I'd like to add one thing to John's list:
3 - The rate of PO4 (phosphate) uptake in your tank.
Plants require Potassium (K), Nitrogen (N) (usually dilivered as NO3, nitrate), and Phosphorus (P) (supplied as PO4, phosphate) along with traces (which include Fe, Iron, Ca, Calcium, Mg, Magnesium, etc.)
Think of traces mainly as being necessary for plants to be able to use the macros (N, P, K), that's not strictly true since they have their own uses but it's an easy way to think of them since they're only supplied (and needed) in very small amounts.
The macros (N, P, K) and I suppose we should include carbon (C) (usually supplied as CO2) combined with light intensity will determine your plant growth rate. If one of these is in short supply, growth will slow and you'll likely see symptoms of a nutrient deficiency. If there's an imbalance you'll start seeing algae. The trick to a successful planted tank is balance.