we wold need:
We then add elements into the ideal that represents our constraints.
For example, to perform dataflow analysis, we need to add constraints
about how if a variable
R = F_2[x0, y0, z0, x1, y1, z1, x2, y2, z2, x3, y3, z3, x100, y100, z100]
z is alive, all variables that are used
100 are alive. This sets up equations that may
have cycles (in the case of loops).
These are usually resolved using the
Kildall algorithm .
However, we can also ask SAGE to kindly solve the Grobner basis. I hypothesize
that the "easy" dataflow problems out to be toric ideals
which admit much faster solutions.