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6108000000FA0200000000000000000000040000002D01080004000000F001000007000000FC02 0000FFFFFF000000040000002D01000004000000F00101001C000000FB021000070000000000BC 02000000000102022253797374656D00774000000036060A4F7DA8F47786A8F477010000000000 3000040000002D010100040000002701FFFF04000000F001020004000000F001030004000000F0 01040004000000F001050004000000F001060004000000F0010700040000002701FFFF03000000 0000 }\plain\f3\fs22\cf2\protect \par \pard\li50\ri2\plain\f3\fs22\cf2\protect \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}sol:=solve(\{eq\},Domain=IntMod(p)) \par \pard\li50\ri6\plain\f3\fs22\cf2\protect Error: Solving over a domain works only for exactly one variable [solvelib::dom\\ \par \pard\li50\ri2\plain\f3\fs22\cf2\protect solve] \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}MatA:=Dom::Matrix(Dom::IntegerMod(p))([[coeff(eq[i],[bet[k] $ k=1..5]),0] $ i=1..nops(eq)]); \par \pard\li50\ri6\plain\f3\fs22\cf2\protect {\pict\wmetafile8\picw12989\pich3094\picwgoal7363\pichgoal1754 0100090000038F08000008001C0000000000050000000B0200000000050000000C02160CBD3203 0000001E00030000001E00050000000C02DA06C41C050000000B020000000014000000FF060000 0600F602000024000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D0100 0004000000F001000008000000FA0200000000000000000000040000002D01000007000000FC02 0000000000000000040000002D0101001C000000FB0210FF000000000000900100000001070000 00417269616C00F47740000000E6050AC47DA8F47786A8F4770100000000003000040000002D01 020005000000020101000000050000000102FFFFFF00050000002E011800000005000000090200 00000004000000080100001C000000FB0210FF0000000000009001000000010700000054696D65 73204E657720526F6D616E007DA8F47786A8F4770100000000003000040000002D0103000B0000 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7786A8F4770100000000003000040000002D010100040000002701FFFF04000000F00102000400 0000F001030004000000F001040004000000F001050004000000F001060004000000F001070004 000000F001080004000000F001090004000000F0010A0004000000F0010B00040000002701FFFF 030000000000 }\plain\f3\fs22\cf2\protect \par \pard\li50\ri2\plain\f3\fs22\cf2\protect \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}Berlekamp:=proc(A,x,p) \par \pard\li600\ri1\fi-300\plain\f3\fs22\cf1 local n,lcoef,a,reste,eq,j,k,sol,b,tab,dimker; \par begin \par n:=degree(A,x); \par lcoef:=lcoeff(A,x); \par a:=poly(A*(lcoef^-1 mod p),[x],IntMod(p)); \par reste:=expr([divide(poly(x^(j*p),[x],IntMod(p)),a,Rem) $ j=0..n-1]); \par eq:=[coeff(expand(_plus(bet[k]*(reste[k+1]-x^k) $ k=0..n-1)),x,n-i) $ i=1..n]; \par MatA:=Dom::Matrix(Dom::IntegerMod(p))([[coeff(eq[i],bet[k]) $ k=0..n-1,0] $ i=1..nops(eq)]); \par sol:=linalg::matlinsolve(MatA); \par dimker:=nops(expr(sol[2])); \par sol:=[bet[k]=_plus(op(expr(sol[2])[i])[k+1]*y[i] $ i=1..dimker) $ k=0..n-1]; \par b:=subs(subs(_plus(bet[k]*x^k $ k=0..n-1),sol),[bet[i]=1 $ i=0..n-1]); \par b:=poly(subs(b,[y[i]=1 $ i=1..dimker]),[x],IntMod(p)); \par tab:=[expr(gcd(a,b-poly(k,[x],IntMod(p)))) $ k=0..p-1]; \par lcoef*_mult(op(tab)) \par end_proc: \par \pard\ri4\plain\f4\fs22\cf0 14. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}Berlekamp(A,x,p) \par \pard\li50\ri6\plain\f3\fs22\cf2\protect {\pict\wmetafile8\picw8701\pich928\picwgoal4932\pichgoal526 010009000003340600000D001C0000000000050000000B0200000000050000000C02A003FD2103 0000001E00030000001E00050000000C020E024513050000000B020000000014000000FF060000 0600F602000024000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D0100 0004000000F001000008000000FA0200000000000000000000040000002D01000007000000FC02 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