Data update

Task/Pascal-matrix-generation/Pluto/pascal-matrix-generation.pluto

@@ -0,0 +1,32 @@
+require "matrix"
+local int = require "int"
+
+local function pascal_upper_triangular(n)
+    local m = {}
+    for i = 1, n do
+        m[i] = {}
+        for j = 1, n do m[i][j] = (j >= i) ? int.binomial(j - 1, i - 1) : 0 end
+    end
+    return matrix.from(m)
+end
+
+local function pascal_symmetric(n)
+    local m = {}
+    for i = 1, n do
+        m[i] = {}
+        for j = 1, n do m[i][j] = int.binomial(i + j - 2, i - 1) end
+    end
+    return matrix.from(m)
+end
+
+local function pascal_lower_triangular(n)
+    return pascal_symmetric(n):cholesky()
+end
+
+local n = 5
+print("Pascal upper-triangular matrix:")
+print(pascal_upper_triangular(n))
+print("\nPascal lower-triangular matrix:")
+print(pascal_lower_triangular(n):format("%d"))
+print("\nPascal symmetric matrix:")
+print(pascal_symmetric(n))