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How to obtain a clear plot of Zeta function....

Asked by: janhardo 700
complex zeta plotting
May 14 2024
1  7


Don't see here the FunctionAdvisor , what is included for every choosen function.

> 

 

How to obtain a clear plot of Zeta function
- via a total plot ?
- via partial plots ?
- further take circle in complex domain : complex plane ( riemann surface) , to be continued..

> 

 

> 

ComplexSurface := proc(complex_function, x_range, y_range, view_opt, orient_opt, grid_opt)
    local f, plot, combined_plot;
    
    # Define the complex function f(z)
    f := unapply(complex_function, z);
    
    # Call the FunctionAdvisor to provide plot recommendations
    FunctionAdvisor(f(z), z = x + I*y, 'view' = view_opt, 'orientation' = orient_opt, 'grid' = grid_opt);
    
    # Plot the complex surface
    plot := plot3d([evalc(Re(f(x + I*y))), evalc(Im(f(x + I*y)))], x = x_range, y = y_range, view = view_opt, orientation = orient_opt, grid = grid_opt, style = surface, title = sprintf("Plot of %a", complex_function));
    
    # Print the combined plot
    combined_plot := plot;
    #printf("Plot of the complex surface:\n");
    print(combined_plot);
    
    # Display additional messages
    printf("Procedure input:\n");
    printf("ComplexSurface(complex_function, x_range, y_range, view_opt, orient_opt, grid_opt)\n");
    printf("complex_function: The complex function to be plotted\n");
    printf("x_range: Range of the real axis\n");
    printf("y_range: Range of the imaginary axis\n");
    printf("view_opt: List of the form [x_min..x_max, y_min..y_max, z_min..z_max], determines the visible region\n");
    printf("orient_opt: List of the form [angle_x, angle_y], determines the viewing angle\n");
    printf("grid_opt: List of the form [x_grid, y_grid], determines the grid resolution\n");
    printf("\n");
    printf("Example usage:\n");
    printf("ComplexSurface(Zeta(z), -50..5, -5..5, [-50..50, -5..5, 0..15], [120, 60], [50, 50]);\n");
    printf("\n");
    printf("Where Zeta(z) is the complex function to be plotted, and the ranges, view options, orientation options, and grid options are specified accordingly.\n");
end proc:
 
> 

 

> 

ComplexSurface(Zeta(z), -50..50, -5..5, [-50..50, -5..5, 0..15], [120, 60], [50, 50]);

 

Procedure input:
ComplexSurface(complex_function, x_range, y_range, view_opt, orient_opt, grid_opt)
complex_function: The complex function to be plotted
x_range: Range of the real axis
y_range: Range of the imaginary axis
view_opt: List of the form [x_min..x_max, y_min..y_max, z_min..z_max], determines the visible region
orient_opt: List of the form [angle_x, angle_y], determines the viewing angle
grid_opt: List of the form [x_grid, y_grid], determines the grid resolution

Example usage:
ComplexSurface(Zeta(z), -50..5, -5..5, [-50..50, -5..5, 0..15], [120, 60], [50, 50]);

Where Zeta(z) is the complex function to be plotted, and the ranges, view options, orientation options, and grid options are specified accordingly.

  
> 

 

> 

ComplexSurface(ln(z), -50..50, -5..5, [-50..50, -5..5, 0..15], [120, 60], [50, 50]);

 

Procedure input:
ComplexSurface(complex_function, x_range, y_range, view_opt, orient_opt, grid_opt)
complex_function: The complex function to be plotted
x_range: Range of the real axis
y_range: Range of the imaginary axis
view_opt: List of the form [x_min..x_max, y_min..y_max, z_min..z_max], determines the visible region
orient_opt: List of the form [angle_x, angle_y], determines the viewing angle
grid_opt: List of the form [x_grid, y_grid], determines the grid resolution

Example usage:
ComplexSurface(Zeta(z), -50..5, -5..5, [-50..50, -5..5, 0..15], [120, 60], [50, 50]);

Where Zeta(z) is the complex function to be plotted, and the ranges, view options, orientation options, and grid options are specified accordingly.

  
> 

 


 

Download complex_oppervlak_zeta_functie_maple_primes.mw

File open not working on Windows system...

Asked by: C_R 3442
open gui startup
May 14 2024
1  3

This is new:

Maple 2024 frozen on opening recent files

Maple 2023 frozen on opening

Maple 2022 frozen on opening start page

Maple 2021 blinking

Maple 2020 opening start page

The above system state is constant for about 30 min. Maple sessions without start page are working. I can enter code but file opeing and saving does not work. The fact that Maple 2020 is also not working makes it unlikely that the Java environement is part of the problem.

I have several times restarted the system. The rest of the system is working.

Something happened to the system and I have no clue what is was and what I can do about it.

Any ideas or suggestions what I could try? Windows 10.

integration in if-statement...

Asked by: Dkunb 70
performance integration syntax
May 13 2024
0  3

How can I get the evaluation of integration inside if-statement?

Thanks for your help in advance,

> 

restart;
> 

#L:=1:sigma:=0.01:beta:=0.2:k0:=-100:
> 

#For Free particle
Projectile := proc({L:=1,sigma:=0.01,beta:=0.2,k0:=-100},n_max) local x0,g,c:
 x0:= beta*L;
 g := unapply(exp(-(x-x0)^2/2/sigma^2),x);
 #c := int(g(x)^2,x=-L/2..L/2,numeric=true);
 ub := (L/2-x0)/sqrt(2)/sigma;
 lb := (-L/2-x0)/sqrt(2)/sigma;
 a := Pi*sqrt(2)*sigma/L;
 b := sqrt(2)*k0*sigma;
 c := Pi*x/L;
 d := k0*x0;
 eq1 := [cos(a*n*z)*cos(b*z)/e^(z^2),cos(a*n*z)*sin(b*z)/e^(z^2),sin(a*n*z)*cos(b*z)/e^(z^2),sin(a*n*z)*sin(b*z)/e^(z^2)];
 eq1 := map(f->unapply(f,n,z),eq1);
 eq2 := [cos(n*c)*cos(d),cos(n*c)*sin(d),sin(n*c)*cos(d),sin(n*c)*sin(d)];
 eq2 := map(f->unapply(f,n,z),eq2);

 for j from 1 to n_max do:
   if (is(j,odd)) then eq11 := int(eq1[1](j,z),z=lb..ub,numeric=true);
   else 0;
   end if;
 end do:

end proc:
> 

 

Warning, (in Projectile) `ub` is implicitly declared local

  

Warning, (in Projectile) `lb` is implicitly declared local

  

Warning, (in Projectile) `a` is implicitly declared local

  

Warning, (in Projectile) `b` is implicitly declared local

  

Warning, (in Projectile) `d` is implicitly declared local

  

Warning, (in Projectile) `eq1` is implicitly declared local

  

Warning, (in Projectile) `eq2` is implicitly declared local

  

Warning, (in Projectile) `j` is implicitly declared local

  

Warning, (in Projectile) `eq11` is implicitly declared local

  
> 

Projectile(1);

int(cos(0.4442882938e-1*z)*cos(1.414213562*z)/e^(z^2), z = -49.49747467 .. 21.21320343)

 (1)
> 

 


Download SolnforProjectile_v3_3.mw

angle that does not turn on the lower arc...

Asked by: JAMET 425
geometry angle
May 13 2024
0  8

restart;
with(geometry);
with(plots);
_EnvHorizontalName := 'x';
_EnvVerticalName := 'y';
cb := color = blue;
t3 := thickness = 3;
l3 := linestyle = 3;
xA := 3;
yA := 0;
xB := -3;
yB := 0;
c := 6;
point(A, xA, yA);
point(B, xB, yB);
R := 5;
alpha := arctan(3/4);
evalf(%*180/Pi);
                          36.86989765

xH := (xA + xB)/2;
yH := (yA + yB)/2;
point(H, xH, yH);
xO1 := 0;
yO1 := 4;
point(O1, xO1, yO1);
xO2 := 0;
yO2 := -4;
point(O2, xO2, yO2);
segment(sAB, A, B);
segment(sHO, H, O1);
segment(sAO, A, O1);
segment(sBO, B, O1);
                              sAB

alpha1 := arctan((yO1 - yA)/(xO1 - xA));
beta := Pi + arctan((yO1 - yB)/(xO1 - xB));
AR1 := plottools[arc]([xO1, yO1], R, alpha1 .. beta, l3);
AR2 := plottools[arc]([xO2, yO2], R, -beta .. -alpha1, l3);
N := 80;
dt := (beta - alpha1)/(N - 1);
dr := draw({O1, O2, sAB, sHO, sAO(cb), sBO(cb)});
tex := textplot([[xA, yA - 0.5, "A"], [xB, yB - 0.5, "B"], [xO1, yO1 + 0.5, "O1"], [xO2, yO2 - 0.5, "O2"], [xH, yH - 0.5, "H"]]);
M1 := seq(plottools[disk]([R*cos(dt*t + alpha1) + xO1, R*sin(dt*t + alpha1) + yO1], 0.2, color = orange), t = 0 .. N);
M2 := seq(plottools[disk]([R*cos(dt*t + Pi + alpha1) + xO2, R*sin(dt*t + Pi + alpha1) + yO2], 0.2, color = orange), t = 0 .. N);
P1 := seq(plottools[polygon]([[R*cos(dt*t + alpha1) + xO1, R*sin(dt*t + alpha1) + yO1], [xA, yA], [xB, yB]], color = aquamarine, linestyle = dash), t = 0 .. N);
P2 := seq(plottools[polygon]([[R*cos(dt*t + Pi + alpha1) + xO1, R*sin(dt*t + Pi + alpha1) + yO1], [xA, yA], [xB, yB]], color = aquamarine, linestyle = dash), t = 0 .. N);
for t to N do
    E[t] := display(dr, tex, AR1, AR2, M1[t], P1[t]);
    F[t] := display(dr, tex, AR1, AR2, M2[t], P2[t]);
end do;
display([seq(E[t], t = 1 .. N), seq(F[t], t = 1 .. N)], insequence = true, axes = none, scaling = constrained, view = [-10 .. 10, -10 .. 10]);

NULL;
angle that does not turn on the lower arc. Thank you.

strange window behavior problem...

Asked by: segfault 145
linux
May 12 2024
0  0

OS Linux

I have Maple 2022 open with a worksheet on a specific workspace.

I then move to a different workspace and want to start a new instance of maple for a new problem.

In command line I exacute

$]xmaple22 –standalone  filename.mw

Unfortunately when the new instance is started, the open maple instance on the first workspace is moved automatically to the second workspace together with the new instance opened, completely messing up the organization.

This is not expected behavior.

How can I make Maple execute absolutely independent instances of xmaple22 without indiscressionately and automatically moving existing open maple instances to the current workspace.

Severely annoying. Maple 9.5 e.g. does not have this behavior at all so Maple 2022 is a step backwards in this regard.

Thanks

Matrix, exponents and sum...

Asked by: Dr. Anthony Queen 10
May 12 2024
2  8

I learnt that MapleFlow (MF) was a product similar (and better) than MathCad (MC). I have a old copy of MC, v.11 (with Maple symbolic engine) and I compared it with MF from my engineering dep. 

Can one kindly explain why Sum of a simple Matrix does not work, if the index is placed as exponent? Here what I did:

ReScaliing a projective vector...

Asked by: Ronan 1341
gcd frontend
May 09 2024
0  1

I want to rescale a projective vector. Have been using gcd on the numerators and denominators. This works in simple situations. It doesn;t work well here, admitadely the points have been just made up for the question.  Square roots seem to make it mal-preform. I run into a lot of squate roots in symbolic situations. What would be a better way? I have been wondering if frontend would help?

> 

restart
> 

Prntmsg::boolean:=true;
Normalise_Projective_Point:=1;
ReScl::boolean:=true;

true

  

1

  

true

 (1)
> 

 

> 

ProjLP:=overload([

      proc(A::Vector[row],B::Vector[row],prnt::boolean:=Prntmsg)
      description "2 projective points to create a projective line vector";
      option overload;
      local Vp ,gcdn,gcdd,vp ;
      uses LinearAlgebra;
       
      Vp:=CrossProduct(A,B)^%T;#print("2nd ",Vp);
      if ReScl then
         gcdn := gcd(gcd(numer(Vp[1]),numer(Vp[2])), numer(Vp[3]));
         gcdd := gcd(gcd(denom(Vp[1]),denom(Vp[2])), denom(Vp[3]));
         Vp:=simplify(Vp*gcdd/gcdn);
      end if;
      if Prntmsg then
         print("Line vector from two projective points. " );
      end if;
      return Vp
      end proc,



      proc(A::Vector[column],B::Vector[column],prnt::boolean:=Prntmsg)
      description "2 lines to get intersection projective point";
      option overload;
      uses LinearAlgebra;
      local  Vp;
    
      Vp:=CrossProduct(A,B)^%T;
     
     
      if Vp[3]<>0 and Normalise_Projective_Point<>0 then
           Vp:=Vp/Vp[3];
      end if;
      if Prntmsg then
           print("Meet of two Lines ");
      end if;
      return Vp
   end proc
     
]);
> 

 

proc () option overload; [proc (A::(Vector[row]), B::(Vector[row]), prnt::boolean := Prntmsg) local Vp, gcdn, gcdd, vp; option overload; description "2 projective points to create a projective line vector"; Vp := LinearAlgebra:-CrossProduct(A, B)^%T; if ReScl then gcdn := gcd(gcd(numer(Vp[1]), numer(Vp[2])), numer(Vp[3])); gcdd := gcd(gcd(denom(Vp[1]), denom(Vp[2])), denom(Vp[3])); Vp := simplify(Vp*gcdd/gcdn) end if; if Prntmsg then print("Line vector from two projective points. ") end if; return Vp end proc, proc (A::(Vector[column]), B::(Vector[column]), prnt::boolean := Prntmsg) local Vp; option overload; description "2 lines to get intersection projective point"; Vp := LinearAlgebra:-CrossProduct(A, B)^%T; if Vp[3] <> 0 and Normalise_Projective_Point <> 0 then Vp := Vp/Vp[3] end if; if Prntmsg then print("Meet of two Lines ") end if; return Vp end proc] end proc

 (2)
> 

#maplemint(ProjLP)
> 

pt1:=<a|sqrt(b^2+c^2)|1>:
pt2:=<c|sqrt(b^2+a^2)|1>:
pt3:=<f^2/sqrt(a^2+b^2)|f^2/sqrt(c^2+b^2)+sqrt(a^2+b^2)|1>:
pt4:=<b^2/sqrt(a^2+b^2)|f^2/sqrt(c^2+b^2)-sqrt(a^2+b^2)|1>:
> 

 

> 

l1:=ProjLP(pt1,pt2)

"Line vector from two projective points. "

  

Vector[column](%id = 36893490491002736020)

 (3)
> 

l2:=ProjLP(pt3,pt4)

"Line vector from two projective points. "

  

Vector[column](%id = 36893490491002712420)

 (4)
> 

l3:=ProjLP(pt1,pt4)

"Line vector from two projective points. "

  

Vector[column](%id = 36893490491064062908)

 (5)
> 

l4:=ProjLP(pt2,pt4)

"Line vector from two projective points. "

  

Vector[column](%id = 36893490491064037372)

 (6)
> 

pl1l2:=simplify(ProjLP(l1,l2))

"Meet of two Lines "

  

Vector[row](%id = 36893490491002741932)

 (7)
> 

pl2l3:=simplify(ProjLP(l2,l3))

"Meet of two Lines "

  

Vector[row](%id = 36893490491113907252)

 (8)
> 

(ProjLP(pl1l2,pl2l3));
length(%)

"Line vector from two projective points. "

  

Vector[column](%id = 36893490491113907972)

  

6223

 (9)
> 

ReScl:=false

false

 (10)
> 

# doing nothing seems to work better here than rescaling
> 

(ProjLP(pl1l2,pl2l3));
length(%)

"Line vector from two projective points. "

  

Vector[column](%id = 36893490491125667468)

  

2796

 (11)
> 

 


 

Download 2024-05-09_Q_Rescale_projective_vector.mw

Wigner J, Clebsch-Gordon...

Asked by: saeedr12 10
physics physics quantum-mechanics
May 07 2024
2  0

Hi,

is there any package out there to calculate Wigner J symbols and Clebsch-Gordon coefficients in Maple

Is this a bug or does Maple hate me? ...

Asked by: Hullzie16 333
physics
May 07 2024
1  1

I am running Maple 2023 - yes I should update - and I found a weird "bug" if you could call it that. For different versions of the Physics package I am getting different answers on the same problem. 
 

This is what I was getting when I run Version 1410:

> 

restart;
> 

with(Physics):

 

> 

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 1744. The version installed in this computer is 1410 created 2023, March 11, 12:59 hours Pacific Time, found in the directory /Users/b2hull/maple/toolbox/2023/Physics Updates/lib/`

 (1)
> 

Setup(mathematicalnotation=true):
> 

g_[arbitrary]:

_______________________________________________________

  

`Systems of spacetime coordinates are:`*{X = (x1, x2, x3, x4)}

  

`Default differentiation variables for d_, D_ and dAlembertian are:`*{X = (x1, x2, x3, x4)}

  

`Setting `*lowercaselatin_is*` letters to represent `*space*` indices`

  

`The arbitrary metric in coordinates `*[x1, x2, x3, x4]

  

`Signature: `(`- - - +`)

  

_______________________________________________________

 (2)
> 

LG :=(g_[~mu,~nu]*Ricci[mu,nu])*sqrt(-%g_[determinant]);

Physics:-g_[`~mu`, `~nu`]*Physics:-Ricci[mu, nu]*(-%g_[determinant])^(1/2)

 (3)
> 

SG:=Intc(LG,X)

Int(Int(Int(Int(Physics:-g_[`~mu`, `~nu`]*Physics:-Ricci[mu, nu]*(-%g_[determinant])^(1/2), x1 = -infinity .. infinity), x2 = -infinity .. infinity), x3 = -infinity .. infinity), x4 = -infinity .. infinity)

 (4)
> 

EQ:=Fundiff(SG,%g_[~delta,~gamma])/sqrt(-%g_[determinant])

((1/2)*%g_[`~mu`, `~nu`]*Physics:-Ricci[mu, nu]*%g_[delta, gamma]*%g_[determinant]/(-%g_[determinant])^(1/2)+Physics:-Ricci[mu, nu]*(-%g_[determinant])^(1/2)*%g_[delta, `~mu`]*%g_[gamma, `~nu`])/(-%g_[determinant])^(1/2)

 (5)
> 

Simplify(subs(%g_=g_,EQ))

-(1/2)*Physics:-g_[delta, gamma]*Physics:-Ricci[nu, `~nu`]+Physics:-Ricci[delta, gamma]

 (6)
> 

 

> 

 

 

And this is what I get if I used the latet update for 2023, Version 1683:

> 

restart;
> 

with(Physics):
> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1744. The version installed in this computer is 1683 created 2024, March 6, 17:43 hours Pacific Time, found in the directory /Users/b2hull/maple/toolbox/2023/Physics Updates/lib/`

 (1)
> 

Setup(mathematicalnotation=true):
> 

g_[arbitrary]:

_______________________________________________________

  

`Systems of spacetime coordinates are:`*{X = (x1, x2, x3, x4)}

  

`Default differentiation variables for d_, D_ and dAlembertian are:`*{X = (x1, x2, x3, x4)}

  

`Setting `*lowercaselatin_is*` letters to represent `*space*` indices`

  

`The arbitrary metric in coordinates `*[x1, x2, x3, x4]

  

`Signature: `(`- - - +`)

  

_______________________________________________________

 (2)
> 

LG :=(g_[~mu,~nu]*Ricci[mu,nu])*sqrt(-%g_[determinant]);

Physics:-g_[`~mu`, `~nu`]*Physics:-Ricci[mu, nu]*(-%g_[determinant])^(1/2)

 (3)
> 

SG:=Intc(LG,X)

Int(Int(Int(Int(Physics:-g_[`~mu`, `~nu`]*Physics:-Ricci[mu, nu]*(-%g_[determinant])^(1/2), x1 = -infinity .. infinity), x2 = -infinity .. infinity), x3 = -infinity .. infinity), x4 = -infinity .. infinity)

 (4)
> 

EQ:=Fundiff(SG,%g_[~delta,~gamma])/sqrt(-%g_[determinant])

-(1/2)*%g_[delta, gamma]*Physics:-g_[`~mu`, `~nu`]*Physics:-Ricci[mu, nu]

 (5)
> 

Simplify(subs(%g_=g_,EQ))

-(1/2)*Physics:-g_[delta, gamma]*Physics:-Ricci[nu, `~nu`]

 (6)
> 

 

 

Strange right? I bring this up because it makes me wonder about potential errors in other computations...

The answer - equation 6 - in 1410 is the correct answer. This is simply a derivation of the Einstein Tensor. 

Union and indexed sets...

Asked by: Johan Bertilsdotter 15
May 06 2024
1  1

Or some other type of calculation in indexed set. I tried the maple android app with no luck. How is done in maple?

why do i have a problem?...

Asked by: miguelbravo 70
windows deep-learning
May 06 2024
0  0

I`m trying execute the example of Deeplearnig:

with(DeepLearning);
v1 := Vector(8, i -> i, datatype = float[8]);
v2 := Vector(8, [-1.0, 1.0, 5.0, 11.0, 19.0, 29.0, 41.0, 55.0], datatype = float[8]);
model := Sequential([DenseLayer(1, inputshape = [1])]);
model := Vector(2, {(1) = Typesetting:-mi("`DeepLearning 

   Model`"), (2) = Typesetting:-mi("`<keras.engine.sequential.Se\

  quential object at 0x000001C5B6520700>`")})


model:-Compile(optimizer = "sgd", loss = "mean_squared_error");
model:-Fit(v1, v2, epochs = 500);
"<Python object: <keras.callbacks.History object at 0x000001C5CC\

  EE9DE0>>"


convert("<Python object: <keras.callbacks.History object at 0x000001C5CCEE9DE0>>", 'symbol');
<Python object: <keras.callbacks.History object at 0x000001C5CCE\

  E9DE0>>


model:-Predict([10]);

 

But, finally, there is this error:

Error, (in Predict) AttributeError: 'CatchOutErr' object has no attribute 'flush'

['Traceback (most recent call last):\n', '  File "C:\\Program Files\\Maple 2023\\Python.X86_64_WINDOWS\\lib\\site-packages\\keras\\utils\\traceback_utils.py", line 70, in error_handler\n    raise e.with_traceback(filtered_tb) from None\n', '  File "C:\\Program Files\\Maple 2023\\Python.X86_64_WINDOWS\\lib\\site-packages\\keras\\utils\\io_utils.py", line 80, in print_msg\n    sys.stdout.flush()\n', "AttributeError: 'CatchOutErr' object has no attribute 'flush'\n"]

What`s is happening?

Thanks!

Evaluate the limitwithout using hopital rule or ta...

Asked by: yangtheary 290
limit
May 05 2024
0  1

Line integral input ?...

Asked by: janhardo 700
calculus integration line-integral
May 04 2024
0  11

Can this be better done in Maple ? , see worksheet.

Display numbers in the contour plot...

Asked by: moh111 20
contourplot plotting
April 26 2024
1  4

How can numbers be displayed inside the contour plot?

 restart;
with(plots);
contourplot(x*exp(-x^2 - y^2), x = -2 .. 2, y = -2 .. 2, axes = boxed);
like this

Unexpected results from GraphTheory:-WienerIndex? ...

Asked by: sursumCorda 1254
graphtheory shortest-distance
April 26 2024
3  3

OEIS A034828 and OEIS A000292 (which give the Wiener index for the cycle graph and the path graph respectively) mention that 

the Wiener index of the cycle of length 19 is 855 and 
the Wiener index of the path with 19 edges is 1330. 

However, 

GraphTheory:-WienerIndex(GraphTheory:-CycleGraph(19));
 = 
                               38

GraphTheory:-WienerIndex(GraphTheory:-PathGraph(20));
 = 
                               38

So what happened here? 

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