On the Saito basis for plane curves

Key Points

• The aim is to explore the Saito module and the torsion submodule of analytic plane curves and develop a computation method.
• Analyzed the Saito module and torsion submodule of analytic plane curves.
• Developed an algorithm for efficient computation.
• Focused on curves with multiplicity less than or equal to three.
• Introduced a method for computing analytic invariants.
• Successfully calculated invariants for given plane curves.
• Identified properties related to the Saito module and torsion structure.