Merge branch 'drinfeld_tau' into morphisms_drinfeld_modules

Author: Xavier Caruso

src/sage/rings/function_field/drinfeld_modules/drinfeld_module.py

@@ -126,8 +126,8 @@ class DrinfeldModule(Parent, UniqueRepresentation):
     - ``gen`` -- the generator of the Drinfeld module; as a list of
       coefficients or an Ore polynomial
 
-    - ``name`` -- (default: ``'τ'``) the name of the Ore polynomial ring
-      generator
+    - ``name`` -- (default: `\tau`) the name of the Ore
+      polynomial ring generator
 
     .. RUBRIC:: Construction
 
@@ -161,7 +161,7 @@ class DrinfeldModule(Parent, UniqueRepresentation):
         False
 
     In those examples, we used a list of coefficients (``[z, 1, 1]``) to
-    represent the generator `\phi_T = z + τ + τ^2`. One can also use
+    represent the generator `\phi_T = z + \tau + \tau^2`. One can also use
     regular Ore polynomials::
 
         sage: ore_polring = phi.ore_polring()
@@ -521,7 +521,7 @@ def __classcall_private__(cls, function_ring, gen, name='τ'):
         - ``gen`` -- the generator of the Drinfeld module; as a list of
           coefficients or an Ore polynomial
 
-        - ``name`` -- (default: ``'τ'``) the name of the variable of
+        - ``name`` -- (default: `\tau`) the name of the variable of
           the Ore polynomial
 
         OUTPUT: a DrinfeldModule or DrinfeldModule_finite
@@ -633,7 +633,7 @@ def __init__(self, gen, category):
         - ``gen`` -- the generator of the Drinfeld module; as a list of
           coefficients or an Ore polynomial
 
-        - ``name`` -- (default: ``'τ'``) the name of the variable of
+        - ``name`` -- (default: `\tau`) the name of the variable of
           the Ore polynomial ring
 
         TESTS::

src/sage/rings/function_field/drinfeld_modules/finite_drinfeld_module.py

@@ -138,7 +138,7 @@ def __init__(self, gen, category):
         - ``gen`` -- the generator of the Drinfeld module as a list of
           coefficients or an Ore polynomial
 
-        - ``name`` -- (default: ``'τ'``) the name of the variable of
+        - ``name`` -- (default: `\tau`) the name of the variable of
           the Ore polynomial ring
 
         TESTS::
@@ -235,7 +235,7 @@ def frobenius_endomorphism(self):
 
         Let `q` be the order of the base field of the function ring. The
         *Frobenius endomorphism* is defined as the endomorphism whose
-        defining Ore polynomial is `τ^q`.
+        defining Ore polynomial is `\tau^q`.
 
         EXAMPLES::
 
@@ -273,14 +273,14 @@ def frobenius_charpoly(self, var='X', algorithm=None):
 
         Let `\chi = X^r + \sum_{i=0}^{r-1} A_{i}(T)X^{i}` be the
         characteristic polynomial of the Frobenius endomorphism, and
-        let `τ^n` be the Ore polynomial that defines the Frobenius
+        let `\tau^n` be the Ore polynomial that defines the Frobenius
         endomorphism of `\phi`; by definition, `n` is the degree of `K`
         over the base field `\mathbb{F}_q`. Then we have
 
         .. MATH::
 
-            \chi(τ^n)(\phi(T))
-            = τ^{nr} + \sum_{i=1}^{r} \phi_{A_{i}}τ^{n(i)}
+            \chi(\tau^n)(\phi(T))
+            = \tau^{nr} + \sum_{i=1}^{r} \phi_{A_{i}}\tau^{n(i)}
             = 0,
 
         with `\deg(A_i) \leq \frac{n(r-i)}{r}`.