X-Git-Url: https://git.distorted.org.uk/~mdw/catacomb/blobdiff_plain/ceb8d344ecb165be756a77ac8527c870b36945b2..a5591f917bd97e7b0874ee0f1fb158681382ae3e:/math/gfreduce.c?ds=sidebyside

diff --git a/math/gfreduce.c b/math/gfreduce.c
index 37703a43..582b723f 100644
--- a/math/gfreduce.c
+++ b/math/gfreduce.c
@@ -49,14 +49,15 @@ DA_DECL(instr_v, gfreduce_instr);
  * 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.