  We present a unified framework for modelling genomes and their rearrangements
in a genome algebra, as elements that simultaneously incorporate all physical
symmetries. Building on previous work utilising the group algebra of the
symmetric group, we explicitly construct the genome algebra for the case of
unsigned circular genomes with dihedral symmetry and show that the maximum
likelihood estimate (MLE) of genome rearrangement distance can be validly and
more efficiently performed in this setting. We then construct the genome
algebra for the general case, that is, for genomes represented by elements of
an arbitrary group and symmetry group, and show that the MLE computations can
be performed entirely within this framework. There is no prescribed model in
this framework; that is, it allows any choice of rearrangements with arbitrary
weights. Further, since the likelihood function is built from path
probabilities -- a generalisation of path counts -- the framework may be
utilised for any distance measure that is based on path probabilities.
