* sense fast. Here, we do efficient reduction modulo sparse polynomials.
* (It works for arbitrary polynomials, but isn't efficient for dense ones.)
*
- * Suppose that %$p(x) = x^n + p'(x) = \sum_{0\le i<n} p_i x^i$%, hopefully
- * with only a few other %$p_i \ne 0$%. We're going to compile %$p$% into a
- * sequence of instructions which can be used to perform reduction modulo
- * %$p$%. The important observation is that %$x^n \equiv p' \pmod p$%.
+ * Suppose that %$p = x^n + p'$% where %$p' = \sum_{0\le i<n} p_i x^i$%,
+ * hopefully with only a few %$p_i \ne 0$%. We're going to compile %$p$%
+ * into a sequence of instructions which can be used to perform reduction
+ * modulo %$p$%. The important observation is that
+ * %$x^n \equiv p' \pmod p$%.
*
* Suppose we're working with %$w$%-bit words; let %$n = N w + n'$% with
* %$0 \le n' < w$%. Let %$u(x)$% be some arbitrary polynomial. Write
- * %$u = z x^k + u'$% with %$\deg u' < k \ge n$%; then a reduction step uses
+ * %$u = z x^k + u'$% with %$\deg u' < k \ge n$%. Then a reduction step uses
* that %$u \equiv u' + z p' x^{k-n} \pmod p$%: the right hand side has
* degree %$\max \{ \deg u', k + \deg p' - n + \deg z \} < \deg u$%, so this
* makes progress towards a complete reduction.