Ryze's AP, Mana, Arcane Mastery while using Seraph's and Rabadon's; WITHOUT Recursion

So lately i have been figuring out these values from only using the starting values of Ryze. The main issue was that it is a recursive equation. I/we can now figure out his Final Mana, Final AP, Final Arcane mastery %, Final Rabadon's Passive amount, and Final Seraph's Embrace Passive Amount, While ONLY using starting ap and starting mana (ap and mana without Rabadon's passive, seraph's passive, or arcane mastery effecting it. Do add in Rabadon's and seraph's flat ap/mana to the starting values)

End_AP = (0.000021 • End_AP • Starting_Mana) + (0.042 • Starting_Mana) + (1.4 • Starting_AP) End_Mana = ((0.000021 • End_Mana) + (0.0007 • Starting_AP) + 1) • Starting_Mana Arcane_Mastery = (0.0005 • (0.042 • End_Mana + 1.4 • Starting_AP)) Rabadon's_Deathcap = (0.012 • End_Mana) + (0.4 • Starting_AP) Seraph's_Embrace = End_Mana • 0.03

X = Mana Y = AP A = Arcane Mastery R = Rabadon's S = Seraph's Subscript 0 = Starting Value (Only applies to Mana and AP) Subscript n = End Value (Only applies to Mana and AP)

Yₙ = 0.000021YₙX₀ + 0.042X₀ + 1.4Y₀ Xₙ = (0.000021Xₙ + 0.0007Y₀ + 1) • X₀ A = (0.0005 • (0.042Xₙ + 1.4Y₀)) R = 0.012Xₙ + 0.4Y₀ S = Xₙ • 0.03 Arcane mastery, Rabadon's Deathcap, and Seraph's Embrace require Xₙ (End_Mana) to be known before they can be figured out. See my comment below for equations that don't use End values at all.

EDIT: Please note that in game, it takes a few seconds for ryze's AP and Mana to settle on their final values - if riot used these equations, The related values would be solved FASTER than they are currently - @Riot please