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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) = { @@ -230,4 +244,50 @@ steps: steps, 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 + ) } \ No newline at end of file