is there any difference between (with-modular-arithmetic prime body) and (fpoly-mod (progn body) prime)? If so, then we may as well forget about with-modular-arithmetic altogether and just take the modulo at the end of the computation.
this is false. although the final result may be the same, intermediate results must also be guaranteed to be performed modulo prime. this is why we need it.
is there any difference between (with-modular-arithmetic prime body) and (fpoly-mod (progn body) prime)? If so, then we may as well forget about with-modular-arithmetic altogether and just take the modulo at the end of the computation.