Hey! This sounds really interesting! I've used Macaulay2 in the past for my 
research, and it seemed pretty helpful.

On Thursday, 16 March 2017 14:41:30 UTC-4, Grayson Jorgenson wrote:
>
> Hi all,
>
> I am a second year math PhD student at Florida State University studying 
> algebraic geometry. Last year I had the chance to work on Sage through GSoC 
> and implemented basic functionality for algebraic curves. During the course 
> of that project I came across some generic algebraic geometry functionality 
> that I think would be nice to have in Sage, including more support for 
> general schemes (in order to handle gluing) and blow ups for schemes via 
> the Rees algebra construction.
>
> I'd love to have the opportunity to participate in GSoC a second time and 
> have been working on a project proposal for this year to implement an 
> assortment of general algebraic geometry functionality, most of which in 
> the direction of what Magma currently offers that's not yet in Sage. In 
> addition to the above topics, some other goals I've been investigating for 
> this project include implementing basic support for working with algebraic 
> surfaces such as parameterization/implicitization (at least for certain 
> special types of rational surfaces), and more functionality for projecting 
> projective schemes to subspaces. I have discussed potential mentorship for 
> such a project with Benjamin Hutz, but it would help a lot to have another 
> mentor if possible.
>
> Would anyone be interested in mentoring an algebraic geometry focused 
> project like this? I'm currently investigating potential additional topics 
> to add to the proposal, but I lack the expertise in some areas such as 
> toric varieties to determine what kinds of functionality there might be 
> desirable/feasible to implement in Sage. I would be very grateful for any 
> guidance or topic suggestions.
>
> Thank you,
> Grayson
>

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