SageMath gives the user to perform calculations with Riemann surfaces, and as part of a Google Summer of Code project titled "Rigorous integration and the Abel-Jacobi map" I worked with Nils Bruin, one of the functionalities initial authors, to add the ability to calculate the Abel-Jacobi map. This work was done over the course of Sage trac tickets #30698, #31996, #32014, #32018, #32059, #32289, and #32297. These tickets were concerned with
- numerical integration techniques (tickets #30698, #32014, #32018, #32289), and
- implementing these numerical techniques within the Riemann surfaces package (tickets #31996, #32059, #32297).
For each ticket, to see the contributions of the author look at the commits in the change history. At the time of writing, edits from #30698, #32014, #32018, and #32059 have been merged into the develop branch for Sage 9.4, and so the code from these edits is accesible there (follow these instructions). The edits from ticket #32289 are no longer required, and so they have been left. The edits in tickets #31996 and #32297 were concerned with the Sage source file riemann_surface.py, and so to allow the use and developement of this code before it is merged, I am presenting it here. To use the version of the code here, once downloaded, run load("PATH_TO_FILE/riemann_surface.py") in your shell.