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changed QQ // ZZ to / in WeylGroups::scalarProduct
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mahrud committed Aug 14, 2024
1 parent a1e3396 commit 80e30c8
Showing 1 changed file with 3 additions and 3 deletions.
6 changes: 3 additions & 3 deletions M2/Macaulay2/packages/WeylGroups.m2
Original file line number Diff line number Diff line change
Expand Up @@ -539,19 +539,19 @@ scalarProduct = method()
--the scalar product of the i-th fundamental weight with the j-th
scalarProduct(RootSystem,ZZ,ZZ) := (R,i,j) ->
(
((R.CartanMatrixTrInv)_(j-1,i-1))*(R.RootNorms#(j-1))//2
((R.CartanMatrixTrInv)_(j-1,i-1))*(R.RootNorms#(j-1)) / 2
)

--the scalar product of two general weights
scalarProduct(RootSystem,Weight,Weight) := (R,u,v) ->
(
sum apply(apply(entries((R.CartanMatrixTrInv)*u),entries(v),(x,y)->x*y),R.RootNorms,(x,y)->x*y)//2
sum apply(apply(entries((R.CartanMatrixTrInv)*u),entries(v),(x,y)->x*y),R.RootNorms,(x,y)->x*y) / 2
)

--the scalar product of the i-th fundamental weight with a general weight
scalarProduct(RootSystem,ZZ,Weight) := (R,i,v) ->
(
(((R.CartanMatrixTrInv)*v)_(i-1))*(R.RootNorms#(i-1))//2
(((R.CartanMatrixTrInv)*v)_(i-1))*(R.RootNorms#(i-1)) / 2
)

--the dual of a root evaluated at something
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