Hi everyone,
I am a newcomer to SageMath and have written some functions that I would
like to contribute to Sage.
Specifically, I have developed functions to:
1. Compute the bases of Weak Jacobi forms for both integral weights and
half-integral indices.
2. Compute the coefficients of elliptic genera represented by Chern numbers.
3. Compute integrations of cohomology classes of homogeneous spaces and
their complete intersections.
I have a few questions regarding these functions:
Question 1:
Would it be appropriate to push these functions as a ‘Geometry and
Topology’ library in Sage?
Question 2:
I cannot find any SageMath polynomial library that supports polynomials of
rational degrees.
However, elliptic genera are Laurent polynomial series of rational degrees.
What is the most appropriate representation for this?
Question 3:
In my code, I have redefined the zeta function only for negative integers
due to computation time.
Is it acceptable to use such ad-hoc coding, or should I use the zeta
function of the SageMath library in the code to be published?
Here are some additional details about my codes:
1. Compute the bases of Weak Jacobi forms for both integral weights and
half-integral indices.
* For each pair of integers n and half-integer k, the function outputs
a list of bases of the space of weak Jacobi forms of weight n and index k.
* For any weak Jacobi form of weight n and index k, the function
outputs the coefficients when we express the form by the basis which is
output by the above function.
2. Compute the coefficients of elliptic genera represented by Chern numbers
* For each dimension d, the function outputs the elliptic genera of
varieties of dimension d whose coefficients are written by Chern numbers.
3. Compute integrations of cohomology classes of homogeneous spaces and
their complete intersections.
* We define abstract classes of varieties and vector bundles with
abstract functions 'Chern classes', 'Chern characters', and 'Todd classes'.
* We also define classes of homogeneous spaces, equivariant vector
bundles on them, and their complete intersections, which implements the
above abstract classes and computes the integrations of any cohomology
classes on them.
* By combining these, we can compute the Chern numbers of these spaces.
Thank you for your time and consideration.
Kenta Kobayashi,
Ph.D student at Tokyo University
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