In the short version, the representations are isomorphic, that is you can take all formulas from our Siggraph cheat sheets and replace all operators by Eric's '

In the short version, the representations are isomorphic, that is you can take all formulas from our Siggraph cheat sheets and replace all operators by Eric's 'anti-operators'. You can review the discussion with Eric here : https://discourse.bivector.net/t/why-use-dual-space-in-pga-r-3-0-1-vs-r-3-0-1/101/53?u=enki https://discourse.bivector.net/t/why-use-dual-space-in-pga-r... (its a long discussion, the link points to my last summary). There are still some unanswered questions on Eric's method (most notably how to define his duality mathematically - or how to arrive at the metric for the dual algebra - I'm looking forward to his views on this.) The 26th of February I'm giving a new talk at the GAME2020 workshop that is all about the reason the view nobody is used to might in fact be a natural choice.