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


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.

 

 


 

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