# propagateWeights -- propagate (Lie theoretic) weights along equivariant maps

## Synopsis

• Optional inputs:
• Forward => ..., default value false, propagate weights from domain to codomain
• LeadingTermTest => ..., default value true, check the columns of the input matrix for repeated leading terms
• MinimalityTest => ..., default value true, check that the input map is minimal

## Description

Let $T$ be a torus which acts on a polynomial ring compatibly with the grading. Assume the variables in the ring are weight vectors for the action of $T$.

Use this method on a $T$-equivariant map of graded free modules, to obtain the weights of the domain from the weights of the codomain (or viceversa).

The weights of the variables in the ring must be set a priori, using the method setWeights.

This method is called by other methods in this package. The only reason for using this method directly is that it returns a complete list of weights for the domain (resp. codomain) of an equivariant map, instead of the highest weights decomposition.

This method implements an algorithm introduced in Galetto - Propagating weights of tori along free resolutions.