From b9b46fb67aeb45baa83e91c699bd3fae0f4fe4af Mon Sep 17 00:00:00 2001
From: Lucas Schwebler <lucas.schwebler@gmail.com>
Date: Wed, 13 Mar 2024 21:03:21 +0100
Subject: add inv, log, exp of formal power series

---
 math/transforms/seriesOperations.cpp | 55 ++++++++++++++++++++++++++++++++++++
 1 file changed, 55 insertions(+)
 create mode 100644 math/transforms/seriesOperations.cpp

diff --git a/math/transforms/seriesOperations.cpp b/math/transforms/seriesOperations.cpp
new file mode 100644
index 0000000..3851a1e
--- /dev/null
+++ b/math/transforms/seriesOperations.cpp
@@ -0,0 +1,55 @@
+vector<ll> poly_inv(vector<ll> a, int n){
+	vector<ll> q = {powMod(a[0], mod-2, mod)};
+	for(int len = 1; len < n; len *= 2){
+		vector<ll> a2 = a, q2 = q;
+		a2.resize(2*len), q2.resize(2*len);
+		ntt(q2);
+		for(int j = 0; j < 2; j++){
+			ntt(a2);
+			for(int i = 0; i < 2*len; i++) a2[i] = a2[i] * q2[i] % mod;
+			ntt(a2, true);
+			for(int i = 0; i < len; i++) a2[i] = 0;
+		}
+		for(int i = len; i < min(n, 2*len); i++) q.push_back((mod - a2[i]) % mod);
+	}
+	return q;
+}
+
+vector<ll> poly_deriv(vector<ll> a){
+	for(int i = 0; i < sz(a)-1; i++)
+		a[i] = a[i+1] * (i+1) % mod;
+	a.pop_back();
+	return a;
+}
+
+vector<ll> poly_integr(vector<ll> a){
+	if(a.empty()) return {0};
+	a.push_back(a.back() * powMod(sz(a), mod-2, mod) % mod);
+	for(int i = sz(a)-2; i > 0; i--)
+		a[i] = a[i-1] * powMod(i, mod-2, mod) % mod;
+	a[0] = 0;
+	return a;
+}
+
+vector<ll> poly_log(vector<ll> a, int n){
+	a = mul(poly_deriv(a), poly_inv(a, n));
+	a.resize(n-1);
+	a = poly_integr(a);
+	return a;
+}
+
+vector<ll> poly_exp(vector<ll> a, int n){
+	vector<ll> q = {1};
+	for(int len = 1; len < n; len *= 2){
+		vector<ll> p = poly_log(q, 2*len);
+		for(int i = 0; i < 2*len; i++)
+			p[i] = (mod - p[i] + (i < sz(a) ? a[i] : 0)) % mod;
+		vector<ll> q2 = q;
+		q2.resize(2*len);
+		ntt(p), ntt(q2);
+		for(int i = 0; i < 2*len; i++) p[i] = p[i] * q2[i] % mod;
+		ntt(p, true);
+		for(int i = len; i < min(n, 2*len); i++) q.push_back(p[i]);
+	}
+	return q;
+}
\ No newline at end of file
-- 
cgit v1.2.3


From 36e9961fe1f3a63693c86da020cf2c38893170b9 Mon Sep 17 00:00:00 2001
From: Lucas Schwebler <lucas.schwebler@gmail.com>
Date: Wed, 13 Mar 2024 22:21:49 +0100
Subject: new crt

---
 math/chineseRemainder.cpp | 47 +++++++++++++----------------------------------
 1 file changed, 13 insertions(+), 34 deletions(-)

diff --git a/math/chineseRemainder.cpp b/math/chineseRemainder.cpp
index 623f94b..a1aa480 100644
--- a/math/chineseRemainder.cpp
+++ b/math/chineseRemainder.cpp
@@ -1,35 +1,14 @@
-// Laufzeit: O(n * log(n)), n := Anzahl der Kongruenzen. Nur für
-// teilerfremde Moduli. Berechnet das kleinste, nicht negative x,
-// das alle Kongruenzen simultan löst. Alle Lösungen sind
-// kongruent zum kgV der Moduli (Produkt, da teilerfremd).
-struct ChineseRemainder {
-	using lll = __int128;
-	vector<lll> lhs, rhs, mods, inv;
-	lll M; // Produkt über die Moduli. Kann leicht überlaufen.
+struct CRT{
+	using lll = __int128_t;
+  lll M = 1, sol = 0; // Solution unique modulo M
+  bool hasSol = true;
 
-	ll g(const vector<lll> &vec) {
-		lll res = 0;
-		for (int i = 0; i < sz(vec); i++) {
-			res += (vec[i] * inv[i]) % M;
-			res %= M;
-		}
-		return res;
-	}
-
-	// Fügt Kongruenz l * x = r (mod m) hinzu.
-	void addEquation(ll l, ll r, ll m) {
-		lhs.push_back(l);
-		rhs.push_back(r);
-		mods.push_back(m);
-	}
-
-	ll solve() { // Löst das System.
-		M = accumulate(all(mods), lll(1), multiplies<lll>());
-		inv.resize(sz(lhs));
-		for (int i = 0; i < sz(lhs); i++) {
-			lll x = (M / mods[i]) % mods[i];
-			inv[i] = (multInv(x, mods[i]) * (M / mods[i]));
-		}
-		return (multInv(g(lhs), M) * g(rhs)) % M;
-	}
-};
+  // Adds congruence x = a (mod m)
+  void add(ll a, ll m){
+    ll s, t, d = extendedEuclid(M, m, s, t);
+    if((a - sol) % d != 0) hasSol = false;
+    lll z = M/d * s;
+    M *= m/d;
+    sol = (z % M * (a-sol) % M + sol + M) % M;
+  }
+};
\ No newline at end of file
-- 
cgit v1.2.3