MinimalDemo2014.mw

> restart; 1; with(plots); -1
 

>
 

> implicitplot3d(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2)), `*`(`^`(z, 2))) = 1, x = -2 .. 2, y = -2 .. 2, z = -2 .. 2); 1
 

Plot_2d
 

>
 

> plot3d([`+`(`/`(`*`(2, `*`(s)), `*`(`+`(`*`(`^`(s, 2)), `*`(`^`(t, 2)), 1)))), `+`(`/`(`*`(2, `*`(t)), `*`(`+`(`*`(`^`(s, 2)), `*`(`^`(t, 2)), 1)))), `/`(`*`(`+`(`-`(`*`(`^`(s, 2))), `-`(`*`(`^`(t, 2)...
 

Plot_2d
 

>
 

> plot3d(sqrt(`+`(`-`(`*`(`^`(x, 2))), `-`(`*`(`^`(y, 2))), 1)), x = -2 .. 2, y = -2 .. 2, scaling = constrained); 1
 

Plot_2d
 

>
 

> DE := `+`(`*`(`+`(1, `*`(`^`(diff(f(x, y), y), 2))), `*`(diff(f(x, y), x, x))), `-`(`*`(2, `*`(diff(f(x, y), x), `*`(diff(f(x, y), y), `*`(diff(f(x, y), x, y)))))), `*`(`+`(1, `*`(`^`(diff(f(x, y), x)...
DE := `+`(`*`(`+`(1, `*`(`^`(diff(f(x, y), y), 2))), `*`(diff(f(x, y), x, x))), `-`(`*`(2, `*`(diff(f(x, y), x), `*`(diff(f(x, y), y), `*`(diff(f(x, y), x, y)))))), `*`(`+`(1, `*`(`^`(diff(f(x, y), x)...
 

`+`(`*`(`+`(1, `*`(`^`(diff(f(x, y), y), 2))), `*`(diff(diff(f(x, y), x), x))), `-`(`*`(2, `*`(diff(f(x, y), x), `*`(diff(f(x, y), y), `*`(diff(diff(f(x, y), x), y)))))), `*`(`+`(1, `*`(`^`(diff(f(x, ... (1)
 

>
 

> eval(DE, f(x, y) = `+`(`*`(3, `*`(x)), `*`(4, `*`(y)))); 1
 

0 (2)
 

> eval(DE, f(x, y) = arctan(`/`(`*`(y), `*`(x)))); 1
 

`+`(`*`(`+`(1, `/`(1, `*`(`^`(x, 2), `*`(`^`(`+`(1, `/`(`*`(`^`(y, 2)), `*`(`^`(x, 2)))), 2))))), `*`(`+`(`/`(`*`(2, `*`(y)), `*`(`^`(x, 3), `*`(`+`(1, `/`(`*`(`^`(y, 2)), `*`(`^`(x, 2))))))), `-`(`/`... (3)
 

> simplify(%); 1
 

0 (4)
 

> plot3d(arctan(`/`(`*`(y), `*`(x))), x = 0 .. 1, y = -1 .. 1); 1
 

Plot_2d
 

> implicitplot3d(`*`(x, `*`(tan(z))) = y, x = -1 .. 1, z = -1.5 .. 1.5, y = -1 .. 1, numpoints = 4000); 1
 

Plot_2d
 

> CAT := arccosh(sqrt(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2))))); 1
 

arccosh(`*`(`^`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2))), `/`(1, 2)))) (5)
 

> eval(DE, f(x, y) = CAT); 1
 

`+`(`*`(`+`(1, `/`(`*`(`^`(y, 2)), `*`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2))), `*`(`+`(`*`(`^`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2))), `/`(1, 2))), `-`(1)), `*`(`+`(`*`(`^`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2)...
`+`(`*`(`+`(1, `/`(`*`(`^`(y, 2)), `*`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2))), `*`(`+`(`*`(`^`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2))), `/`(1, 2))), `-`(1)), `*`(`+`(`*`(`^`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2)...
`+`(`*`(`+`(1, `/`(`*`(`^`(y, 2)), `*`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2))), `*`(`+`(`*`(`^`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2))), `/`(1, 2))), `-`(1)), `*`(`+`(`*`(`^`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2)...
`+`(`*`(`+`(1, `/`(`*`(`^`(y, 2)), `*`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2))), `*`(`+`(`*`(`^`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2))), `/`(1, 2))), `-`(1)), `*`(`+`(`*`(`^`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2)...
`+`(`*`(`+`(1, `/`(`*`(`^`(y, 2)), `*`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2))), `*`(`+`(`*`(`^`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2))), `/`(1, 2))), `-`(1)), `*`(`+`(`*`(`^`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2)...
`+`(`*`(`+`(1, `/`(`*`(`^`(y, 2)), `*`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2))), `*`(`+`(`*`(`^`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2))), `/`(1, 2))), `-`(1)), `*`(`+`(`*`(`^`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2)...		 (6)
 

> simplify(%); 1
 

0 (7)
 

> plot3d(CAT, x = -3 .. 3, y = -3 .. 3); 1
 

Plot_2d
 

> SCHERK := ln(`/`(`*`(cos(y)), `*`(cos(x)))); 1
 

ln(`/`(`*`(cos(y)), `*`(cos(x)))) (8)
 

> eval(DE, f(x, y) = SCHERK); 1
 

`+`(`*`(`+`(1, `/`(`*`(`^`(sin(y), 2)), `*`(`^`(cos(y), 2)))), `*`(`+`(`/`(`*`(`^`(sin(x), 2)), `*`(`^`(cos(x), 2))), 1))), `*`(`+`(`/`(`*`(`^`(sin(x), 2)), `*`(`^`(cos(x), 2))), 1), `*`(`+`(`-`(1), `... (9)
 

> simplify(%); 1
 

0 (10)
 

> plot3d(SCHERK, x = -1 .. 1., y = `+`(`-`(`*`(`/`(1, 2), `*`(Pi)))) .. `+`(`*`(`/`(1, 2), `*`(Pi)))); 1
 

Plot_2d