## "Fossies" - the Fresh Open Source Software Archive

### Source code changes of the file "src/functions/number_fields/bnfisprincipal" betweenpari-2.13.0.tar.gz and pari-2.13.1.tar.gz

About: PARI/GP is a computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves...), but also contains a large number of other mathematical functions.

bnfisprincipal  (pari-2.13.0):bnfisprincipal  (pari-2.13.1)
Function: bnfisprincipal Function: bnfisprincipal
Section: number_fields Section: number_fields
C-Name: bnfisprincipal0 C-Name: bnfisprincipal0
Prototype: GGD1,L, Prototype: GGD1,L,
Help: bnfisprincipal(bnf,x,{flag=1}): bnf being output by bnfinit, gives Help: bnfisprincipal(bnf,x,{flag=1}): bnf being output by bnfinit, gives
[e,t], where e is the vector of exponents on [e,t], where e is the vector of exponents on the class group generators and
the class group generators and t is the generator of the resulting t is the generator of the resulting principal ideal. In particular x is
principal ideal. In particular x is principal if and only if is the zero principal if and only if e is the zero vector. flag is optional, whose
vector. flag is optional, whose binary digits mean 1: output [e,t] (only e binary digits mean 1: output [e,t] (only e if unset); 2: increase precision
if unset); 2: increase precision until alpha can be computed (do not insist until alpha can be computed (do not insist if unset); 4: return alpha in
if unset); 4: return alpha in factored form (compact representation). factored form (compact representation).
Doc: $\var{bnf}$ being the \sidx{principal ideal} Doc: $\var{bnf}$ being the \sidx{principal ideal}
number field data output by \kbd{bnfinit}, and $x$ being an ideal, this number field data output by \kbd{bnfinit}, and $x$ being an ideal, this
function tests whether the ideal is principal or not. The result is more function tests whether the ideal is principal or not. The result is more
complete than a simple true/false answer and solves a general discrete complete than a simple true/false answer and solves a general discrete
logarithm problem. Assume the class group is $\oplus (\Z/d_i\Z)g_i$ logarithm problem. Assume the class group is $\oplus (\Z/d_i\Z)g_i$
(where the generators $g_i$ and their orders $d_i$ are respectively given by (where the generators $g_i$ and their orders $d_i$ are respectively given by
\kbd{bnf.gen} and \kbd{bnf.cyc}). The routine returns a row vector $[e,t]$, \kbd{bnf.gen} and \kbd{bnf.cyc}). The routine returns a row vector $[e,t]$,
where $e$ is a vector of exponents $0 \leq e_i < d_i$, and $t$ is a number where $e$ is a vector of exponents $0 \leq e_i < d_i$, and $t$ is a number
field element such that field element such that
$$x = (t) \prod_i g_i^{e_i}.$$ $$x = (t) \prod_i g_i^{e_i}.$$
End of changes. 1 change blocks.
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