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# Product between PolyVar and Monomial -> Monomial
function Base.:(*)(x::PolyVar{true}, y::PolyVar{true})
if x === y
Monomial{true}([x], [2])
else
Monomial{true}(x > y ? [x,y] : [y,x], [1,1])
end
end
function multiplyvar(v::Vector{PolyVar{true}}, x::PolyVar{true})
i = findfirst(w->w <= x, v)
if (i != nothing && i > 0) && v[i] == x
multiplyexistingvar(v, x, i)
else
insertvar(v, x, (i == nothing || i == 0) ? length(v)+1 : i)
end
end
function Base.:(*)(x::PolyVar{true}, y::Monomial{true})
w, updatez = multiplyvar(y.vars, x)
Monomial{true}(w, updatez(y.z))
end
Base.:(*)(y::MonomialVector{true}, x::PolyVar{true}) = x * y
function Base.:(*)(x::PolyVar{true}, y::MonomialVector{true})
w, updatez = multiplyvar(y.vars, x)
MonomialVector{true}(w, updatez.(y.Z))
end
function multdivmono(v::Vector{PolyVar{true}}, x::Monomial{true}, op)
if v == x.vars
# /!\ no copy done here for efficiency, do not mess up with vars
w = v
updatez = z -> op.(z, x.z)
else
w, maps = mergevars([v, x.vars])
updatez = z -> begin
newz = zeros(Int, length(w))
I = maps[1]; i = 1; lI = length(I)
J = maps[2]; j = 1; lJ = length(J)
while i <= lI || j <= lJ
if i > lI || (j <= lJ && J[j] < I[i])
newz[J[j]] = op(0, x.z[j])
j += 1
elseif j > lJ || (i <= lI && I[i] < J[j])
newz[I[i]] = op(z[i], 0)
i += 1
else
@assert I[i] == J[j]
newz[I[i]] = op(z[i], x.z[j])
i += 1
j += 1
end
end
newz
end
end
w, updatez
end
function MP.mapexponents(f, x::Monomial{true}, y::Monomial{true})
w, updatez = multdivmono(x.vars, y, f)
Monomial{true}(w, updatez(x.z))
end
function Base.:(*)(x::Monomial{true}, y::MonomialVector{true})
w, updatez = multdivmono(y.vars, x, +)
MonomialVector{true}(w, updatez.(y.Z))
end
Base.:(*)(y::MonomialVector{true}, x::Monomial{true}) = x * y
Base.:(*)(x::Monomial{true}, y::PolyVar{true}) = y * x
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