Split into finer subsections

Author: Chillee

content/numerical/PolyIntegDeriv.h

@@ -0,0 +1,22 @@
+/**
+ * Author: chilli, Andrew He, Adamant
+ * Date: 2019-04-27
+ * Description: A FFT based Polynomial class.
+ */
+#pragma once
+#include "PolyBase.h"
+
+poly deriv(poly a) {
+	if (a.empty()) return {};
+	poly b(sz(a) - 1);
+	rep(i, 1, sz(a)) b[i - 1] = a[i] * num(i);
+	return b;
+}
+poly integr(poly a) {
+	if (a.empty()) return {0};
+	poly b(sz(a) + 1);
+	b[1] = num(1);
+	rep(i, 2, sz(b)) b[i] = b[mod%i]*Mod(-mod/i+mod);
+	rep(i, 1 ,sz(b)) b[i] = a[i-1] * b[i];
+	return b;
+}

content/numerical/PolyInterpolate.h

@@ -1,7 +1,9 @@
 /**
  * Author: chilli, Andrew He, Adamant
  * Date: 2019-04-27
- * Description: A FFT based Polynomial class.
+ * Description: Given $n$ points (x[i], y[i]), computes an n-1-degree polynomial $p$ that
+ *  passes through them: $p(x) = a[0]*x^0 + ... + a[n-1]*x^{n-1}$.
+ * Time: O(n \log^2 n)
  */
 #pragma once
 

content/numerical/PolyLogExp.h

@@ -0,0 +1,24 @@
+/**
+ * Author: chilli, Andrew He, Adamant
+ * Date: 2019-04-27
+ * Description: A FFT based Polynomial class.
+ */
+#pragma once
+
+#include "PolyBase.h"
+#include "PolyIntegDeriv.h"
+
+poly log(poly a) {
+	return modK(integr(deriv(a) * inverse(a)), sz(a));
+}
+poly exp(poly a) {
+	poly b(1, num(1));
+	if (a.empty())
+		return b;
+	while (sz(b) < sz(a)) {
+		b.resize(sz(b) * 2);
+		b *= (poly({num(1)}) + modK(a, sz(b)) - log(b));
+		b.resize(sz(b) / 2 + 1);
+	}
+	return modK(b, sz(a));
+}

content/numerical/PolyPow.h

@@ -6,35 +6,8 @@
 #pragma once
 
 #include "PolyBase.h"
-poly deriv(poly a) {
-	if (a.empty())
-		return {};
-	poly b(sz(a) - 1);
-	rep(i, 1, sz(a)) b[i - 1] = a[i] * num(i);
-	return b;
-}
-poly integr(poly a) {
-	if (a.empty()) return {0};
-	poly b(sz(a) + 1);
-	b[1] = num(1);
-	rep(i, 2, sz(b)) b[i] = b[mod%i]*Mod(-mod/i+mod);
-	rep(i, 1 ,sz(b)) b[i] = a[i-1] * b[i];
-	return b;
-}
-poly log(poly a) {
-	return modK(integr(deriv(a) * inverse(a)), sz(a));
-}
-poly exp(poly a) {
-	poly b(1, num(1));
-	if (a.empty())
-		return b;
-	while (sz(b) < sz(a)) {
-		b.resize(sz(b) * 2);
-		b *= (poly({num(1)}) + modK(a, sz(b)) - log(b));
-		b.resize(sz(b) / 2 + 1);
-	}
-	return modK(b, sz(a));
-}
+#include "PolyLogExp.h"
+
 poly pow(poly a, ll m) {
 	int p = 0, n = sz(a);
 	while (p < sz(a) && a[p].x == 0)

content/numerical/Polynomial.h

@@ -3,6 +3,8 @@ \chapter{Numerical}
 \kactlimport{GoldenSectionSearch.h}
 \kactlimport{PolyBase.h}
 \kactlimport{PolyMod.h}
+\kactlimport{PolyIntegDeriv.h}
+\kactlimport{PolyLogExp.h}
 \kactlimport{PolyPow.h}
 \kactlimport{PolyInterpolate.h}
 \kactlimport{PolyEvaluate.h}

content/numerical/chapter.tex

@@ -420,6 +420,8 @@ typedef vector<num> poly;
 
 #include "../../content/numerical/PolyBase.h"
 #include "../../content/numerical/PolyMod.h"
+#include "../../content/numerical/PolyIntegDeriv.h"
+#include "../../content/numerical/PolyLogExp.h"
 #include "../../content/numerical/PolyPow.h"
 #include "../../content/numerical/PolyEvaluate.h"
 #include "../../content/numerical/PolyInterpolate.h"