Crate secondary_product

Crate secondary_product 

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Computes products in $\Mod_{C\lambda^2}$.

§Usage

The program asks for a module $M$ and an element $x \in \Ext^{*, *}(M, k)$. It then computes the secondary product of the standard lift of $x$ with all (standard lifts of) elements in $\Ext^{*, *}(M, k)$ that survive $d_2$.

These products are computed for all elements whose product with $x$ lies in the specified bidegree of $M$, and $k$ is resolved as far as necessary to support this computation.

Running this program requires computing the secondary resolution of both $M$ and $k$, i.e. the calculations performed by secondary. The user is encouraged to make use of a save file to reuse these calculations for different products. (When $M$ is not equal to $k$, the user will be prompted for the save directory of $k$)

§Output

This prints the corresponding products in $\Mod_{C\lambda^2}$. In particular, $x$ multiplies on the left, and the sign twist of $(-1)^{s’t}$ is inserted.

§Notes

The program verifies that $x$ is indeed permanent.