From d52d1c3c1c91f00a6a36a8bf7bc60f4dfc352a0e Mon Sep 17 00:00:00 2001
From: Sebastiano Tronto <sebastiano@tronto.net>
Date: Thu, 27 Feb 2025 15:49:08 +0100
Subject: Small changes

---
 images/number-line.png | Bin 0 -> 36204 bytes
 images/number-line.svg | 262 -------------------------------------------------
 index.html             |  15 +--
 3 files changed, 8 insertions(+), 269 deletions(-)
 create mode 100644 images/number-line.png
 delete mode 100644 images/number-line.svg

diff --git a/images/number-line.png b/images/number-line.png
new file mode 100644
index 0000000..27531cb
Binary files /dev/null and b/images/number-line.png differ
diff --git a/images/number-line.svg b/images/number-line.svg
deleted file mode 100644
index bc765a7..0000000
--- a/images/number-line.svg
+++ /dev/null
@@ -1,262 +0,0 @@
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diff --git a/index.html b/index.html
index 29d9e58..eb66c15 100644
--- a/index.html
+++ b/index.html
@@ -1,7 +1,7 @@
 <!doctype html>
 <html lang="en">
 <head>
-	<title>Elliptic Curves and the ECM algorithm</title>
+	<title>Elliptic Curves and the ECM Algorithm</title>
 	<meta name="viewport" content="width=device-width" />
 
 	<!-- Import MathJax script -->
@@ -36,6 +36,7 @@
 		.slide ul { margin-left: 1.5vw; }
 		.slide ol { margin-left: 1.5vw; }
 		.slide p { margin-left: 1.5vw; }
+		.slide li { margin: 3.0vh 0; }
 
 		.slide.titlepage p, a { text-align: center; }
 		.slide.titlepage span.title { font-size: 3.6vw; font-weight: bold; }
@@ -93,7 +94,7 @@ background-blend-mode: overlay;">
 <div class="slide" tabindex="-1">
 <h1>The integers</h1>
 
-<img alt="The number line" src="images/number-line.svg"
+<img alt="The number line" src="images/number-line.png"
 	style="width: 70%; margin-left: 15%; margin-right: 15%;"/>
 
 <ul>
@@ -410,7 +411,7 @@ def factorize(n: int) -> list:
 
     f = find_factor(n)
 
-    return factorize(n) + factorize(n//f)
+    return factorize(f) + factorize(n//f)
 </code></pre>
 
 <ul>
@@ -438,7 +439,7 @@ def find_factor(n: int) -> int:
 <div>
 <p><strong>To find a factor of \(n\):</strong><p>
 <ol>
-<li>Take a random Elliptic Curve \(E\)
+<li>Take a random elliptic curve \(E\)
 and a random point \(P\) of \(E\)</li>
 <li>Take a <em>suitable number \(m\)</em></li>
 <li>Try to compute \(m\cdot P = P+P+\cdots+P\quad\) (\(m\) times)
@@ -484,7 +485,7 @@ background-blend-mode: overlay;">
 Q: Aren't we just computing the \(\operatorname{GCD}\) with random numbers?
 </strong></p>
 <p>
-A: Yes, but Elliptic Curve operations produce "good candidates"
+A: Yes, but elliptic curve operations produce "good candidates"
 for these random numbers.
 </p>
 </div>
@@ -504,7 +505,7 @@ Pollard's \(p-1\) Algorithm</a>, but ECM is faster.</p>
 <h1>Elliptic Curve Method - Questions</h1>
 <div class="centertext">
 <p><strong>
-Q: Are there objects that are more complicated than Elliptic Curves
+Q: Are there objects that are more complicated than elliptic curves
 and can make the method even faster?
 </strong></p>
 <p>A: Yes, there are higher-dimensional
@@ -594,7 +595,7 @@ background-blend-mode: overlay;">
 	// Function to add a footer to every slide.
 	function slideFooter() {
 		const start = "<div class=\"footer\"><table class=\"footer-table\"><tr>";
-		const title = "Elliptic Curves and the ECM algorithm"
+		const title = "Elliptic Curves and the ECM Algorithm"
 		const link = "<a href=https://tronto.net/talks/ecm>tronto.net/talks/ecm</a>";
 		const end = "</tr></table></div>";
 		const content =
-- 
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