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Xavier Caruso
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fix pdf documentation
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src/sage/rings/function_field/drinfeld_modules/drinfeld_module.py

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@@ -127,8 +127,8 @@ class DrinfeldModule(Parent, UniqueRepresentation):
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- ``gen`` -- the generator of the Drinfeld module; as a list of
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coefficients or an Ore polynomial
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- ``name`` -- (default: ``'τ'``) the name of the Ore polynomial ring
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generator
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- ``name`` -- (default: `\tau`) the name of the Ore
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polynomial ring generator
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.. RUBRIC:: Construction
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@@ -163,7 +163,7 @@ class DrinfeldModule(Parent, UniqueRepresentation):
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False
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In those examples, we used a list of coefficients (``[z, 1, 1]``) to
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represent the generator `\phi_T = z + τ + τ^2`. One can also use
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represent the generator `\phi_T = z + \tau + \tau^2`. One can also use
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regular Ore polynomials::
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sage: ore_polring = phi.ore_polring()
@@ -533,7 +533,7 @@ def __classcall_private__(cls, function_ring, gen, name='τ'):
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- ``gen`` -- the generator of the Drinfeld module; as a list of
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coefficients or an Ore polynomial
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- ``name`` -- (default: ``'τ'``) the name of the variable of
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- ``name`` -- (default: `\tau`) the name of the variable of
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the Ore polynomial
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OUTPUT: a DrinfeldModule or DrinfeldModule_finite
@@ -645,7 +645,7 @@ def __init__(self, gen, category):
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- ``gen`` -- the generator of the Drinfeld module; as a list of
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coefficients or an Ore polynomial
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- ``name`` -- (default: ``'τ'``) the name of the variable of
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- ``name`` -- (default: `\tau`) the name of the variable of
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the Ore polynomial ring
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TESTS::

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

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

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