# composition of function This post is a wiki. Anyone with karma >750 is welcome to improve it.

f(z1z2) , g(z1)

z1 and z2 are two points on elliptic curve so z1=(z+3a+4) and z2=(z+3a) z1 and z2 addition of two points and z1 is doubling point function

p=5
A=4
B=4
K.<a>=GF(p^2);K.modulus()
#R.<z>=PolynomialRing(K);
R.<z> = PolynomialRing( K, sparse=True )
E = EllipticCurve(GF(p),[0,0,0,A,B]);
#print"EC=",E
#print (E.points()[:4])

#print "\n Take Two point on Elliptic curve "
P =E(1,2)
print"point1=",P                           # select Random point P on elliptic Curve
Q =E(0,2)

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Please give a mathematical description of the functions $f$ and $g$, including their (co)domains. If code is given, then try to find minimal shapes for it that introduce the framework of the problem in a clear way. Above, as in the other post, nothing, really nothing can be understood, not even guessed. For instance, the given curve E is defined simply as
E = EllipticCurve( GF(5), [ 0,0,0,4,4 ] )    # or just [4,4] as coefficients input

And there is no connection to the polynomial ring $K[z]$ in a new variable $z$, that cannot be used in the context. Here, $K$ is the field with $25$ elements, generated by $a$ over F=GF(5), and we neither use (properly) a, nor K, nor R. A point on the curve has two components. And E is defined / F - not even over K. So z is forbidden in E!