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Xavier Caruso
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t -> τ
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conftest.py

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

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Original file line numberDiff line numberDiff line change
@@ -2099,17 +2099,17 @@ def frobenius_relative(self, n=1):
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sage: phi = DrinfeldModule(A, [1, z, z])
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sage: phi.frobenius_relative()
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Drinfeld Module morphism:
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From: Drinfeld module defined by T |--> z*t^2 + z*t + 1
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To: Drinfeld module defined by T |--> (2*z^2 + 4*z + 4)*t^2 + (2*z^2 + 4*z + 4)*t + 1
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Defn: t
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From: Drinfeld module defined by T |--> z*τ^2 + z*τ + 1
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To: Drinfeld module defined by T |--> (2*z^2 + 4*z + 4)*τ^2 + (2*z^2 + 4*z + 4)*τ + 1
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Defn: τ
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sage: phi.frobenius_relative(2)
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Drinfeld Module morphism:
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From: Drinfeld module defined by T |--> z*t^2 + z*t + 1
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To: Drinfeld module defined by T |--> (3*z^2 + 1)*t^2 + (3*z^2 + 1)*t + 1
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Defn: t^2
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From: Drinfeld module defined by T |--> z*τ^2 + z*τ + 1
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To: Drinfeld module defined by T |--> (3*z^2 + 1)*τ^2 + (3*z^2 + 1)*τ + 1
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Defn: τ^2
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When `n` is the degree of `F` over `\FF_q(\gamma(T))`, we obtain
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the Frobenius endomorphism::
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If `F` is finite and `n` is the degree of `F` over `\FF_q(\gamma(T))`,
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we obtain the Frobenius endomorphism::
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sage: phi.frobenius_relative(3) == phi.frobenius_endomorphism()
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True
@@ -2119,11 +2119,11 @@ def frobenius_relative(self, n=1):
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sage: psi = DrinfeldModule(A, [z, z, 1])
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sage: psi.frobenius_relative()
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Endomorphism of Drinfeld module defined by T |--> t^2 + z*t + z
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Defn: t^3
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Endomorphism of Drinfeld module defined by T |--> τ^2 + z*τ + z
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Defn: τ^3
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sage: psi.frobenius_endomorphism()
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Endomorphism of Drinfeld module defined by T |--> t^2 + z*t + z
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Defn: t^3
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Endomorphism of Drinfeld module defined by T |--> τ^2 + z*τ + z
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Defn: τ^3
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When the characteristic is zero, the relative Frobenius is not defined
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and an error is raised::

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