Testing stuff to be moved later

Author: scheinerman

development/points2line.jl

@@ -0,0 +1,50 @@
+using LinearAlgebraX
+
+"""
+    points2line(x1::Union{Rational,Integer}, y1::Union{Rational,Integer}, x2::Union{Rational,Integer}, y2::Union{Rational,Integer})
+
+Given points `x1,y1` and `x2,y2` return `a,b,c` such that both points satisfy `a*x + b*y = c`.
+"""
+function points2line(
+    x1::Union{Rational,Integer},
+    y1::Union{Rational,Integer},
+    x2::Union{Rational,Integer},
+    y2::Union{Rational,Integer},
+)
+    M = [x1 y1 1; x2 y2 1]
+    abc = collect(nullspacex(M))
+    dlist = denominator.(abc)
+    d = lcm(dlist...)
+    abc *= d
+    if abc[1] < 0
+        abc *= -1
+    end
+    abc[3] *= -1
+
+    a, b, c = Int.(abc)
+
+    return a, b, c
+end
+
+function points2line(z1, z2)
+    x1, y1 = reim(z1)
+    x2, y2 = reim(z2)
+    return points2line(x1, y1, x2, y2)
+end
+
+"""
+    points2inequality(z1, z2, w)
+
+Print an inequality for the halfspace bounded by the line through
+`z1` and `z2` that contains `w`.
+"""
+function points2inequality(z1, z2, w)
+    a, b, c = points2line(z1, z2)
+
+    x, y = reim(w)
+
+    if a*x + b*y < c
+        a, b, c = -a, -b, -c
+    end
+    println("$a*x + $b*y ≥ $c")
+end

development/polygon_example.jl

@@ -0,0 +1,62 @@
+include("points2line.jl")
+using SimpleDrawing, SimpleDrawingObjects, Clines, SimplexTableaux
+
+function my_points()
+    [1+im, 5+2im, 6+3im, 5+5im, 3+5im, 2+4im]
+end
+
+function make_lines(plist)
+    newdraw()
+    w = 3 + 3im
+
+    P = FilledPolygon(plist)
+    set_fillcolor!(P, "lightgray")
+    draw(P)
+
+    draw_xaxis(8)
+    draw_xaxis(-1)
+    draw_xtick(1:7)
+
+    draw_yaxis(7)
+    draw_yaxis(-1)
+    draw_ytick(1:6)
+
+    np = length(plist)
+    for i in 1:(np - 1)
+        points2line(plist[i], plist[i + 1])
+        points2inequality(plist[i], plist[i + 1], w)
+    end
+    points2line(plist[1], plist[end])
+    points2inequality(plist[1], plist[end], w)
+
+    for p in plist
+        P = Point(p)
+        set_pointsize!(P, 3)
+        draw(P)
+    end
+
+    L = Line(0, 10, 10, 0)
+    draw(L)
+    L = Line(2, 0, 0, 2)
+    draw(L)
+
+    finish()
+    #    np = length(plist)
+
+end
+
+make_lines() = make_lines(my_points())
+
+function make_hex_Abc()
+    A = [-1 4; -1 1; -2 -1; 0 -1; 1 -1; 3 -1]
+    b = [3, -3, -15, -5, -2, 2]
+    c = [1; 1]
+    return A, b, c
+end
+
+function make_hex_tableau()
+    B = [1, 2, 3, 4, 7, 8]
+    T = Tableau(make_hex_Abc()...)
+    set_basis!(T, B)
+    return T
+end