# How to derive formulas for addition and multiplication in Jacobian coordinates

Is there a way to derive the formulas for point addition and multiplication on elliptic curves in Jacobian format by yourself? How could I have derived these formulas by myself?

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The $Z^2$ or $Z^3$ aspect is just shuffling multiplications around to make doubling slightly faster versus addition or vice-versa or to do with being able to add an affine point to a projective point more quickly. It tends not to matter too much. If you want faster calculations you should be choosing perhaps an Edwards curve representation and/or maths over an appropriately fast extension field.