commit d52d1c3c1c91f00a6a36a8bf7bc60f4dfc352a0e
parent 7f1b8a358515b45d717c3c4b5baf2fbc0f568170
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date: Thu, 27 Feb 2025 15:49:08 +0100
Small changes
Diffstat:
3 files changed, 8 insertions(+), 269 deletions(-)
diff --git a/images/number-line.png b/images/number-line.png
Binary files differ.
diff --git a/images/number-line.svg b/images/number-line.svg
@@ -1,262 +0,0 @@
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diff --git 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 =
