# CheckSomos¶

CheckSomos is an auxiliary package that translates the representation of Somos at url{https://web.archive.org/web/20190709153133/http://eta.math.georgetown.edu/eta07.gp} in terms of Euler functions to our representation in terms of eta functions.

fromEta: (NonNegativeInteger, Polynomial Integer) -> Polynomial Integer

fromEta(m, p) expresses a polynomial p in variables Ei (corresponding to eta(i*tau)) in terms of variables q and ui where the ui correspond to the Euler functions of level m. https://en.wikipedia.org/wiki/Euler_function).

member?: (NonNegativeInteger, Polynomial Integer, List Polynomial Integer) -> Boolean

member?(m, s, gb) returns true if s is in the ideal given by the (assumed degrevlex) Groebner bases gb for the eta relations of level m.

toEta: (NonNegativeInteger, Polynomial Integer) -> Polynomial Integer

toEta(m, p) expresses the p (given as a polynomial in variables ui and q where the ui correspond to the Euler functions of level m https://en.wikipedia.org/wiki/Euler_function) into an expression in variables Ei (corresponding to eta(i*tau)). The ui and Ei correspond to level m.