The easiest way to use FIRE is to work in pure Laporta mode. In this case one has only to specify the IBP's, the symmetries and the boundary conditions.

One of the differences between FIRE and most Laporta algorithms is the following: after specifying the initial data the use can simply request FIRE for an integral; there is no need to go through sectors (topologies) and seed the dots and numerators step by step. To the contrary, FIRE starts from the top-level integrals, generates the required IBP's, solves them, then goes down and so on. During this procedure the tail-masking is performed to avoid the growth of coefficients. After reducing everything to master-integrals the substituion is performed.

However FIRE is not only a Laporta algorithm. It turns most powerful in case the s-bases are constructed in most sectors. In this case one no longer need to solve IBP's in those sectors, but simply to substitute the values into the existing solutions.

The following sections will use one more term: a region, - a subset of indices (a_1,...a_n) where some of the a_i are positive and some are non-positive. A region is defined by a set of 1s, -1s and 0s; the indices corresponding to 1 are positive, the ones corresponding to -1 are non-positive, the ones corresponding to 0 can be of any sign.

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