added poly x poly + horner

gallery/example4.typ

@@ -32,3 +32,16 @@ $
   [quotient: #poly.display(div.quotient)],
   [rest: #poly.display(div.rest)],
 ))
+
+#let r = poly.poly(6, -11, 6, -1)
+#let horner = poly.horner(r, 2)
+$
+  r = #poly.display(r, var: "lambda") =
+  (#poly.display(horner.root-factor, var: "lambda"))
+  (#poly.display(horner.factor, var: "lambda"))
+$
+
+#(horner.display)()
+
+#let a = poly.mul(horner.root-factor, horner.factor)
+$#poly.display(a, var: "lambda")$

src/poly.typ

@@ -38,7 +38,7 @@
   return poly(..original.coefs)
 }
 
-#let display(poly) = {
+#let display(poly, var: "x") = {
   _check(poly)
 
   let fractions = (2, 3, 4, 5, 6)
@@ -73,7 +73,7 @@
       res += str(beautify-frac(calc.abs(coef)))
     }
     if poly.deg - i > 0 {
-      res += "x"
+      res += var
     }
     if poly.deg - i > 1 {
       res += "^" + str(poly.deg - i)
@@ -115,8 +115,22 @@
 }
 
 #let mul(poly1, f) = {
-  let coefs = poly1.coefs.map(c => c * f)
-  return poly(..coefs)
+  if is-poly(f) {
+    let coefs = (0,) * (poly1.deg + f.deg + 1)
+
+    for (i, c1) in poly1.coefs.enumerate() {
+      for (j, c2) in f.coefs.enumerate() {
+        coefs.at(i + j) += c1 * c2
+      }
+    }
+    return poly(..coefs)
+
+  } else if type(f) == int or type(f) == float {
+    let coefs = poly1.coefs.map(c => c * f)
+    return poly(..coefs)
+  } else {
+    panic("Invalid type: f must be a polynomial or a number")
+  }
 }
 
 #let to-cells(poly) = {
@@ -231,3 +245,49 @@
     display: make-table
   )
 }
+
+#let horner(poly1, root) = {
+  let coefs = poly1.coefs.rev()
+  let initial = ("", ..coefs)
+  let mid = ("", $arrow.b$)
+  let result = (root, coefs.first())
+
+  for i in range(coefs.len() - 1) {
+    let a = result.at(i+1) * root
+    mid.push(a)
+    let b = initial.at(i+2) + a
+    result.push(b)
+  }
+
+  let make-table() = {
+    let split(cells) = {
+      let cells2 = ()
+      cells2.push([$#cells.first()$])
+      cells2.push(table.vline())
+      for c in cells.slice(1,cells.len()-1) {
+        cells2.push([$#c$])
+      }
+      cells2.push(table.vline())
+      cells2.push([$#cells.last()$])
+      return cells2
+    }
+    
+    table(
+      columns: coefs.len() + 1,
+      align: right,
+      stroke: none,
+      ..split(initial),
+      ..mid.map(c => $#c$),
+      table.hline(),
+      ..result.map(c => $#c$)
+    )
+  }
+
+  return (
+    poly: poly1,
+    root: root,
+    root-factor: poly(-root, 1),
+    factor: poly(..result.rev().slice(1, -1)),
+    display: make-table
+  )
+}