paul zimmermann on Tue, 12 Jan 2016 15:02:27 +0100 |
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review of character functions |
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