New formulas for cup-i products and fast computation of Steenrod squares

Operations on the cohomology of spaces are important tools enhancing descriptive power this computable invariant. For with mod 2 coefficients, Steenrod squares most significant these operations. Their effective computation relies formulas defining a cup-$i$ construction, structure (co)chains which is in its own right, having connections to lattice field theory, convex geometry and higher category theory among others. In article we present new use them introduce fast algorithm for finite simplicial complexes. forthcoming work axiomatically characterize construction they define, showing additionally that all other literature define same up isomorphism.