backsolve

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backsolve

$\begin{usage} backsolve(a,p,st,r,c)\\ backsolve(a,p,st,r,b)\\ backsolve(a,p,st,r,c,d)\\ backsolve(a,p,st,r,b,d) \end{usage}$

$\begin{signatures} backsolve:& (M, Z $\to$\ Z,\htmlref{\texttt{PrimitiveArray}... ...rray} Z,Z,M,R)$\to$(M,\htmlref{\texttt{Vector}}{Vector} R)\\\end{signatures}$

$\begin{params} {\em a} & M & A matrix representing a Row Echelon Form (REF)\\ ... ...} & R & A maximal denominator needed for a dependence relation\\\end{params}$

where
Z == MachineInteger

$\begin{descr} Backsolves a triangular system. The triple $(a,p,st)$\ represent... ...rm th}}$\ column is called leading if $j=st(i)$\ for some $i$).\\\end{descr}$

$\begin{retval} backsolve(a,p,st,r,c) returns a primitive vector $v$\ such that... ... $s(j,l)\neq 0$\ only if the ${j}^{{\rm th}}$\ column is leading.\end{retval}$

Manuel Bronstein 2000-12-13