Hi,

I'm trying to plot a 3 dimensional vector equation of motion in Maple for my dissertation. The equation is as follows:

vec(v_r) = (v_b)*i + (v_g*cos(Omega*t))*j + (v_g*sin(Omega*t))*k

where Omega is the gyrofrequency, v_b is the velocity parallel with the i direction, and v_g is the perpendicular velocity of gyration. v_g and v_b are both in terms of the velocity of incidence and two angles, which are all just numerical values that I've introduced.

It should look like a helix spiralling around the i axis, but I'm fairly new to Maple and I've tried everything I can think of and I can't get it to work.

When I use plot3d it turns out looking like a sphere or a cylinder. When I use spacecurve, it doesn't work at all and I get the error message " Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct.".

Any help is greatly appreciated.

I have an ODE. I solved it numerically by Runge Kutta method.

The solution is X(t).

Now, I want to multiply X(t) by sin(y) and to plot in 3D.

How can we do it? 

question.mw

I am trying to find the number a and b (-20 < a < 20, -20 < b <20) so that two circles (x+1)^2+(y+3)^2 = 125 and (x-a)^2+(y-b)^2 = 225 cut at two points A and B and coordinates A and B are pairs of integers.
I tried
 

restart; L := []; 
for a from -20 to 20 do 
for b from -20 to 20 do 
for x from -20 to 20 do 
for y from -20 to 20 do 
if (x+1)^2+(y+3)^2 = 125 and (x-a)^2+(y-b)^2 = 225 and nops({a, b, x, y}) = 4 and x*y*a*b <> 0 then 
L := {op(L), {[a, b], [x, y]}} 
od: od: od: od:
nops(L); 
L

How to select the number a and b so that the system of equations (x+1)^2+(y+3)^2 = 125  and (x-a)^2+(y-b)^2 = 225 have two integral solutions. For example
 

restart; 
solve({(x-6)^2+(y+2)^2 = 225, (x+1)^2+(y+3)^2 = 125}, {x, y})

restart;

Digits := 32;

t0 := 1;

eq := 1-w*v^2-2*v*exp(-t/v);

equ := eval(eq, v = -t/ln(u));

us := solve(eval(equ, t = t0), u);

vs := -t0/ln(us);

plot(Re(vs), w = 0 .. 10, view = 0 .. 1)

I want to plot the solution of this equation, but it doesn't quite work. I tried to transform it, because I thought the singularity in the denominator of the exponential causes the issues.

any suggestions?

Dear all.

Trying to plot the function below:

         epsilon                                            
    f := ------- = 0.78417289325174246201875653872811303 + (
          2 Pi                                              
    -24.020590879328464004990474127244023 + Y 

      (671.68643760557259657756434855357346 + (
    -314.15926532756339731350799859659950 Y

       - 48.382487297515945228479754993851165)^2))^(1/2)

want the (x-axis) be epsilon/(2*Pi) and the y-axis is Y
implicitplot(f,epsilon=0..100,Y=0..10,numpoints=1000,axes=boxed,thickness=2,color=black,font=[1,1,20],tickmarks=[3, 3],linestyle=1);

many thanks in advanced.

example1 := (x -> (2 + 3));
example2 := (x -> int(1, y));

When I execute these, Maple evaluates the "2 + 3" into 5, but it does not evaluate the "int(1, y)" into "y". Why does it evaluate the former but not the latter?

Also, how can I modifiy example 2 so that it evaluates the "int(1, y)" and returns "x -> y"?

I try to plot this matrix as shown below and I keep getting this error. First how do I simplify these units? Secondly how do I plot this because it seems like it doesn't let plot with units.

Using allvalues (twice) I can uncover the three roots of this expression: 1 real, 2 complex. But fsolve gives me just one real and 1 complex. Interestingly the free version of Woldframalpha.com gives the same single complex root.

Is there any way of coercing fsolve to give both?

Many thanks for any advice

Fsolve5.mw
 

Download Fsolve5.mw

What is the simplest method for adding a color bar for plottings? (a scale that shows the correspondence 
between numbers and colors)

and could you interpret the graphics and the color bar?  I need your valuable comments.

I use Maple 2018.

For example;  

question.mw

I mean

Hello Everyone,

First of all I want to thank you to pay attention to my post.

For some reasons I want to know when does the root of my solution is equal to 0 isolating α, which yields the following equation
 

When I substitute 1/2 it verifies the equation, but when I substitute other solutions my equation is not verified. For instance substituting "α=-1/l" I get something different from 0 as you can see

This code used to work OK in an earlier version of Maple 2018. I do not know what changed and if it some change in Physics package that caused it.

restart;
pde:=diff(u(r,theta),r$2)+1/r*diff(u(r,theta),r)+1/r^2*diff(u(r,theta),theta$2)=0;
bc:=u(r,0)=0,u(r,Pi)=0,u(0,theta)=0,u(1,theta)=f(theta);
sol:=pdsolve([pde,bc],u(r,theta),HINT = boundedseries(r = 0));

Now it gives the error 

Error, (in assuming) when calling 'assume'. Received: 'invalid arguments'

Workaround is to remove the HINT above. So the following now works

restart;
pde:=diff(u(r,theta),r$2)+1/r*diff(u(r,theta),r)+1/r^2*diff(u(r,theta),theta$2)=0;
bc:=u(r,0)=0,u(r,Pi)=0,u(0,theta)=0,u(1,theta)=f(theta);
sol:=pdsolve([pde,bc],u(r,theta));

Should this error message show up when using the HINT option?

Maple 2018.2 with Physics package cloud version 205.

Here is screen shot showing it was working in Physics 170

How can I calculate the Euler-Lagrange equation from the Lagrangian density from Gauged Baby Skyrme model in maple using the physics package? Here, the rules of the operation in the inner space are the same that of the vectors conventional: dot and cross products, etc...
Following below the Lagrangian density.

Errata:

Hello everyone!
Can you help me with my problem?
How can I automatically paste parts of denominator from one equations to another? Now I must do this manualy. Example of my problem is in file2.

File_2.mw

Hello! 

I have system of equations to solve. It has 118 equations and all variables have to be binary. I know for that system that the minial number for x=1 is 32 (I cheked it in solution chapter at the end of the book) but I always get 33 of ones. I changed MaxSols=500 and still got 33. If I change MaxSols to some bigger number the time for calculation is larger and I still don't get the correct solution. Is there any faster way to do this?

I'm thinking (but I don't know how to do in Maple): Is there any way to show solutions only with number of ones in interval, for example 30 to 33.

try1.mw

I have a question about Hilbert Series of the quotient of an algebra by a non-homogenous ideal. 

In maple help: https://www.maplesoft.com/support/help/maple/view.aspx?path=Groebner%2FHilbertSeries, it is said that 

The algorithms for HilbertSeries and HilbertPolynomial use the leading monomials of a total degree Groebner basis for J. Here J is an ideal.

I checked the following example. Let 

J:= [(x[2]-x[1])*(x[2]-x[3]), (x[4]-x[1])*(-x[5]+x[4]), (x[4]-x[2])*(x[4]-x[6]), (-x[3]+x[5])*(x[5]-x[6]), x[1]^3-1, x[2]^3-1, x[3]^3-1, x[4]^3-1, x[5]^3-1, x[6]^3-1];

and

t1:=map(LeadingMonomial, l, grlex(x[1], x[2], x[3], x[4], x[5], x[6], x[7], x[8], x[9], x[10], x[11], x[12]));

Then t1 is the ideal generated by the following monomials.
t1 := [x[1]*x[2], x[1]*x[4], x[2]*x[4], x[3]*x[5], x[1]^3, x[2]^3, x[3]^3, x[4]^3, x[5]^3, x[6]^3]

Using the commands:

l2:={x[1],x[2],x[3],x[4],x[5],x[6],x[7],x[8],x[9],x[10],x[11],x[12]};

factor(HilbertSeries(J, l2, t));

factor(HilbertSeries(t1, l2, t));

We obtain Hilbert(J,t)=(t^2+t+1)*(5*t^4+11*t^3+11*t^2+5*t+1)
Hilbert(t1, t) = (t^2+t+1)*(3*t^2+3*t+1)*(2*t^2+2*t+1)

These two polynomials are not equal. How does maple compute Hilbert Series for the quotient of an algebra by a non-homogenous ideal? Thank you very much.