From 0d31a6e90009cd885a6a82950e2c320dcf354841 Mon Sep 17 00:00:00 2001
From: Ed Scheinerman <ers@jhu.edu>
Date: Wed, 29 Nov 2023 17:10:07 -0500
Subject: [PATCH] rank-nullity fix

---
 src/nullspacex.jl | 18 +++++++++++++++---
 src/rankx.jl      | 26 +++-----------------------
 2 files changed, 18 insertions(+), 26 deletions(-)

diff --git a/src/nullspacex.jl b/src/nullspacex.jl
index 9322a0a..19a619f 100644
--- a/src/nullspacex.jl
+++ b/src/nullspacex.jl
@@ -3,7 +3,7 @@ export nullspacex
 """
 `nullspacex(A)` returns an exact basis for the nullspace of the matrix `A`
 """
-nullspacex(A::AbstractMatrix{T}) where T = _nullspacex(A)
+nullspacex(A::AbstractMatrix{T}) where {T} = _nullspacex(A)
 
 
 function _nullspacex(A::AbstractMatrix{T}) where {T}
@@ -44,7 +44,19 @@ function nullspacex(A::AbstractMatrix{T}) where {T<:IntegerX}
     return nullspacex(big.(A) // 1)
 end
 
-function nullspacex(A::AbstractMatrix{T}) where T<:AbstractAlgebraicFunction
+function nullspacex(A::AbstractMatrix{T}) where {T<:AbstractAlgebraicFunction}
     A = SimpleRationalFunction.(A)
     return _nullspacex(A)
-end
\ No newline at end of file
+end
+
+"""
+    nullityx(A::AbstractMatrix{T})::Int where {T}
+
+Return the nullity of the matrix `A`.
+"""
+function nullityx(A::AbstractMatrix{T})::Int where {T}
+    NS = nullspacex(A)
+    r, c = size(NS)
+    return c
+end
+export nullityx
diff --git a/src/rankx.jl b/src/rankx.jl
index fe5c19e..2d75430 100644
--- a/src/rankx.jl
+++ b/src/rankx.jl
@@ -5,27 +5,7 @@ export rankx
 
 `rankx(A)` computes the rank of the exact matrix `A`
 """
-function rankx(A::AbstractMatrix{T})::Int where {T}
-    r, c = size(A)
-
-    AA = deepcopy(A)
-    try
-        AA //= 1  # convert to rational if need be
-        try
-            rrefx!(AA)
-        catch
-            AA = big.(AA)
-            rrefx!(AA)
-        end
-    catch
-        rrefx!(AA)
-    end
-
-    count = 0
-    for i = 1:r
-        if any(AA[i, :] .!= 0)
-            count += 1
-        end
-    end
-    return count
+function rankx(A::AbstractMatrix{T})::Int where T
+    r,c = size(A)
+    return c-nullityx(A)
 end