Crate secondary

Crate secondary 

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This computes $d_2$ differentials in the Adams spectral sequence. This only works for fairly specific modules, but tends to cover most cases of interest.

§Usage

This asks for a module in the usual way, and verifies that the module satisfies the conditions necessary for the algorithm the work. It only works with the Milnor basis.

§Output

We omit differentials if the target bidegree is zero.

§Sharding

This section applies to all of the secondary scripts, namely secondary, secondary_product and secondary_massey.

Most of the computation can be fully distributed. Rudimentary sharding over multiple machines is currently supported, where each machine works on a single s.

These machines should share the same save directory (e.g. over a network-mounted drive), and all prerequisites for the computation must have been computed. This includes the “primary” data (resolutions, lifts, etc.) as well as the secondary prerequisites (the secondary resolution for secondary products, secondary products for secondary Massey product). Otherwise, conflicts may arise.

To compute data for a single s, run the script with the environment variable SECONDARY_JOB=s. The minimum value of s is the cohomological degree shift of the secondary homotopy (i.e. the difference in degrees between the input class and the λ part of the answer; 2 in the case of secondary), and the maximum value of s is the max_s of the resolution.

After running this script for all s in the range, run it as usual to produce the final output. An example script is as follows:

#!/bin/sh

cargo run --example resolve_through_stem S_2 /tmp/save 40 20;

cargo build --example secondary
for n in `seq 20 -1 2`; do
    SECONDARY_JOB=$n target/debug/examples/secondary S_2 /tmp/save 40 20 &
done

wait

target/debug/examples/secondary S_2 /tmp/save 40 20;