Fix equations using |

Fixes #554

docs/basic-usage/array-arithmetic.rst

@@ -292,7 +292,7 @@ Advanced arithmetic
     :collapsible:
 
     The Discrete Fourier Transform (DFT) of size $n$ over the finite field $\mathrm{GF}(p^m)$ exists when
-    there exists a primitive $n$-th root of unity. This occurs when $n\ |\ p^m - 1$.
+    there exists a primitive $n$-th root of unity. This occurs when $n \mid p^m - 1$.
 
     .. ipython-with-reprs:: int,poly,power
 
@@ -310,7 +310,7 @@ Advanced arithmetic
     :collapsible:
 
     The inverse Discrete Fourier Transform (DFT) of size $n$ over the finite field $\mathrm{GF}(p^m)$
-    exists when there exists a primitive $n$-th root of unity. This occurs when $n\ |\ p^m - 1$.
+    exists when there exists a primitive $n$-th root of unity. This occurs when $n \mid p^m - 1$.
 
     .. ipython-with-reprs:: int,poly,power
 

src/galois/_codes/_linear.py

@@ -383,11 +383,11 @@ def generator_to_parity_check_matrix(G: FieldArray) -> FieldArray:
 
     Arguments:
         G: The $(k, n)$ generator matrix $\mathbf{G}$ in systematic form
-            $\mathbf{G} = [\mathbf{I}_{k,k}\ |\ \mathbf{P}_{k,n-k}]$.
+            $\mathbf{G} = [\mathbf{I}_{k,k} \mid \mathbf{P}_{k,n-k}]$.
 
     Returns:
         The $(n-k, n)$ parity-check matrix
-        $\mathbf{H} = [-\mathbf{P}_{k,n-k}^T\ |\ \mathbf{I}_{n-k,n-k}]$`.
+        $\mathbf{H} = [-\mathbf{P}_{k,n-k}^T \mid \mathbf{I}_{n-k,n-k}]$`.
 
     Examples:
         .. ipython:: python
@@ -423,10 +423,10 @@ def parity_check_to_generator_matrix(H: FieldArray) -> FieldArray:
 
     Arguments:
         H: The $(n-k, n)$ parity-check matrix $\mathbf{G}$ in systematic form
-            $\mathbf{H} = [-\mathbf{P}_{k,n-k}^T\ |\ \mathbf{I}_{n-k,n-k}]$`.
+            $\mathbf{H} = [-\mathbf{P}_{k,n-k}^T \mid \mathbf{I}_{n-k,n-k}]$`.
 
     Returns:
-        The $(k, n)$ generator matrix $\mathbf{G} = [\mathbf{I}_{k,k}\ |\ \mathbf{P}_{k,n-k}]$.
+        The $(k, n)$ generator matrix $\mathbf{G} = [\mathbf{I}_{k,k} \mid \mathbf{P}_{k,n-k}]$.
 
     Examples:
         .. ipython:: python

src/galois/_modular.py

@@ -82,7 +82,7 @@ def euler_phi(n: int) -> int:
     Notes:
         This function implements the Euler totient function
 
-        $$\phi(n) = n \prod_{p\ |\ n} \bigg(1 - \frac{1}{p}\bigg) = \prod_{i=1}^{k} p_i^{e_i-1} \big(p_i - 1\big)$$
+        $$\phi(n) = n \prod_{p \mid n} \bigg(1 - \frac{1}{p}\bigg) = \prod_{i=1}^{k} p_i^{e_i-1} \big(p_i - 1\big)$$
 
         for prime $p$ and the prime factorization $n = p_1^{e_1} \dots p_k^{e_k}$.
 

src/galois/_polys/_conway.py

@@ -47,10 +47,10 @@ def is_conway(f: Poly, search: bool = False) -> bool:
     Notes:
         A degree-$m$ polynomial $f(x)$ over $\mathrm{GF}(p)$ is the *Conway polynomial*
         $C_{p,m}(x)$ if it is monic, primitive, compatible with Conway polynomials $C_{p,n}(x)$ for all
-        $n\ |\ m$, and is lexicographically first according to a special ordering.
+        $n \mid m$, and is lexicographically first according to a special ordering.
 
         A Conway polynomial $C_{p,m}(x)$ is *compatible* with Conway polynomials $C_{p,n}(x)$ for
-        $n\ |\ m$ if $C_{p,n}(x^r)$ divides $C_{p,m}(x)$, where $r = \frac{p^m - 1}{p^n - 1}$.
+        $n \mid m$ if $C_{p,n}(x^r)$ divides $C_{p,m}(x)$, where $r = \frac{p^m - 1}{p^n - 1}$.
 
         The Conway lexicographic ordering is defined as follows. Given two degree-$m$ polynomials
         $g(x) = \sum_{i=0}^m g_i x^i$ and $h(x) = \sum_{i=0}^m h_i x^i$, then $g < h$ if and only if
@@ -106,7 +106,7 @@ def is_conway(f: Poly, search: bool = False) -> bool:
 def is_conway_consistent(f: Poly, search: bool = False) -> bool:
     r"""
     Determines whether the degree-$m$ polynomial $f(x)$ over $\mathrm{GF}(p)$ is consistent
-    with smaller Conway polynomials $C_{p,n}(x)$ for all $n\ |\ m$.
+    with smaller Conway polynomials $C_{p,n}(x)$ for all $n \mid m$.
 
     .. question:: Why is this a method and not a property?
         :collapsible:
@@ -123,7 +123,7 @@ def is_conway_consistent(f: Poly, search: bool = False) -> bool:
 
     Returns:
         `True` if the polynomial $f(x)$ is primitive and consistent with smaller Conway polynomials
-        $C_{p,n}(x)$ for all $n\ |\ m$.
+        $C_{p,n}(x)$ for all $n \mid m$.
 
     Raises:
         LookupError: If `search=False` and a smaller Conway polynomial $C_{p,n}$ is not found in Frank Luebeck's
@@ -134,7 +134,7 @@ def is_conway_consistent(f: Poly, search: bool = False) -> bool:
 
     Notes:
         A degree-$m$ polynomial $f(x)$ over $\mathrm{GF}(p)$ is *compatible* with Conway polynomials
-        $C_{p,n}(x)$ for $n\ |\ m$ if $C_{p,n}(x^r)$ divides $f(x)$, where
+        $C_{p,n}(x)$ for $n \mid m$ if $C_{p,n}(x^r)$ divides $f(x)$, where
         $r = \frac{p^m - 1}{p^n - 1}$.
 
         A Conway-consistent polynomial has all the properties of a Conway polynomial except that it is not
@@ -230,10 +230,10 @@ def conway_poly(characteristic: int, degree: int, search: bool = False) -> Poly:
     Notes:
         A degree-$m$ polynomial $f(x)$ over $\mathrm{GF}(p)$ is the *Conway polynomial*
         $C_{p,m}(x)$ if it is monic, primitive, compatible with Conway polynomials $C_{p,n}(x)$ for all
-        $n\ |\ m$, and is lexicographically first according to a special ordering.
+        $n \mid m$, and is lexicographically first according to a special ordering.
 
         A Conway polynomial $C_{p,m}(x)$ is *compatible* with Conway polynomials $C_{p,n}(x)$ for
-        $n\ |\ m$ if $C_{p,n}(x^r)$ divides $C_{p,m}(x)$, where $r = \frac{p^m - 1}{p^n - 1}$.
+        $n \mid m$ if $C_{p,n}(x^r)$ divides $C_{p,m}(x)$, where $r = \frac{p^m - 1}{p^n - 1}$.
 
         The Conway lexicographic ordering is defined as follows. Given two degree-$m$ polynomials
         $g(x) = \sum_{i=0}^m g_i x^i$ and $h(x) = \sum_{i=0}^m h_i x^i$, then $g < h$ if and only if

src/galois/_polys/_irreducible.py

@@ -49,7 +49,7 @@ def is_irreducible(f: Poly) -> bool:
 
         This function implements Rabin's irreducibility test. It says a degree-$m$ polynomial $f(x)$
         over $\mathrm{GF}(q)$ for prime power $q$ is irreducible if and only if
-        $f(x)\ |\ (x^{q^m} - x)$ and $\textrm{gcd}(f(x),\ x^{q^{m_i}} - x) = 1$ for
+        $f(x) \mid (x^{q^m} - x)$ and $\textrm{gcd}(f(x),\ x^{q^{m_i}} - x) = 1$ for
         $1 \le i \le k$, where $m_i = m/p_i$ for the $k$ prime divisors $p_i$ of $m$.
 
     References:

src/galois/_polys/_poly.py

@@ -903,7 +903,7 @@ def is_conway(self) -> bool:
     def is_conway_consistent(self) -> bool:
         r"""
         Determines whether the degree-$m$ polynomial $f(x)$ over $\mathrm{GF}(p)$ is consistent
-        with smaller Conway polynomials $C_{p,n}(x)$ for all $n\ |\ m$.
+        with smaller Conway polynomials $C_{p,n}(x)$ for all $n \mid m$.
         """
         # Will be monkey-patched in `_conway.py`
         raise NotImplementedError

src/galois/_polys/_primitive.py

@@ -42,7 +42,7 @@ def is_primitive(f: Poly) -> bool:
 
     Notes:
         A degree-$m$ polynomial $f(x)$ over $\mathrm{GF}(q)$ is *primitive* if it is
-        irreducible and $f(x)\ |\ (x^k - 1)$ for $k = q^m - 1$ and no $k$ less than
+        irreducible and $f(x) \mid (x^k - 1)$ for $k = q^m - 1$ and no $k$ less than
         $q^m - 1$.
 
     References:

src/galois/_prime.py

@@ -644,7 +644,7 @@ def legendre_symbol(a: int, p: int) -> int:
         .. math::
             \bigg(\frac{a}{p}\bigg) =
                 \begin{cases}
-                    0, & p\ |\ a
+                    0, & p \mid a
 
                     1, & a \in Q_p
 
@@ -1278,7 +1278,7 @@ def f(x):
 @export
 def divisors(n: int) -> list[int]:
     r"""
-    Computes all positive integer divisors $d$ of the integer $n$ such that $d\ |\ n$.
+    Computes all positive integer divisors $d$ of the integer $n$ such that $d \mid n$.
 
     Arguments:
         n: An integer.