\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;\red0\green0\blue255;} \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}p[1]:=x+y+z-6: \par \pard\li600\ri1\fi-300\plain\f3\fs22\cf1 p[2]:=x^2+y^2+z^2-14: \par p[3]:=x^4+y^4+z^4-98: \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}q[2]:=polylib::resultant(p[1],p[2],x) \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}q[3]:=polylib::resultant(p[1],p[3],x) \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}r[3]:=polylib::resultant(q[2],q[3],y) \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}factor(r[3]) \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}factor(subs(q[2],z=1)) \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}factor(subs(q[2],z=2)) \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}factor(subs(q[2],z=3)) \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}factor(subs(p[1],[y=2,z=1])) \par \pard\ri4\plain\f4\fs22\cf0 10. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}factor(subs(p[1],[y=3,z=1])) \par \pard\ri4\plain\f4\fs22\cf0 11. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}solve([p[i] $ i=1..3]) \par \pard\ri4\plain\f4\fs22\cf0 12. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}p[1]:=x^3+y^2-2: \par \pard\li600\ri1\fi-300\plain\f3\fs22\cf1 p[2]:=(x-y)^2-3: \par \pard\ri4\plain\f4\fs22\cf0 13. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}f:=factor(polylib::resultant(p[1],p[2],y)) \par \pard\ri4\plain\f4\fs22\cf0 14./15. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}delete r: \par \pard\li600\ri1\fi-300\plain\f3\fs22\cf1 Qr:=Dom::AlgebraicExtension(Dom::Rational,subs(f,x=r),r): \par \pard\ri4\plain\f4\fs22\cf0 16. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}p[1]:=poly(subs(p[1],x=r),[y],Qr): \par \pard\li600\ri1\fi-300\plain\f3\fs22\cf1 expr(factor(p[1])) \par \pard\ri4\plain\f4\fs22\cf0 17. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}p[2]:=poly(subs(p[2],x=r),[y],Qr): \par \pard\li600\ri1\fi-300\plain\f3\fs22\cf1 expr(factor(p[2])) \par \pard\ri4\plain\f4\fs22\cf0 18. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}solve([x^3+y^2-2,(x-y)^2-3]) \par }