instBaseSMulZeroClass — Mathlib

English

For any x and y with a given support restriction, the coefficient of (of R).symm (x • y) at a is given by a sum over the VAddAntidiagonal with the right-hand side.

Русский

При заданном ограничении опоры коэффициент (of R).symm (x • y) при a равен сумме по VAddAntidiagonal справа.

LaTeX

$$$((of\,R).symm \lvert x \cdot y\rvert).coeff\ a = \sum_{ij \in VAddAntidiagonal\,x.isPWO\_support\,((of\,R).symm\,y).isPWO\_support\ a} x.coeff i.fst \cdot ((of\,R).symm\,y).coeff i.snd$$$

Lean4

instance instBaseSMulZeroClass [SMulZeroClass R V] : SMulZeroClass R (HahnModule Γ R V) :=
  inferInstanceAs <| SMulZeroClass R (HahnSeries Γ V)

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