From c82370afcc5fa397d0b062edbcc1ff27e12e4372 Mon Sep 17 00:00:00 2001
From: RandomGamingDev <83996185+RandomGamingDev@users.noreply.github.com>
Date: Fri, 24 Nov 2023 00:38:01 -0500
Subject: [PATCH 1/2] Fixed `determinant_fast()`

---
 LinearAlgebraPurePython.py | 10 ++++++++--
 1 file changed, 8 insertions(+), 2 deletions(-)

diff --git a/LinearAlgebraPurePython.py b/LinearAlgebraPurePython.py
index 2b1f87a..ed5c4f4 100644
--- a/LinearAlgebraPurePython.py
+++ b/LinearAlgebraPurePython.py
@@ -327,8 +327,14 @@ def determinant_fast(A):
 
     # Section 2: Row manipulate A into an upper triangle matrix
     for fd in range(n):  # fd stands for focus diagonal
-        if AM[fd][fd] == 0:
-            AM[fd][fd] = 1.0e-18  # Cheating by adding zero + ~zero
+        if AM[fd][fd] == 0: # Do a row swap with a row that won't result in a pivot of 0
+            for i in range(fd+1,n):
+                if AM[i][fd] != 0:
+                    temp = AM[fd]
+                    AM[fd] = AM[i]
+                    AM[i] = temp
+                    break
+            return 0 # If there are no other rows that can do that then return the determinant of 0
         for i in range(fd+1, n):  # skip row with fd in it.
             crScaler = AM[i][fd] / AM[fd][fd]  # cr stands for "current row".
             for j in range(n):  # cr - crScaler * fdRow, one element at a time.

From 7cab1c8c42cb8cad15c4d3f9437f07c70890d884 Mon Sep 17 00:00:00 2001
From: RandomGamingDev <83996185+RandomGamingDev@users.noreply.github.com>
Date: Fri, 24 Nov 2023 01:17:14 -0500
Subject: [PATCH 2/2] Update LinearAlgebraPurePython.py

---
 LinearAlgebraPurePython.py | 10 ++++++++--
 1 file changed, 8 insertions(+), 2 deletions(-)

diff --git a/LinearAlgebraPurePython.py b/LinearAlgebraPurePython.py
index ed5c4f4..ccaf130 100644
--- a/LinearAlgebraPurePython.py
+++ b/LinearAlgebraPurePython.py
@@ -326,15 +326,20 @@ def determinant_fast(A):
     AM = copy_matrix(A)
 
     # Section 2: Row manipulate A into an upper triangle matrix
+    odd_swaps = False
     for fd in range(n):  # fd stands for focus diagonal
         if AM[fd][fd] == 0: # Do a row swap with a row that won't result in a pivot of 0
+            found = False
             for i in range(fd+1,n):
                 if AM[i][fd] != 0:
                     temp = AM[fd]
                     AM[fd] = AM[i]
                     AM[i] = temp
+                    found = True
+                    odd_swaps = not odd_swaps
                     break
-            return 0 # If there are no other rows that can do that then return the determinant of 0
+            if not found:
+                return 0 # If there are no other rows that can do that then return the determinant of 0
         for i in range(fd+1, n):  # skip row with fd in it.
             crScaler = AM[i][fd] / AM[fd][fd]  # cr stands for "current row".
             for j in range(n):  # cr - crScaler * fdRow, one element at a time.
@@ -344,7 +349,8 @@ def determinant_fast(A):
     product = 1.0
     for i in range(n):
         product *= AM[i][i]  # ... product of diagonals is determinant
-
+    if odd_swaps:
+        product *= -1
     return product