In [1], we construct singular varieties
associated to a polynomial mapping
where
such that if G is a local submersion
but is not a fibration, then the 2-dimensional homology and intersection
homology (with total perversity) of the variety
are not trivial. In [2], the
authors prove that if there exists a so-called
very good projection with
respect to the regular value of a polynomial mapping
, then this value is an
atypical value of G if and only if the Euler characteristic of the fibers is
not constant. This paper provides relations of the results obtained in the
articles [1] and [2]. Moreover, we provide some examples to illustrate these
relations, using the software Maple to complete the calculations of the
examples. We provide some discussions on these relations. This paper is an
example for graduate students to apply a software that they study in the
graduate program in advanced researches.