摘要：在本論文中，我們研究一個在德林費爾德模上的邦別里-瓦勒-馬瑟理論問
題。我們建立了一種演算法來計算在基本多項式環上定義的德林費爾德模上，由有
限多個整數點所生成的子模的秩。在附錄中，我們利用SageMath提供了計算結果和
程式碼。

In this thesis, we study a problem of Bombieri-Vaaler-Masser theorem for Drinfeld modules. We establish an effective algorithm to compute the rank of the submodule generated by a finite set of integral points of a Drinfeld module defined over the base polynomial ring. In the appendix, we provide computational results and the programming code in SageMath.

Declaration of Authorship i
Abstract ii
Acknowledgements iii
1 Notation and Introduction 1
1.1 Introduction 1
1.2 Notation 2
1.3 Main theorem 2
1.4 Outline of the proof of main theorem 3
2 Preliminaries 5
2.1 Anderson t-motives and Ext modules 5
2.2 Drinfeld modules and their associated Frobenius modules 9
3 The main result 12
3.1 Main theorem 12
3.2 The algorithm 15
3.3 Time complexity 16
A Code and Examples 17
A.1 Code 17
A.2 Examples 20

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