I have written some SageMath functions to assist with doing computations and examples in my PhD research. The Tits_Representation_Coxeter notebook sets up the standard reflection representation of a Coxeter system, and provides functions to compute the action of a group element on the root system, the elementary roots as well as some code to compute the root system of a dihedral reflection subgroup.
yeekayau/Coxeter-Systems
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Some SageMath and Magma code to assist with computations with Coxeter root systems
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