 <!--  Presentation generated by Internet Assistant for Microsoft PowerPoint 97 -->  <HTML> <HEAD>  <meta name="GENERATOR" content="Microsoft Internet Assistant for Microsoft PowerPoint 97">  <TITLE>Valence Smith Form of a matrix A</TITLE>  </HEAD>  <BODY     >  <CENTER> <TABLE WIDTH=100%>       <TR> <TD WIDTH=85% ALIGN=CENTER>          <IMG SRC="img014.gif" usemap="#Objmap" WIDTH=640 HEIGHT=512 BORDER=0>          <TD WIDTH=15% ALIGN=CENTER>         <A HREF="sld001.htm"><IMG SRC="first.gif" BORDER=0 ALT="Premier"></A><BR>           <A HREF="sld013.htm"><IMG SRC="prev.gif" BORDER=0 ALT="Prcdent"></A><BR>           <A HREF="sld015.htm"><IMG SRC="next.gif" BORDER=0 ALT="Suivant"></A><BR>           <A HREF="sld034.htm"><IMG SRC="last.gif" BORDER=0 ALT="Dernier"></A><BR>  <BR>           <A HREF="index.htm"><IMG SRC="info.gif" BORDER=0 ALT="Index "></A><BR>           <A HREF=""><IMG SRC="home.gif" BORDER=0 ALT="Dmarrage"></A><BR>           <A HREF="tsld014.htm"><IMG SRC="text.gif" BORDER=0 ALT="Texte "></A><BR>           </TD>         </TD></TABLE> <P>Diapositive 14 sur 34</P> </CENTER> <!-- <UL> <H2>Valence Smith Form of a matrix A</H2> </UL></P> <P><UL> <LI><H2>Valence Computation </H2> <UL> <LI>Product of at least all the primes appearing in the invariant factors of A <LI> </UL></UL><UL> <LI><H2>Set of primes </H2> <UL> <LI>factor the valence v, L is the set of primes dividing v <LI> </UL></UL><UL> <LI><H2>Integer Rank </H2> <UL> <LI>q ? L, r = rankq(A)  ? there are r non-zero invariant factors </UL></UL><UL> <LI><H2> </H2> </UL><UL> <LI><H2>Non-trivial invariant factors </H2> <UL> <LI>?p?L, compute Sp, the local Smith form at p. S = S ? Sp <LI> </UL></UL><UL> <LI><H2>Return S</H2> </UL></P> <P><UL> <LI>Valence Computation <UL> <LI>Product of at least all the primes appearing in the invariant factors of A <LI> </UL></UL><UL> <LI>Set of primes <UL> <LI>factor the valence v, L is the set of primes dividing v <LI>Reduce the size of L  </UL></UL><UL> <LI>Integer Rank <UL> <LI>q ? L, r = rankq(A)  ? there are r non-zero invariant factors </UL></UL><UL> <LI> </UL><UL> <LI>Non-trivial invariant factors <UL> <LI>?p?L, compute Sp, the local Smith form at p. S = S ? Sp <LI> </UL></UL><UL> <LI>Return S</UL></P> <P>  --> </Body> </HTML> 
