amortizedHGM

Sage code supporting

• [ arXiv DOI ] Hypergeometric L-functions in average polynomial time by Edgar Costa, Kiran Kedlaya and David Roe
• [ arXiv ] Hypergeometric L-functions in average polynomial time, II by Edgar Costa, Kiran Kedlaya and David Roe

The previous version of the code was not a pip package, and can be found here.

This code depends on pyrforest.

Install

sage -pip install --upgrade  git+https://github.com/edgarcosta/amortizedHGM.git@main

If you don't have permissions to install it system wide, please add the flag --user to install it just for you.

sage -pip install --user --upgrade git+https://github.com/edgarcosta/amortizedHGM.git@main

Example

sage: from amortizedHGM import AmortizingHypergeometricDatamodp # the version of the first paper
....: H = AmortizingHypergeometricDatamodp(10**2,   cyclotomic=([4,2,2], [3,3]))
....: H.amortized_padic_H_values(1/5) # this uses the rforest library
{11: 9,
 13: 9,
 17: 13,
 19: 13,
 23: 21,
 29: 2,
 31: 25,
 37: 4,
 41: 0,
 43: 35,
 47: 29,
 53: 39,
 59: 54,
 61: 57,
 67: 59,
 71: 62,
 73: 65,
 79: 75,
 83: 2,
 89: 83,
 97: 6}
 sage: H.amortized_padic_H_values(1/5, use_c=False) # this code uses AccRemForest
 {11: 9,
 13: 9,
 17: 13,
 19: 13,
 23: 21,
 29: 2,
 31: 25,
 37: 4,
 41: 0,
 43: 35,
 47: 29,
 53: 39,
 59: 54,
 61: 57,
 67: 59,
 71: 62,
 73: 65,
 79: 75,
 83: 2,
 89: 83,
 97: 6}
sage: from amortizedHGM import AmortizingHypergeometricData # the version of the second paper
sage: H = AmortizingHypergeometricData(cyclotomic=[[3,3],[2,1,1,1]])
sage: H.weight()
 2
sage: _ = H.compare(12, 314/159, log2N_sage=12, verbose=True)
2^12
Amortized Gamma: 0.02 s
Additional precomputation: 0.01 s
Amortized HG: 0.04 s
Sage (p): 7.28 s

Timings

To recreate the timings in Table 1 of the paper, run sage -python amortizedHGM/generate_table_paper.py; it will print latex to generate the table.