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# Example of Graphics

## Real function

### in real domain

Input your function, click the re button. e.g.
1. re(pow(x,x))
First graph is real function, second graph is complex function, where blue line is real part re(z) and red line is imag part im(z) by convert to complex with tocomplex(x)
2. re2D(pow(x,x))

### in imag domain

Input your function, click the im button. e.g.
3. im(pow(x,x))
First graph is real function, second graph is complex function, where blue line is real part re(z) and red line is imag part im(z) by convert to complex with tocomplex(x)
4. im2D(pow(2,x))
More in complex2D 2 curves of real and imag parts

### in Laplace domain

First graph is in real domain, second graph is in Laplace domain by Lapalce transform laplace(x)
Input your function, click the laplace button. e.g.
5. laplace(sin(x))

### in Fourier domain

First graph is in real domain, second graph is in Fourier domain by Fourier transform fourier(x)
Input your function, click the Fourier button. e.g.
6. fourier(exp(x))
7. sine wave
8. Weierstrass function animation

### in convolution domain

First graph is in real domain, second graph is in convolution domain by convolution transform convolute(x) with x
Input your function, click the convolute button. e.g.
9. convolute(exp(x))

### in contour domain

put your function f(x,y) into sin(f(x,y)) by contour transform sin(z). First graph is in real domain, second graph is in contour domain.
Input your function, click the plot button. e.g.
10. sin(x*x+y*y-1)
Input your function, click the plot2D button. e.g.
11. plot2D( sin(x*x+y*y-1) )

### in polar domain

Input equation r=x, click the plot button. e.g.
12. r=x
Input your function, click the polar button. e.g.
13. polarplot(x)
Input equation x=cos(t),y=sin(t), click the plot button. e.g.
14. x=cos(t),y=sin(t)
by parametric( ) button
15. parametricplot(cos(t),sin(t))
by parametric2D( ) button
16. parametric2D(cos(t),sin(t))
by parametric3D( ) button
17. parametric3D(cos(t),sin(t))

### in 3D polar domain

by parametric3D, e.g.
18. parametric3D(x)
19. parametric3D(cos(t),sin(t),t)
by wireframe3D. e.g.
20. wireframe3D(x)
21. wireframe3D(cos(x),sin(x),x)

More is in graph.

## Complex function

### in WebXR domain

22. color WebXR surface of complex function on complex plane

### in complex domain

Input your function, click the complex button. e.g.
23. complexplot(z)
Input your function, click the complex button. e.g.
24. plotcomplex(z)
Input your function, click the complex3D button. e.g.
25. complex3D(pow(x,x))

More in complex function

## Complex

1. complex - complex function - complex math
2. complex animate(z) or complex2D(x) for phase animation in complex plane, the independent variable must be z.
3. complex plot(z) for phase and/or modulus in complex plane, the independent variable must be z.
4. plot complex(z) for phase and/or modulus in complex plane, the independent variable must be z.
5. complex2D show re2D(x) and im2D(x) for complex 2 curves of real and imag parts in real and imag domain, the independent variable must be x.
6. complex3D(x) for 3 dimensional graph, the independent variable must be x.
7. color WebXR surface of complex function on complex plane
8. Riemann surface - Complex Branches - complex coloring

## References

1. math handbook content 2 chapter 10 complex function
2. math handbook content 3 chapter 10 complex function
3. math handbook content 4 chapter 10 complex function
4. Complex analysis
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