = [blue]);

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

homotopy pertubation...

Hi guys,
I am trying write a code for homotopy perturbation, i have already generated the polynomial as you can see, i have also  solve for concentration equation since is not couple. But i have a lot of error massages for temperature, velocity and induced magnetic field. can some one please go through the code?

 >
 > PDEtools[declare](f(x),theta(x),u(x),w(x), prime=x):
 (1)
 >
 >

 > f(x):=sum((p^(i))*f[i](x),i=0..N);
 (2)
 >
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 >
 >
 (4)
 >
 >
 (5)
 >
 (6)
 >
 (7)
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 (8)
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 (9)
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 (10)
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 (11)
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 (12)
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 (13)
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 (14)

 >
 (15)
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 (16)

 >
 (17)

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Edge thickness of arcs in DrawGraph...

Hi everyone,

I was wondering how I could modify the thickness of edges in a graph displayed as a Maple plot through DrawGraph. The point is, the graph comprises 100 vertices and 1000 edges. By default, edge thickness is set as 2 but due to the high number of edges I would like to set edge thickness to1 or even 0. How can I do so?

Here is an example with a random graph:

with(GraphTheory) : with(RandomGraphs) : G := RandomGraph(100, 1000) : DrawGraph(G)

Thank you very much

Is this modification correct?...

This worksheet is a modification to Kitonum's excellent http://www.mapleprimes.com/posts/202222-Contour-Curves-With-Labels.

The mod adds the ability to display labelled contours for expressions in x and y defined parametrically.

Contourplot_with_labels.mw

How to improve menu speed in Maple 2016...

How to improve menu speed in Maple 2016?

I am using Maple 2016, when I right click the equation, it really takes a long time to show the menu. It seems that the CPU usage and Memory usage is low, it should be fast as it is only a showing menu action, what's wrong with that?

How can the physics in this worksheet be enhanced?...

The worksheet below rolls an ellipse along the y axis with constant energy.

How can the physics be enhanced to roll the ellipse along a non-linear curve (e.g. a sine curve) with constant energy?

EllipseRoll.mw

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