nemo exponential

gistfile1.txt

function exp{T <: Ring}(a::T)
   a != 0 && error("Exponential of nonzero element")
   return one(T)
end

function exp{T<: Ring, S}(a::PowerSeries{T, S})
   if a == 0
      return PowerSeries(PowerSeries{T, S}, [one(T)], a.prec)
   elseif a.prec == nothing
      error("Unable to compute exponential of infinite precision power series")
   end
   d = Array(T, a.prec)
   d[0+1] = exp(coeff(a, 0))
   len = length(a)
   for k = 1 : a.prec-1
      s = zero(T)
      for j = 1 : min(k+1, len) - 1
         s += j * coeff(a, j) * d[k-j+1]
      end
      d[k+1] = s / k
   end
   b = PowerSeries(PowerSeries{T, S}, d, a.prec)
   return b
end

function exp{S}(a::PowerSeries{QQ, S})
   if a == 0
      return PowerSeries(PowerSeries{QQ, S}, [QQ(1)], nothing)
   elseif a.prec == nothing
      error("Unable to compute exponential of infinite precision power series")
   end
   b = PowerSeries(PowerSeries{QQ, S}, Array(QQ, 0), a.prec)
   ccall((:fmpq_poly_exp_series, :libflint), Void, 
                (Ptr{PowerSeries}, Ptr{PowerSeries}, Int), 
               &b, &a, a.prec)
   return b
end