\title	{Propiedades algebraicas II}
\author	{XIAO Gang}
\email	{xiao@unice.fr}
\format	{html}

\text{yes=Siempre verdadero}
\text{no=Siempre falso}
\text{dep=Depende}
\text{bad=\yes,\no,\dep}
\text{ABCs=shuffle(A,B,C)}
\text{At=item(1,\ABCs)}
\text{Bt=item(2,\ABCs)}
\text{Ct=item(3,\ABCs)}
\text{ABBA=random(AB,BA)}
\text{aplusb=random(\At+\Bt,\Bt+\At)}
\text{terms=shuffle(\At,\At\Bt,\At\Bt\Ct,\Ct^2)}
\text{term1=item(1,\terms)}
\text{term2=item(2,\terms)}
\text{term3=item(3,\terms)}
\text{eq=random(=,\ne)}
\text{yesno=\eq issametext \ne?\no:\yes}
\integer{n=random(2..10)}
\text{pm=random(+,-)}
\text{comma=random(\At \pm I_\n,\At \pm \At^2,\At^2 \pm \At,I_\n \pm \At)}

\matrix{data=
\(\At\Bt \eq \Bt\At), \dep
\(\term1 + \term2 \eq \term2 + \term1), \yesno
\(\term1 + \Bt\Ct \eq \Ct\Bt + \term1), \dep
\(\At(\Bt\Ct) \eq (\At\Bt)\Ct), \yesno
\(\At(\Bt\Ct) \eq random((\At\Ct)\Bt,(\Bt\Ct)\At)), \dep
\(\At + (\Bt + \Ct) \eq A + (B + C)), \yesno
\((\At + \Bt)(\At - \Bt) \eq \At^2 - \Bt^2), \dep
\((\At + \Bt)^2 \eq \At^2 +2\At\Bt + \Bt^2), \dep
\(\At(\Bt+\Ct) \eq (\Bt+\Ct)\At), \dep
\(\At(\Bt+\Ct) \eq \At(\Ct+\Bt)), \yesno
\(\At(\Bt+\Ct) \eq \Bt(\Ct+\At)), \dep
\(\At^2 + \At\Bt \eq \At(\aplusb)), \yesno
\(\At^2 + \Bt\At \eq \At(\aplusb)), \dep
\(\At^2 + \At\Bt \eq (\aplusb)\At), \dep
\(\At^2 + \Bt\At \eq (\aplusb)\At), \yesno
\(\At^2\Bt \eq \At(\At\Bt)), \yesno
\(\At\Bt^2 \eq (\At\Bt)\Bt), \yesno
\(\At^2\Bt \eq random((\At\Bt)\At,\At(\Bt\At))), \dep
\(\At\Bt^2 \eq random((\Bt\At)\Bt,\Bt(\Bt\At))), \dep
\(\At(\Bt+\Ct)\At \eq random(\At^2(\Bt+\Ct),(\Bt+\Ct)\At^2)), \dep
\(\At(\comma) \eq (\comma)\At), \yesno

}

text{data=
\(\At^2 + \At\Bt \eq \At(\aplusb)), \yesno
}

\text{data=randomrow(\data)}
\text{prop=item(1,\data)}
\text{good=item(2,\data)}

\if{C isin \prop}{
 \text{mats=Sean \(A), \(B), \(C) tres matrices \n×\n }
}{
 \if{B isin \prop}{
  \text{mats=Sean \(A), \(B) dos matrices \n×\n }
 }{
  \text{mats=Sea \(A) una matriz \n×\n }
 }
}

\statement{\mats. ¿Es cierta la siguiente propiedad?
<p><center>
 \prop
</center><p>
\if{I_\n isin \prop}{
 (\(I_\n) es la matriz identidad \n×\n .)
}
}

\choice{La respuesta}{\good}{\bad}
