F17.mw

> with(plots); -1
 

> plot3d(0, x = `+`(`-`(sqrt(2))) .. sqrt(2), y = 0 .. `+`(2, `-`(`*`(`^`(x, 2)))), axes = framed, color = red); -1
 

> plot3d(`+`(4, `-`(`*`(`^`(y, 2)))), x = `+`(`-`(sqrt(2))) .. sqrt(2), y = 0 .. `+`(2, `-`(`*`(`^`(x, 2)))), color = blue); -1
 

> implicitplot3d(y = 0, x = `+`(`-`(sqrt(2))) .. sqrt(2), y = -1 .. 1, z = 0 .. 4, color = green); -1
 

> display(%, `%%`, `%%%`)
 

Plot
 

>
 

> int(int(int(1, z = 0 .. `+`(4, `-`(`*`(`^`(y, 2))))), y = 0 .. `+`(2, `-`(`*`(`^`(x, 2))))), x = `+`(`-`(sqrt(2))) .. sqrt(2))
 

`+`(`*`(`/`(288, 35), `*`(`^`(2, `/`(1, 2))))) (1)
 

> int(int(int(1, x = `+`(`-`(sqrt(`+`(2, `-`(y))))) .. sqrt(`+`(2, `-`(y)))), z = 0 .. `+`(4, `-`(`*`(`^`(y, 2))))), y = 0 .. 2)
 

`+`(`*`(`/`(288, 35), `*`(`^`(2, `/`(1, 2))))) (2)
 

>
 

Plot i cylinderkoordinater: 

> plot3d(r(theta, z), theta = a .. b, z = c .. d, coords = cylindrical)
 

>
 

> plot3d(z, theta = 0 .. `+`(`*`(2, `*`(Pi))), z = 0 .. sqrt(`/`(1, 2)), coords = cylindrical, scaling = constrained); -1
 

> plot3d(sqrt(`+`(1, `-`(`*`(`^`(z, 2))))), theta = 0 .. `+`(`*`(2, `*`(Pi))), z = sqrt(`/`(1, 2)) .. 1, coords = cylindrical); -1
 

> display(%, `%%`)
 

Plot
 

> int(int(int(r, z = r .. sqrt(`+`(1, `-`(`*`(`^`(r, 2)))))), r = 0 .. sqrt(`/`(1, 2))), theta = 0 .. `+`(`*`(2, `*`(Pi))))
 

`+`(`*`(`/`(1, 4), `*`(`^`(2, `/`(1, 2)), `*`(`^`(Pi, `/`(3, 2)), `*`(`+`(`/`(`*`(`/`(4, 3), `*`(`^`(2, `/`(1, 2)))), `*`(`^`(Pi, `/`(1, 2)))), `-`(`/`(`*`(`/`(2, 3)), `*`(`^`(Pi, `/`(1, 2)))))))))), ... (3)
 

> simplify(%)
 

`+`(`*`(`/`(1, 3), `*`(`^`(2, `/`(1, 2)), `*`(Pi, `*`(`+`(`*`(`^`(2, `/`(1, 2))), `-`(1))))))) (4)
 

>
 

Plot i sfæriske koordinater: 

> plot3d(rho(theta, phi), theta = a .. b, phi = c .. d, coords = spherical)
 

>
 

> plot3d(1, theta = 0 .. `+`(`*`(2, `*`(Pi))), phi = 0 .. `+`(`*`(`/`(1, 4), `*`(Pi))), coords = spherical, scaling = constrained); -1
 

> implicitplot3d(phi = `+`(`*`(`/`(1, 4), `*`(Pi))), rho = 0 .. 1, theta = 0 .. `+`(`*`(2, `*`(Pi))), phi = 0 .. `+`(`*`(`/`(1, 2), `*`(Pi))), coords = spherical); -1
 

> display(%, `%%`)
 

Plot
 

> int(int(int(`*`(`^`(rho, 2), `*`(sin(phi))), rho = 0 .. 1), phi = 0 .. `+`(`*`(`/`(1, 4), `*`(Pi)))), theta = 0 .. `+`(`*`(2, `*`(Pi))))
 

`+`(`*`(`/`(2, 3), `*`(Pi)), `-`(`*`(`/`(1, 3), `*`(`^`(2, `/`(1, 2)), `*`(Pi))))) (5)
 

>
 

> `:=`(f, proc (x, y) options operator, arrow; `+`(`*`(`^`(x, 2), `*`(y)), `-`(`*`(4, `*`(x, `*`(y)))), `*`(2, `*`(x, `*`(`^`(y, 2))))) end proc)
 

proc (x, y) options operator, arrow; `+`(`*`(`^`(x, 2), `*`(y)), `-`(`*`(4, `*`(x, `*`(y)))), `*`(2, `*`(x, `*`(`^`(y, 2))))) end proc (6)
 

> plot3d(f(x, y), x = 0 .. 4, y = 0 .. `+`(2, `-`(`*`(`/`(1, 2), `*`(x)))))
 

Plot
 

> f(`/`(4, 3), `/`(2, 3))
 

-`/`(32, 27) (7)
 

>