We give an introduction to the transalgebraic theory of simply connected
log-Riemann surfaces with a finite number of infinite ramification points
(transalgebraic curves of genus 0). We define the base vector space of
transcendental functions and establish by elementary means some transcendental
properties. We introduce the Ramificant Determinant constructed with
transcendental periods and we give a closed-form formula that gives the main
applications to transalgebraic curves. We prove an Abel-like Theorem and a
Torelli-like Theorem. Transposing to the transalgebraic curve the base vector
space of transcendental functions, they generate the structural ring from which
the points of the transalgebraic curve can be recovered algebraically,
including infinite ramification points.Comment: see also arXiv:1512.0377
