Kodaira symbols have their own type KodSym. Apart from the two functions that determine symbols for elliptic curves, there is a special creation function and a comparison operator, to test Kodaira symbols.

KodairaSymbol(E, p) : GeomEC -> MonStgElt

Given an elliptic curve E, defined over Q with integral coefficients, and a prime number p, this function returns the reduction type of E modulo p in the form of a Kodaira symbol.

Given an elliptic curve E, defined over Q with integral coefficients, this function returns the reduction types of E modulo the bad primes in the form of a sequence of Kodaira symbols.

Given a string s, return a Kodaira symbol it represents. The values of s that are allowed are: "I0", "I1", "I2", ..., "In", "II", "III", "IV", and "I0*", "I1*", "I2*", ..., "In*", "II*", "III*", "IV*". The dots stand for "Ik" with k a positive integer. This creation function is primarily useful for comparing values returned by the functions determining the Kodaira symbol for a curve.

Given two Kodaira symbols h and k, this functin returns true if and only if either both are identical, or one is generic (of the form "In", or "In*") and the other is specific of the same type: "In" will compare equal with any of "I1", "I2", "I3", etc., and "In*" will compare equal with any of "I1*", "I2*", "I3*", etc. Note however that "In" and "I3" are different from the point of view of set creation.