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\section{Component expansion}
# algorithm:
#
# - need to cache information because there are potentially many operations
# - need to canonicalise indices
#
# Eval first works at C_{\alpha} level.
#
#
# Estimates:
#
# Kretschmann in 10d: 10^4 values to sum over. So we need to be able to cut
# this down to the non-zero ones early: as soon as a zero combination is found
# for one of the factors, remove this branch of the search tree.
# Need to:
# a) make the algorithm work at the top, recursively down, since
we need to keep memory/cache of already evaluated objects.
# b) for all levels recursively visited, determine whether substitution
# rules fix the value (hence allowing D_1 + E_1 -> 3 even if E_1 is
# not known as a component.
# c) use a 'base n' type notation to map an index value combination for
# an n-valent tensor to an integer, so that we can make a map from
# integers to expressions for any tensor, avoiding repeated substitutions.
#
# A_m ( B_m + C_m ) D_n Q_n:
#
# - collect free and dummy indices.
# - do a depth-first walk
# - for each node, determine the index values for which
# a rule is available
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