\mnb150ÿ{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\fmodern\fprq1 Courier New;}{\f4\froman\fcharset1 Times New Roman;}} {\colortbl\red0\green0\blue0;\red255\green0\blue0;} \deflang1031\pard\ri4\plain\f4\fs22\cf0 01. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}a:=x^3-4 \par \pard\ri4\plain\f4\fs22\cf0 02. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}divide(a,x-4^(1/3),Quo) \par \pard\ri4\plain\f4\fs22\cf0 03. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}divide(a,x-4^(1/3),Rem) \par \pard\ri4\plain\f4\fs22\cf0 04. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}Qr:=Dom::AlgebraicExtension(Dom::Rational,r^3-4): \par \pard\li600\ri1\fi-300\plain\f3\fs22\cf1 a:=poly(x^3-4,[x],Qr): \par b:=poly(x-r,[x],Qr): \par q[1]:=divide(a,b,Quo) \par \pard\ri4\plain\f4\fs22\cf0 05. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}Qrs:=Dom::AlgebraicExtension(Qr,s^2+r*s+r^2,s): \par \pard\li600\ri1\fi-300\plain\f3\fs22\cf1 c:=poly(x-s,[x],Qrs): \par q[1]:=poly(x^2+r*x+r^2,[x],Qrs): \par q[2]:=divide(q[1],c,Quo) \par \pard\ri4\plain\f4\fs22\cf0 06. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}collect((x-r)*(x-s)*(x-t),x) \par \pard\ri4\plain\f4\fs22\cf0 07. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}a:=x^3-4: \par \pard\li600\ri1\fi-300\plain\f3\fs22\cf1 q[1]:=divide(a,x-RootOf(x^3-4,x),Quo) \par \pard\ri4\plain\f4\fs22\cf0 08. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}divide(q[1],x-RootOf(x^3-4,x),Quo) \par \pard\ri4\plain\f4\fs22\cf0 09. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}subs(solve(subs(q[1],RootOf(x^3-4,x)=t),x),t=RootOf(x^3-4,x)) \par }