Clean up math equations

galois/_modular.py

@@ -170,7 +170,7 @@ def carmichael_lambda(n: int) -> int:
  Returns
  -------
  :
- The smallest positive integer :math:`m` such that :math:`a^m \equiv 1 (\textrm{mod}\ n)` for
+ The smallest positive integer :math:`m` such that :math:`a^m \equiv 1\ (\textrm{mod}\ n)` for
  every :math:`a` in :math:`[1, n)` that is coprime to :math:`n`.
 
  See Also
@@ -183,14 +183,16 @@ def carmichael_lambda(n: int) -> int:
 
  Examples
  --------
- The Carmichael lambda function and Euler totient function are often equal. However, there are notable exceptions.
+ The Carmichael :math:`\lambda(n)` function and Euler :math:`\phi(n)` function are often equal. However, there are
+ notable exceptions.
 
  .. ipython:: python
 
  [galois.euler_phi(n) for n in range(1, 20)]
  [galois.carmichael_lambda(n) for n in range(1, 20)]
 
- For prime :math:`n`, :math:`\phi(n) = \lambda(n) = n - 1`. And for most composite :math:`n`, :math:`\phi(n) = \lambda(n) < n - 1`.
+ For prime :math:`n`, :math:`\phi(n) = \lambda(n) = n - 1`. And for most composite :math:`n`,
+ :math:`\phi(n) = \lambda(n) < n - 1`.
 
  .. ipython:: python
 

galois/_prime.py

@@ -120,14 +120,14 @@ def primes(n: int) -> List[int]:
 @set_module("galois")
 def kth_prime(k: int) -> int:
  r"""
- Returns the :math:`k`-th prime.
+ Returns the :math:`k`-th prime, where :math:`k = \{1,2,3,4,\dots\}` for primes :math:`p = \{2,3,5,7,\dots\}`.
 
  :group: primes-generation
 
  Parameters
  ----------
  k
- The prime index (1-indexed), where :math:`k = \{1,2,3,4,\dots\}` for primes :math:`p = \{2,3,5,7,\dots\}`.
+ The prime index (1-indexed).
 
  Returns
  -------