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200 27 "We do a chan ge of variables" }}}{EXCHG {PARA 214 "> " 0 "" {MPLTEXT 1 217 25 "f:=s qrt(5)/((x^2+3*x-2));" }}{PARA 213 "" 1 "" {XPPMATH 20 "6#>I\"fG6\"*& \"\"&#\"\"\"\"\"#,(*$I\"xGF%F*F)F-\"\"$!\"#F)!\"\"" }{TEXT 216 1 " " } }}{EXCHG {PARA 214 "> " 0 "" {MPLTEXT 1 217 24 "L := changeOfVars(LB,f );" }}{PARA 213 "" 1 "" {XPPMATH 20 "6#>I\"LG6\",(*(I\"DG6$I*protected GF*I(_syslibGF%\"\"#,&I\"xGF%F,\"\"$\"\"\"F0,(*$F.F,F0F.F/!\"#F0\"\"%F 0*(,(F2F,F.\"\"'\"#8F0F0F(F0F1F/F0*&,.\"\"&F0*&I#nuGF%F,F.F4F0*&F=F,F. F/F7*&F=F,F.F,F;*&F=F,F.F0!#7*$F=F,F4F0F-F/!\"\"" }{TEXT 216 1 " " }}} {EXCHG {PARA 212 "" 0 "" {TEXT 200 32 "The field of constants is Q(nu) ." }}{PARA 212 "" 0 "" }{PARA 212 "" 0 "" {TEXT 200 41 "One factor of \+ the leading coefficient is:" }}}{EXCHG {PARA 214 "> " 0 "" {MPLTEXT 1 217 16 "q1 := x^2+3*x-2:" }}}{EXCHG {PARA 212 "" 0 "" {TEXT 200 41 "Th e corresponding generalized exponent is" }}}{EXCHG {PARA 214 "> " 0 "" {MPLTEXT 1 217 28 "gen_exp(L, t, x=RootOf(q1));" }}{PARA 213 "" 1 "" {XPPMATH 20 "6#7#7$,&*&-I'RootOfG6$I*protectedGF*I(_syslibG6\"6#,&!\"& \"\"\"*$I#_ZGF,\"\"#\"# " 0 "" {MPLTEXT 1 217 23 "s := solve(17*x^2-5,x);" }}{PARA 213 "" 1 "" {XPPMATH 20 "6#>I\"sG6\"6$,$*$\"#&)#\"\"\"\"\"##F+\"#<,$F(#!\"\"F." } {TEXT 216 1 " " }}}{EXCHG {PARA 214 "> " 0 "" {MPLTEXT 1 217 29 "d := \+ op(1,[s])/t-op(2,[s])/t;" }}{PARA 213 "" 1 "" {XPPMATH 20 "6#>I\"dG6\" ,$*&\"#&)#\"\"\"\"\"#I\"tGF%!\"\"#F+\"#<" }{TEXT 216 1 " " }}}{EXCHG {PARA 214 "> " 0 "" {MPLTEXT 1 217 18 "d-1/t*sqrt(20/17);" }}{PARA 213 "" 1 "" {XPPMATH 20 "6#\"\"!" }{TEXT 216 1 " " }}}{EXCHG {PARA 212 "" 0 "" {TEXT 200 36 "The exponent difference is a zero of" }}} {EXCHG {PARA 214 "> " 0 "" {MPLTEXT 1 217 16 "q2 := 17*x^2-20;" }} {PARA 213 "" 1 "" {XPPMATH 20 "6#>I#q2G6\",&*$I\"xGF%\"\"#\"# " 0 "" {MPLTEXT 1 217 48 "r := evala(Primfield(\{RootOf(q 1), RootOf(q2)\})):" }}}{EXCHG {PARA 214 "> " 0 "" {MPLTEXT 1 217 34 " r := subs(_Z=x,op(1,lhs(r[1,1])));" }}{PARA 213 "" 1 "" {XPPMATH 20 "6 #>I\"rG6\",,*$I\"xGF%\"\"#\"$l(F(!%3b!%kG\"\"\"*$F(\"\"%\"$*G*$F(\"\"$ \"%M<" }{TEXT 216 1 " " }}}{EXCHG {PARA 212 "" 0 "" {TEXT 200 43 "This field is now generated by a zero of r." }}{PARA 212 "" 0 "" }{PARA 212 "" 0 "" {TEXT 200 20 "We compute subfields" }}}{EXCHG {PARA 214 "> " 0 "" {MPLTEXT 1 217 37 "S := evala(Subfields(\{r\}, 2, \{\}, x));" }}{PARA 213 "" 1 "" {XPPMATH 20 "6#>I\"SG6\"<%-I'RootOfG6$I*protectedG F*I(_syslibGF%6#,&*$I#_ZGF%\"\"#\"\"\"!# " 0 "" {MPLTEXT 1 217 16 "dsolveBessel(L);" }} {PARA 215 "" 1 "" {XPPMATH 20 "6#,&*&I$_C1G6\"\"\"\"-I(BesselIG6$I*pro tectedGF+I(_syslibGF&6$I#nuGF&*&\"\"&#F'\"\"#,(*$I\"xGF&F2F'F5\"\"$!\" #F'!\"\"F'F'*&I$_C2GF&F'-I(BesselKGF*F-F'F'" }{TEXT 218 1 " " }{TEXT 218 1 " " }}}{EXCHG {PARA 214 "> " 0 "" }}{PARA 216 "" 0 "" }{PARA 217 "" 0 "" }}{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }