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add goss polynomials documentation rubric
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DavidAyotte committed Oct 9, 2023
1 parent 7bcd4f6 commit c3ac0c7
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Expand Up @@ -74,6 +74,22 @@ class DrinfeldModule_charzero(DrinfeldModule):
z + ((1/(T^2+T))*z^2) + ((1/(T^8+T^6+T^5+T^3))*z^4) + O(z^8)
sage: phi.logarithm()
z + ((1/(T^2+T))*z^2) + ((1/(T^6+T^5+T^3+T^2))*z^4) + O(z^8)
.. RUBRIC:: Goss polynomials
Goss polynomials are a sequence of polynomials related with the
analytic theory of Drinfeld module. They provide a function field
analogue of certain classical trigonometric functions::
sage: A = GF(2)['T']
sage: K.<T> = Frac(A)
sage: phi = DrinfeldModule(A, [T, 1])
sage: phi.goss_polynomial(1)
X
sage: phi.goss_polynomial(2)
X^2
sage: phi.goss_polynomial(3)
X^3 + (1/(T^2 + T))*X^2
"""
@cached_method
def _compute_coefficient_exp(self, k):
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