高斯函數
Author: 藍邦偉  老師

$ O $

$ 高斯函數 $

$對任意實數\;x， [x]是不超過x的$
$最大整數，稱[x]為高斯函數.  $

$ f(x)=[x] $

$ 性質：$
$x-1<[x]≤x<[x]+1 $

$ 定義域 $
$D=\left\lbrace x∈\mathbb{R}|x∉\mathbb{Z} \right\rbrace $

$ 值域 $
$R=\left\lbrace  y∈\mathbb{Z}\right\rbrace $

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
Q_2: 0.7 * Corner[1] + 0.3 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
f_1(x) = floor(x)
List_{11} = Sequence((k, k - 1), k, -10, 10)
List_{12} = Sequence(Circle[(k + 0.01, k - 1.001), 0.05], k, -10, 10)
n = 0 (slider from 0 to 3, step 1)
k = 1 (slider from 1 to 5, step 1)
f_2(x) = floor(x / k)
text21: "$f(x)=\left [ \; \frac{x}{" + (LaTeX[k]) + "}\;\right ] $"
f_3(x) = floor(k * x)
text31: "$ f(x)=\left [\; " + (LaTeX[If[k ≠ 1, k, ""]]) + "x\; \right ]  $"
List_{21} = Sequence((k * t + k, t), t, -7, 7, 1)
List_{22} = Sequence(Circle[(k * t + k + 0.01, t - 0.0010), 0.05], t, -10, 10)
List_{31} = Sequence(((t + 1) / k, t), t, -7, 7, 1)
List_{32} = Sequence(Circle[((t + 1) / k + 0.01, t - 0.0010), 0.05], t, -10, 10)