added matrix + vector functions

src/vec.typ

@@ -0,0 +1,65 @@
+#let vec(..args) = {
+  let comps = args.pos()
+  let size = comps.len()
+  return (
+    comps: comps,
+    size: size
+  )
+}
+
+#let of-size(size) = {
+  let comps = (0,) * size
+  return vec(..comps)
+}
+
+#let display(vec) = math.vec(..vec.comps.map(c => [#c]))
+
+#let add(vec1, vec2) = {
+  if vec1.size != vec2.size {
+    panic("Can't add vectors of size " + str(vec1.size) + " and " + str(vec2.size))
+  }
+
+  let comps = vec1.comps.zip(vec2.comps).map(p => p.sum())
+  return vec(..comps)
+}
+
+#let sub(vec1, vec2) = {
+  if vec1.size != vec2.size {
+    panic("Can't subtract vectors of size " + str(vec1.size) + " and " + str(vec2.size))
+  }
+
+  let comps = vec1.comps.zip(vec2.comps).map(p => p.first() - p.last())
+  return vec(..comps)
+}
+
+#let dot(vec1, vec2) = {
+  if vec1.size != vec2.size {
+    panic("Can't compute dot product of vectors of size " + str(vec1.size) + " and " + str(vec2.size))
+  }
+
+  let res = vec1.comps.zip(vec2.comps)
+                      .map(p => p.product())
+                      .sum(default: 0)
+  
+  return res
+}
+
+#let cross(vec1, vec2) = {
+  if vec1.size != 3 or vec2.size != 3 {
+    panic("Can only compute cross product of vectors of size 3")
+  }
+
+  let vec3 = of-size(3)
+  for i in range(3) {
+    let i1 = calc.rem(i + 1, 3)
+    let i2 = calc.rem(i1 + 1, 3)
+    vec3.comps.at(i) = vec1.comps.at(i1) * vec2.comps.at(i2)
+    vec3.comps.at(i) -= vec1.comps.at(i2) * vec2.comps.at(i1)
+  }
+  return vec3
+}
+
+#let to-mat(vec) = {
+  import "mat.typ" as _mat
+  return _mat.mat(..vec.comps.map(c => (c,)))
+}