We provide an algorithm for computing the number of integral points lying in certain triangles that do not have integral vertices. We use techniques from Algebraic Geometry such as the Riemann-Roch formula for weighted projective planes and resolution of singularities. We analyze the complexity of the method and show that the worst case is given by the Fibonacci sequence. At the end of the manuscript a concrete example is developed in detail where the interplay with other invariants of singularity theory is also treated.

翻译：我们提出了一种算法，用于计算不含整数顶点的特定三角形内整数点的数量。该算法运用了代数几何技术，如加权射影平面上的Riemann-Roch公式以及奇点消解。我们分析了该方法的复杂度，并证明其最坏情况由斐波那契数列给出。在手稿末尾，通过一个具体实例详细展示了该方法与奇点理论中其他不变量的相互作用。