Drinfeld Modular Forms

This is a SageMath package for computing with Drinfeld modular forms and their expansion at infinity.

This work is licensed under a GNU General Public License.

Installation

This package has been tested on SageMath version 9.8 and higher. It is not guaranteed to work on previous versions.

• Install from PyPI

The easiest way to install this package is via the Python package index. You simply have to run SageMath first and then type the following command:

sage: pip install drinfeld-modular-forms

• Install from source code

You can also install this package by cloning the source code from the Github repo.

Next, you have to run make install inside the project’s folder. You can also run the following command:

sage -pip install --upgrade --no-index -v .

If any updates are made to the package, then you have to pull them from the repo and run the above command again.

Usage

After running SageMath, you can import the functionalities of this package by typing the following command:

sage: from drinfeld_modular_forms import *

Table of Contents

• Background material and notations
• Ring of Drinfeld modular forms
  • DrinfeldModularFormsRing
• Elements of Drinfeld modular forms rings
  • DrinfeldModularFormsRingElement
• Expansion at infinity for rank 2
  • coefficient_A_expansion()
  • coefficient_petrov_expansion()
  • compute_A_expansion()
  • compute_delta_rank_2()
  • compute_eisentein_series_rank_2()
  • compute_h_rank_2()
  • compute_petrov_expansion()
  • inverse_cyclotomic_polynomial()
  • j_invariant()
  • parameter_at_infinity()
• Goss polynomials and exponentials
  • bracket()
  • drinfeld_exponential()
  • drinfeld_logarithm()
  • goss_polynomial()
  • lcm_of_monic_polynomials()
  • product_of_monic_polynomials()
• Drinfeld modules
  • CarlitzModule
  • DrinfeldModule

Indices and Tables

• Index

• Module Index

• Search Page