  In this paper we present the detailed formalism at the core of the Spectral
Line Identification and Modelling (SLIM) within the MAdrid Data CUBe Analysis
(MADCUBA) package and their main data handling functionalities. These tools
have been developed to visualize, analyze and model large spectroscopic data
cubes. We present the highly interactive on-the-fly visualization and modelling
tools of MADCUBA and SLIM, which includes an stand-alone spectroscopic
database. The parameters stored therein are used to solve the full radiative
transfer equation under Local Thermodynamic Equilibrium (LTE). SLIM provides
tools to generate synthetic LTE model spectra based on input physical
parameters of column density, excitation temperature, velocity, line width and
source size. SLIM also provides an automatic fitting algorithm to obtain the
physical parameters (with their associated errors) better fitting the
observations. Synthetic spectra can be overlayed in the data cubes/spectra to
easy the task of multi-molecular line identification and modelling.We present
the Java-based MADCUBA and its internal module SLIM packages which provide all
the necessary tools for manipulation and analysis of spectroscopic data cubes.
We describe in detail the spectroscopic fitting equations and make use of this
tool to explore the breaking conditions and implicit errors of commonly used
approximations in the literature. Easy-to-use tools like MADCUBA allow the
users to derive the physical information from spectroscopic data without the
need of resourcing to simple approximations. SLIM allows to use the full
radiative transfer equation, and to interactively explore the space of physical
parameters and associated uncertainties from observational data.
