{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 0 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 14 0 0 0 0 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "# RATIONAL FUNCTIONS in the unknown x ------- f/g and f, g polys in g" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "f:= x^2 + 3*x + 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,(*$%\"xG\"\"#\"\"\"F'\"\"$F(F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "g:= x^2 + 5*x + 6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG,(*$%\"xG\"\"#\"\"\"F'\"\"&\"\"'F)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "h:= f/g; numer(h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG*&,(*$%\"xG\"\"#\"\"\"F(\"\"$F)F*F*,(F 'F*F(\"\"&\"\"'F*!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$%\"xG\" \"#\"\"\"F%\"\"$F&F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "wha ttype(h); op(h); op(2,h); whattype(\"); op(\"\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"*G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,(*$%\"xG \"\"#\"\"\"F%\"\"$F&F'*$,(F$F'F%\"\"&\"\"'F'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$,(*$%\"xG\"\"#\"\"\"F&\"\"&\"\"'F(!\"\"" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#%\"^G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,(*$%\" xG\"\"#\"\"\"F%\"\"&\"\"'F'!\"\"" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "normal (h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"F&F&F&, &F%F&\"\"$F&!\"\"" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "factor(f,x); \+ # just to check" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\" \"\"#F&F&,&F%F&F&F&F&" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "factor(g,x );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"\"\"$F&F&,&F%F&\" \"#F&F&" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "# So MAPLE does not d o simplification automatically of rational expressions into a form whe re the numer and" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "# denom are rel atively prime." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "gcd(f,g);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG\"\"\"\"\"#F%" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "# why not automatically???????? time consum ing, try ... the fllowing" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "normal( (x^100 - 1) / (x-1));" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#,dw\"\"\"F$*$%\"xG\"\"#F$F&F$*$F&\"#** F$*$F&\"#(*F$*$F&\"#)*F$*$F&\"#'*F$*$F&\"#&*F$*$F&\"#%*F$*$F&\"#$*F$*$ F&\"##*F$*$F&\"#\"*F$*$F&\"#!*F$*$F&\"#*)F$*$F&\"#))F$*$F&\"#()F$*$F& \"#')F$*$F&\"#&)F$*$F&\"#%)F$*$F&\"#$)F$*$F&\"##)F$*$F&\"#\")F$*$F&\"# !)F$*$F&\"#zF$*$F&\"#yF$*$F&\"#xF$*$F&\"#wF$*$F&\"#vF$*$F&\"#uF$*$F&\" #tF$*$F&\"#sF$*$F&\"#rF$*$F&\"#qF$*$F&\"#pF$*$F&\"#oF$*$F&\"#nF$*$F&\" #mF$*$F&\"#lF$*$F&\"#kF$*$F&\"#jF$*$F&\"#iF$*$F&\"#hF$*$F&\"#gF$*$F&\" #fF$*$F&\"#eF$*$F&\"#dF$*$F&\"#cF$*$F&\"#bF$*$F&\"#aF$*$F&\"#`F$*$F&\" #_F$*$F&\"#^F$*$F&\"#]F$*$F&\"#\\F$*$F&\"#[F$*$F&\"#ZF$*$F&\"#YF$*$F& \"#XF$*$F&\"#WF$*$F&\"#VF$*$F&\"#UF$*$F&\"#TF$*$F&\"#SF$*$F&\"#RF$*$F& \"#QF$*$F&\"#PF$*$F&\"#OF$*$F&\"#NF$*$F&\"#LF$*$F&\"#KF$*$F&\"#JF$*$F& \"#IF$*$F&\"#HF$*$F&\"#GF$*$F&\"#FF$*$F&\"#EF$*$F&\"#DF$*$F&\"#CF$*$F& \"#BF$*$F&\"#AF$*$F&\"#@F$*$F&\"#?F$*$F&\"#>F$*$F&\"#=F$*$F&\"# " 0 "" {MPLTEXT 1 0 41 "p1:= 7*x^4 - 2* \+ x^3 + x^2 - 3*x + 6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p1G,,*$% \"xG\"\"%\"\"(*$F'\"\"$!\"#*$F'\"\"#\"\"\"F'!\"$\"\"'F/" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 18 "readlib(cost)(p1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%*additionsG\"\"%%0multiplicationsG\"\"*" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 26 "p7:=convert(p1, 'horner');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p7G,&\"\"'\"\"\"*&,&!\"$F'*&,&F'F'*&,&!\"#F'%\"xG \"\"(F'F0F'F'F'F0F'F'F'F0F'F'" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "cos t(p7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%*additionsG\"\"%%0multipl icationsGF%" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "# convert the poly f or efficiency reasons" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "expand(p7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$%\"xG\"\"%\"\"(*$F%\"\"$!\"#*$F%\"\"#\"\"\"F%!\"$\"\"'F-" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "# expansion to the expanded canonic al form" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "p8:= (x+1) ^8;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p8G*$,&%\"xG\"\"\"F(F(\"\")" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#,4*$%\"xG\"\")\"\"\"*$F%\"\"(F&*$F%\"\"'\"#G*$F%\"\"&\"#c*$F%\"\"%\" #q*$F%\"\"$F/*$F%\"\"#F,F%F&F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "# distributes powers over sums" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " # however not for negative powers" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "p9:=(x+1)^(-2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% #p9G*$,&%\"xG\"\"\"F(F(!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$,&%\"xG\"\"\"F&F& !\"#" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "# polys defined over finite fields -------- e.g Expansion over Z8" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Expand( (x+1)^5) mod 8;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.* $%\"xG\"\"&\"\"\"*$F%\"\"%F&*$F%\"\"$\"\"#*$F%F,F,F%F&F'F'" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "# FACTORIZATION of a poly over the ration als in irreducible factors" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "# ---over Z2, Z3, Z5" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Factor(p 1) mod 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"xG\"\"\",(*$F$\"\"$F %F$F%F%F%F%" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 " Factor(p1) mod 3; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"xG\"\"#,&F$\"\"\"F%F'F%" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Factor(p1) mod 5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,(*$%\"xG\"\"$\"\"\"*$F'\"\"#F)F)F)F),&F'F)F(F)F )F+" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "# END" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }