First day: Intro to linear equations.sagews

%typeset_mode True
# Declare some usual variables
var('x,y,z')
color = rainbow(5)

($\displaystyle x$, $\displaystyle y$, $\displaystyle z$)

# Plot a first plane, x+y+z = 1
f = x+y+z-1
L = implicit_plot3d(f==0, [x,-2,2], [y,-2, 2], [z,-2,2],color=color[0],opacity=.9)
show(L,viewer='threejs')

3D rendering not yet implemented

# Plot a second plane, x-y-2z = 0
g = x-y-2*z
V = implicit_plot3d(g==0, [x,-2,2], [y,-2,2], [z,-2,2],color=color[1])
show(L+V)

3D rendering not yet implemented

# Show the intersection of the two planes
#  AKA: The solution of the linear system!
sol = solve([f,g],[x,y,z])
F = parametric_plot3d([1/2*z+1/2, -3/2*z+1/2, z], [-2, 2], thickness=3, color="black")
show(L+V+F)
show(F)

3D rendering not yet implemented

3D rendering not yet implemented

# Plot another plane, x-y+z = 0
h = x-y+z
W = implicit_plot3d(h, [x,-2,2], [y,-2,2], [z,-2,2], color=color[2])
show(L+V+W)

3D rendering not yet implemented

# Solution is... a point!
_=solve([f,g,h],[x,y,z])
F = sphere(center=[1/2, 1/2, 0], size=.1, color="black")
show(L+V+W+F)

3D rendering not yet implemented

# What if we add yet another plane?
k = -x+2*y-z+1
R = implicit_plot3d(k, [x,-2,2], [y,-2,2], [z,-2,2], color=color[3])
show(L+V+W+R)

3D rendering not yet implemented

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