  Motivated by the foundational work of Tarasov, who pointed out that the
algebraic relations of the type considered here can lead to functional
reduction of Feynman integrals, we suitably modify the original method to be
able to implement and automatize it and present a $\textit{Mathematica}$
package $\texttt{AlgRel.wl}$. The purpose of this package is to help derive the
algebraic relations with arbitrary kinematic quantities, for the product of
propagators. Under specific choices of the arbitrary parameters that appear in
these relations, we can write the original integral with all massive
propagators in general, as a sum of integrals which have fewer massive
propagators. The resulting integrals are of reduced complexity for
computational purposes. For the one-loop cases, with all different and non-zero
masses, this would result in integrals with one massive propagator. We also
devise a strategy so that the method can also be applied to higher-loop
integrals. We demonstrate the procedure and the results obtained using the
package for various one-loop and higher-loop examples. Due to the fact that the
Feynman integrals are intimately related to the hypergeometric functions, a
useful consequence of these algebraic relations is in deriving the sets of
non-trivial reduction formulae. We present various such reduction formulae and
further discuss how, more such formulae can be obtained than described here.
The $\texttt{AlgRel.wl}$ package and an example notebook $\texttt{Examples.nb}$
can be found at
https://github.com/TanayPathak-17/Algebraic-relation-for-the-product-of-propagators
