review of character functions

[paul zimmermann <Paul.Zimmermann@inria.fr>]

diff --git a/src/functions/number_fields/bnrconductor b/src/functions/number_fields/bnrconductor
index a397b77..407c06e 100644
--- a/src/functions/number_fields/bnrconductor
+++ b/src/functions/number_fields/bnrconductor
@@ -25,7 +25,7 @@ Doc: conductor $f$ of the subfield of a ray class field as defined by $[A,B,C]$
  In place of a subgroup $H$, this function also accepts a character
  \var{chi}  $=(a_j)$, expressed as usual in terms of the generators
  \kbd{bnr.gen}: $\chi(g_j) = \exp(2i\pi a_j / d_j)$, where $g_j$ has
- has order $d_j = \kbd{bnr.cyc[j]}$. In which case, the function returns
+ order $d_j = \kbd{bnr.cyc[j]}$. In which case, the function returns
  respectively
 
  If $\fl = 0$, the conductor $f$ of $\text{Ker} \chi$.
diff --git a/src/functions/number_theoretical/charconj b/src/functions/number_theoretical/charconj
index 93b6bc0..19c0231 100644
--- a/src/functions/number_theoretical/charconj
+++ b/src/functions/number_theoretical/charconj
@@ -7,7 +7,7 @@ Help: charconj(cyc,chi): given a finite abelian group (by its elementary
 Doc: let \var{cyc} represent a finite abelian group by its elementary
  divisors, i.e. $(d_j)$ represents $\sum_{j \leq k} \Z/d_j\Z$ with $d_k
  \mid \dots \mid d_1$; any object which has a \kbd{.cyc} method is also
- allowed, e.g. the output of \kbd{znstar} or \kbd{bnrinit}. A character
+ allowed, e.g.~the output of \kbd{znstar} or \kbd{bnrinit}. A character
  on this group is given by a row vector $\chi = [a_1,\ldots,a_n]$ such that
  $\chi(\prod g_j^{n_j}) = \exp(2\pi i\sum a_j n_j / d_j)$, where $g_j$ denotes
  the generator (of order $d_j$) of the $j$-th cyclic component.
diff --git a/src/functions/number_theoretical/charker b/src/functions/number_theoretical/charker
index 92062b0..a752ae1 100644
--- a/src/functions/number_theoretical/charker
+++ b/src/functions/number_theoretical/charker
@@ -7,7 +7,7 @@ Help: charker(cyc,chi): given a finite abelian group (by its elementary
 Doc: let \var{cyc} represent a finite abelian group by its elementary
  divisors, i.e. $(d_j)$ represents $\sum_{j \leq k} \Z/d_j\Z$ with $d_k
  \mid \dots \mid d_1$; any object which has a \kbd{.cyc} method is also
- allowed, e.g. the output of \kbd{znstar} or \kbd{bnrinit}. A character
+ allowed, e.g.~the output of \kbd{znstar} or \kbd{bnrinit}. A character
  on this group is given by a row vector $\chi = [a_1,\ldots,a_n]$ such that
  $\chi(\prod g_j^{n_j}) = \exp(2\pi i\sum a_j n_j / d_j)$, where $g_j$ denotes
  the generator (of order $d_j$) of the $j$-th cyclic component.
diff --git a/src/functions/number_theoretical/charorder b/src/functions/number_theoretical/charorder
index 4c278a5..7a24ccb 100644
--- a/src/functions/number_theoretical/charorder
+++ b/src/functions/number_theoretical/charorder
@@ -7,7 +7,7 @@ Help: charorder(cyc,chi): given a finite abelian group (by its elementary
 Doc: let \var{cyc} represent a finite abelian group by its elementary
  divisors, i.e. $(d_j)$ represents $\sum_{j \leq k} \Z/d_j\Z$ with $d_k
  \mid \dots \mid d_1$; any object which has a \kbd{.cyc} method is also
- allowed, e.g. the output of \kbd{znstar} or \kbd{bnrinit}. A character
+ allowed, e.g.~the output of \kbd{znstar} or \kbd{bnrinit}. A character
  on this group is given by a row vector $\chi = [a_1,\ldots,a_n]$ such that
  $\chi(\prod g_j^{n_j}) = \exp(2\pi i\sum a_j n_j / d_j)$, where $g_j$ denotes
  the generator (of order $d_j$) of the $j$-th cyclic component.
@@ -21,7 +21,7 @@ Doc: let \var{cyc} represent a finite abelian group by its elementary
  ? bnf.cyc
  %4 = [3]
  ? charorder(bnf, [1])
- %5 = [3]
+ %5 = 3
  @eprog
 
 Variant: Also available is
diff --git a/src/functions/number_theoretical/znconreyconductor b/src/functions/number_theoretical/znconreyconductor
index 50eae8b..c38b6f1 100644
--- a/src/functions/number_theoretical/znconreyconductor
+++ b/src/functions/number_theoretical/znconreyconductor
@@ -23,11 +23,11 @@ Doc: Let \var{bid} be associated to $(\Z/q\Z)^*$ (as per \kbd{bid =
  primitive character.
 
  \bprog
- ? G = idealstar(,126000)
+ ? G = idealstar(,126000);
  ? znconreyconductor(G,11)   \\ primitive
  %2 = 126000
  ? znconreyconductor(G,1)    \\ trivial character, not primitive!
  %3 = [1, matrix(0,2)]
  ? znconreyconductor(G,1009) \\ character mod 5^3
- %4 = [125, Mat([5, 3])]
+ %4 = [1, matrix(0,2)] % PZ: bug???
  @eprog\noindent
diff --git a/src/functions/polynomials/polmodular b/src/functions/polynomials/polmodular
index 1aae5a1..cf47c01 100644
--- a/src/functions/polynomials/polmodular
+++ b/src/functions/polynomials/polmodular
@@ -36,7 +36,7 @@ Variant: Also available are
  v, int compute_derivs} which returns the modular polynomial evaluated
  at $J$ modulo $P$ in the variable $v$ (if \kbd{compute\_derivs} is
  non-zero, returns a vector containing the modular polynomial and its
- first and second derivatives, all evaluted at $J$ modulo $P$).
+ first and second derivatives, all evaluated at $J$ modulo $P$).
 
 Function: _polmodular_worker
 Section: programming/internals