ez:=proc(): print(`RP(K,d,x), RC(K,d,x,n), EvalC(C,x,x0), DiffEvalC(C,x,x0) `): end:
RP:=proc(K,d,x) local ra,i:

ra:=rand(-K..K):

add(ra()*x^i,i=0..d):
end:

#RC(K,d,x,n)
RC:=proc(K,d,x,n) local i:
[seq(RP(K,d,x),i=1..n)]:
end:

EvalC:=proc(C,x,x0) local i,C0:
C0:=[subs(x=x0,C[1])]:

for i from 2 to nops(C) do
 C0:=[op(C0),expand(subs(x=C0[i-1],C[i]))]:
od:
C0:
end:


#DiffEvalC(C,x,x0): the derivatives of the chain C evaluated at x0. Try
#DiffEvalC([1+x,x^2+1,x^3],x,2);
DiffEvalC:=proc(C,x,x0) local Cd,C0,i,Cd0:
Cd:=diff(C,x):
C0:=EvalC(C,x,x0):

Cd0:=[subs(x=x0,Cd[1])]:
for i from 2 to nops(C) do
 Cd0:=[op(Cd0),subs(x=C0[i-1],Cd[i])*Cd0[i-1]]:
od:
Cd0:

end:


#DiffEvalCstu(C,x,x0): the derivatives of the chain C evaluated at x0. Try
#DiffEvalCstu([1+x,x^2+1,x^3],x,2);
DiffEvalCstu:=proc(C,x,x0) local y:
subs(y=x0,diff(EvalC(C,x,y),y)):
end: