added Gauss-Jordan

src/gauss.typ

@@ -0,0 +1,53 @@
+#import "mat.typ" as _mat
+
+#let find-next-non-null(mat, x: 0, start-y: 0) = {
+  for y in range(start-y, mat.h) {
+    if mat.rows.at(y).at(x) != 0 {
+      return y
+    }
+  }
+  return none
+}
+
+
+#let echelon(mat) = {
+  _mat._check(mat)
+  let dim = calc.min(mat.w, mat.h)
+  let mat = mat
+  
+  // Gauss
+  for i in range(dim) {
+    let pivot = mat.rows.at(i).at(i)
+
+    // Pivot != 0 -> divide to get 1
+    if pivot != 0 {
+      mat = _mat.div-row(mat, i, pivot)
+
+    } else {
+      let y = find-next-non-null(mat, x: i, start-y: i)
+      if y != none {
+        mat = _mat.add-row(mat, i, y, f: 1 / mat.rows.at(y).at(i))
+      }
+    }
+
+    // Make all rows below 0
+    for y in range(i + 1, mat.h) {
+      mat = _mat.add-row(mat, y, i, f: -mat.rows.at(y).at(i))
+    }
+  }
+
+  // Jordan
+  for y in range(dim) {
+    for x in range(y + 1, dim) {
+      mat = _mat.add-row(mat, y, x, f: -mat.rows.at(y).at(x))
+    }
+  }
+
+  return _mat.round(mat)
+}
+
+// solver = Solver(matrix, constants)
+// solver.solve()
+
+// gauss = Gaussificator(matrix, constants)
+// gauss.echelon()