To illustrate, here is an HTML example that overlays a circle and a letter

<span style="position: relative; font-size: 2em;">&#x25CB;<span style="position: absolute; top: 1.0em; right: 0.4em; font-size: 0.4em;">Y</span></span>

than can be pasted here to visualize.

I am not sure if that is possible with Maples typesetting tags.

Hello everyone!

I have an expression for the resonant frequency in terms of some geometric paremeter, say "x", i.e. f(x). I want to plot it together with the resonant wavelength (lambda=c/f) in the same plot. The "dualaxisplot" produces two curves (f(x), lambda(x)) with two uniform axes to the left and to the right. I am wondering is there a reasonably simple way to make it look as one curve, but with the second (e.g. lambda) axes nonuniformely scaled to fit the curve f(x)?

Many thanks in advance for your suggestions!

How do I combine a number of functions into a composite one?

For example

Combined into a final composite function
such that the function R evaluates x and y as functions themselves.

Many times this sort of function definition makes it easier for the human.

restart;

Frac_C := proc (expr, a, t, alpha) local ig, m, tau;

m := ceil(alpha);

ig := (t-tau)^(m-alpha-1)*(diff(eval(expr, t = tau), tau$m));

`assuming`([(int(ig, tau = a .. t))/GAMMA(m-alpha)], [a < t]);

end proc;
r := .5;

k := .7;

eq1 := Frac_C(x, 0, t, r)-y(t) = 0;

eq2 := Frac_C(y, 0, t, k)-x(t)-2*t = 0;

eq3 := x(0)-y(1) = 0;

eq4 := Frac_C(x, 0, t, r)-(eval(diff(y(x), x), x = 1)) = 0;

eq5 := Frac_C(x, 0, t, r)-(eval(diff(y(x), x, x), x = 1)) = 0;

eq6 := eval(diff(y(x), x), x = 0)-x(1)-2 = 0;

eq7 := y(0) = 0;

N := 5;

x[c] := [seq(a[i], i = 0 .. N)];

y[c] := [seq(b[i], i = 0 .. N)];

for n to N do

subs([seq(x(i) = x[c][i], i = 0 .. n), seq(y(i) = y[c][i], i = 0 .. n)], {eq1, eq2, eq3, eq4, eq5, eq6, eq7});
soln := solve({eq3, eq4, eq5, eq6, eq7, seq(coeff(lhs(eq), t, j) = 0, eq in {eq1, eq2})}, {a[n+1], b[n+1]});

x[c][n+1] := eval(a[n+1], soln);

y[c][n+1] := eval(b[n+1], soln);

end do;

x[s] := add(x[c][i]*t^(i-1), i = 1 .. N+1);

y[s] := add(y[c][i]*t^(i-1), i = 1 .. N+1);

x[s];

y[s];

Hi, i want to calculate fourier transform of functions with fractional powers. how can i do this? for example what is fourier transform of sqrt(x) ? I want a function or an expression as output, not the inetgral itself. thnx in advance

Download fracfourier.mw

How can I export data from the plot? Following is my Maple code.

restart;
with(PDEtools);
v_0 := 1;
vstar := 10;
r_0 := 1;
k := 0.1;
m := 0.1;
PDE := diff(v(r, t), t) = k*(diff(v(r, t), r, r) + diff(v(r, t), r)/r);
                                                / d         \
                           /  2         \   0.1 |--- v(r, t)|
          d                | d          |       \ dr        /
  PDE := --- v(r, t) = 0.1 |---- v(r, t)| + -----------------
          dt               |   2        |           r        
                           \ dr         /                    

ans := pdsolve(PDE, HINT = f(r)*g(t));
                             /                            
                             |                            
                             |                            
ans := Typesetting:-mcomplete|vApplyFunction(rt)equalsf__1
                             |                            
                             |                            
                             \                            

                                              //               
                                              ||               
                                              ||DifferentialD  
  ApplyFunction(r) f__2ApplyFunction(t) where ||-------------- 
                                              ||DifferentialDt 
                                              \\               

  f__2ApplyFunction(t)equals0.1 f__2ApplyFunction(t) _c[1]

               2                                                 
  DifferentialD                                                  
  --------------- f__1ApplyFunction(r)equals1. f__1ApplyFunction(
                2                                                
  DifferentialDr                                                 

                /DifferentialD                      \//  
             1. |-------------- f__1ApplyFunction(r)|||  
                \DifferentialDr                     /||  
  r) _c[1] - ----------------------------------------||, 
                                r                    ||  
                                                     \\  

                    /[           /                           [ /
                    |[           |                           [ |
                    |[           |                           [ |
  Typesetting:-_Hold|[PDESolStruc|v(r, t) = f__1(r) f__2(t), [< 
                    |[           |                           [ |
                    |[           |                           [ |
                    \[           \                           [ \

   d                               
  --- f__2(t) = 0.1 f__2(t) _c[1], 
   dt                              

                                       / d         \\ ]\]\\
    2                               1. |--- f__1(r)|| ]|]||
   d                                   \ dr        /| ]|]||
  ---- f__1(r) = 1. f__1(r) _c[1] - ---------------- >]|]||
     2                                     r        | ]|]||
   dr                                               | ]|]||
                                                    / ]/]//

build(ans);
                  /1         \             /           (1/2)  \
v(r, t) = c__3 exp|-- _c[1] t| c__1 BesselJ\0, (-_c[1])      r/
                  \10        /                                 

             /1         \             /           (1/2)  \
   + c__3 exp|-- _c[1] t| c__2 BesselY\0, (-_c[1])      r/
             \10        /                                 

design;
BC1 := eval(v(r, t) - v_0 = 0, r = 20);
                    BC1 := v(20, t) - 1 = 0

BC2 := D[1](v)(0, t) = 0;
                    BC2 := D[1](v)(0, t) = 0

NULL;
IC := v(r, 0) = v_0 + (vstar - v_0)*exp(-0.5*(r - r_0)^2/m^2)/(m*sqrt(2*Pi));
                                    (1/2)    /            2\
   IC := v(r, 0) = 1 + 25.38853126 2      exp\-50. (r - 1) /

conds := {BC1, BC2, IC};
              /                  
    conds := { v(20, t) - 1 = 0, 
              \                  

                                 (1/2)    /            2\  
      v(r, 0) = 1 + 25.38853126 2      exp\-50. (r - 1) /, 

                       \ 
      D[1](v)(0, t) = 0 }
                       / 

answer:=pdsolve(PDE,conds,HINT=);
Error, invalid =
Typesetting:-mambiguous(answerAssignpdsolveApplyFunction(PDEcomma

  condscommaTypesetting:-mambiguous(HINTequalslowast, 

  Typesetting:-merror("invalid =")))semi)

u := r -> v_0 + (vstar - v_0)*exp((-1)*0.5*(r - r_0)^2/m^2)/(m*sqrt(2*Pi));
u := proc (r) options operator, arrow, function_assign; 

   v_0+(vstar-v_0)*exp(-.5*(r-r_0)^2/m^2)/(m*sqrt(2*Pi)) end proc

plot(u(r), r = 0 .. 10);

conds := {BC1, BC2, IC};
              /                  
    conds := { v(20, t) - 1 = 0, 
              \                  

                                 (1/2)    /            2\  
      v(r, 0) = 1 + 25.38853126 2      exp\-50. (r - 1) /, 

                       \ 
      D[1](v)(0, t) = 0 }
                       / 

BCs := {BC1, BC2};
          BCs := {v(20, t) - 1 = 0, D[1](v)(0, t) = 0}

pde_solve = pdsolve(PDE, BCs, IC);
solution := pdsolve(PDE, conds, numeric);
                  solution := _m1440390954528

t1 = 0 .. 10;
r1 = 0 .. 10;
solution, t1, r1;
                        solution, t1, r1

sol := pdsolve(PDE, conds, numeric, time = t, range = 0 .. 20, spacestep = 0.1, timestep = 0.1);
                     sol := _m1440421519392

sol:-animate(t = 0 .. 20, frames = 100);

M := sol:-value();

sol:-plot3d(r = 0 .. 10, t = 0 .. 20);

I have give this below fit command my data is only continous data either positive or negative float data. Their never any complex number at all.

I use the below fit command

Error, complex argument to max/min

It can be observed it is running into error in C1 I dont know why can someone suggest where should I check and why is this happening kind help.   In Excel we can see the intercept coming big.

I attach the toycode to see the error I get too

toycode.mw

I want to know the exponent of one particular factor of an integer. For example:

k:=24;

ifactor(k) = (2)^3(3)

and I want to write a module to extract the exponent of (3) for any arbitrary k.

I can't select for the presence of 3 because it will pick up the factor (2)^3 and then it gets complicated to decide that I don't want this factor anyway.

If I somehow manage to select the factor (3) using "op" and scanning through each factor in turn, then substitute 3=x, it turns out that degree(%,x) doesn't work because the factor x is enclosed in brackets; similarly trying

log(%,3) fails for the same reason.

There has to be a simple way, but I just don't see it.

Any suggestions are appreciated.

In GraphTheory ,how do you make more than one edge between two points.

Could you help me to solve this problem for the parameter beta?

Download Rootsfind.mw

I put this command and It keep saying  plot(f(x), x = -0.667 .. 1.71, y = -5 .. 20, gridlines); Error, (in plot) unexpected options: [1.71 = -.667 .. 1.71, y = -5 .. 20] . How can I fix this

How can I show all the parameters in title ?

Download animate_plots.mw

Hi all,

I am quite a rookie in using Maple.

A project is going on while I need to use previous formulas and variables defined in A.mw, while I don't want to redefine everything again in my worksheet, is there any approach to inherit everything in A.mw to my current worksheet?

How would I go about creating a tetrad of a specific signature in the Differential Geometry package. The GrahmSchmidt and NullTetrad give me orthonormal and complex null tetrads. But I was wondering if there was a way to generate a tetrad of specific signature.