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T" }{TEXT 205 18 "\303\266rt\303\251" }{TEXT 205 3 "ne t" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 205 18 "2. Algebrai alapok" }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 8 "E 2.1. P" }{TEXT 206 12 "\303\251lda." }{TEXT 206 1 " " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "irem(1,1); irem(1,-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "irem(18,6); irem(30,6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "irem(18,-6); irem(30,-6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "irem(6,-6); irem(-6,6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 8 "E 2.2. P" }{TEXT 206 12 "\303\251lda." } {TEXT 206 1 " " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "igcd(18,30);" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"'" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 8 "E 2.3. P" }{TEXT 206 12 "\303\251lda." } {TEXT 206 1 " " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "sign(-6); abs(6); sign(6); abs(6); sign(0); abs (0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" } }{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "igcd(-18,30); -18*30/igcd(-18,30); abs(-18*30)/igcd(- 18,30); ilcm(-18,30);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "!#!*" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#!*" } }{PARA 11 "" 1 "" {XPPMATH 20 "\"#!*" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 8 "E 2.4 . P" }{TEXT 206 12 "\303\251lda." }{TEXT 206 1 " " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "abs(-6); ab s(6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 8 "E 2.5. P" }{TEXT 206 12 "\303 \251lda." }{TEXT 206 1 " " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "gcd(18,30); 2*18+(-1)*30; (-3)*18+ 2*30; 7*18+(-4)*30;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 19 "A 2. 1. Algoritmus. " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 43 "Euclid:=proc(a,b,x) local c,d,r,ua,ub,uc;\n" } {MPLTEXT 1 0 19 " if nargs<3 then\n" }{MPLTEXT 1 0 27 " c:=abs(a); d:=abs(b);\n" }{MPLTEXT 1 0 8 " else\n" }{MPLTEXT 1 0 59 " ua:=lc oeff(collect(a,x),x); if ua<>0 then c:=a/ua fi;\n" }{MPLTEXT 1 0 59 " \+ ub:=lcoeff(collect(b,x),x); if ub<>0 then d:=b/ub fi;\n" }{MPLTEXT 1 0 7 " fi;\n" }{MPLTEXT 1 0 17 " while d<>0 do\n" }{MPLTEXT 1 0 57 " if nargs<3 then r:=irem(c,d) else r:=rem(c,d,x) fi;\n" }{MPLTEXT 1 0 17 " c:=d; d:=r;\n" }{MPLTEXT 1 0 7 " od;\n" }{MPLTEXT 1 0 19 " if nargs<3 then\n" }{MPLTEXT 1 0 13 " abs(c);\n" }{MPLTEXT 1 0 8 " else\n" }{MPLTEXT 1 0 63 " uc:=lcoeff(collect(c,x),x); if uc<> 0 then c/uc else c fi;\n" }{MPLTEXT 1 0 7 " fi;\n" }{MPLTEXT 1 0 4 "e nd;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6%I\"aG6\"I\"bGF%I\"xGF%6(I\"cG F%I\"dGF%I\"rGF%I#uaGF%I#ubGF%I#ucGF%F%F%C%@%2%&nargsG\"\"$C$>F)-I$abs G%*protectedG6#F$>F*-F76#F&C&>F,-I'lcoeffGF86$-I(collectGF%6$F$F'F'@$0 F,\"\"!>F)*&F$\"\"\"F,!\"\">F--F@6$-FC6$F&F'F'@$0F-FG>F**&F&FJF-FK?(F% FJFJF%0F*FGC%@%F1>F+-I%iremGF86$F)F*>F+-I$remGF%6%F)F*F'>F)F*>F*F+@%F1 -F76#F)C$>F.-F@6$-FC6$F)F'F'@%0F.FG*&F)FJF.FKF)F%F%F%" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 8 "E 2.7. P" }{TEXT 206 12 "\303\251lda." }{TEXT 206 1 " " } }{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "debug(Euclid);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I'EuclidG6\"" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Euclid(18,30);" }}{PARA 9 " " 1 "" {TEXT 207 33 "\{--> enter Euclid, args = 18, 30" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#=" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#I" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#=" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#I" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"#=" }}{PARA 11 "" 1 "" {XPPMATH 20 "\" #7" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#=" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 11 " " 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"'" }}{PARA 9 "" 1 "" {TEXT 207 40 "<-- exit Euclid (now at top lev el) = 6\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 19 "A 2.2. Algoritmus. " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "EEA:=proc(a,b,s,t,x) local c,c1,c2, d,d1,d2,q,r,r1,r2,ua,ub,uc;\n" }{MPLTEXT 1 0 19 " if nargs<5 then\n" }{MPLTEXT 1 0 27 " c:=abs(a); d:=abs(b);\n" }{MPLTEXT 1 0 8 " else \n" }{MPLTEXT 1 0 59 " ua:=lcoeff(collect(a,x),x); if ua<>0 then c: =a/ua fi;\n" }{MPLTEXT 1 0 59 " ub:=lcoeff(collect(b,x),x); if ub<> 0 then d:=b/ub fi;\n" }{MPLTEXT 1 0 7 " fi;\n" }{MPLTEXT 1 0 31 " c1 :=1; d1:=0; c2:=0; d2:=1;\n" }{MPLTEXT 1 0 17 " while d<>0 do\n" } {MPLTEXT 1 0 57 " if nargs<5 then q:=iquo(c,d) else q:=quo(c,d,x) f i;\n" }{MPLTEXT 1 0 23 " r:=expand(c-q*d);\n" }{MPLTEXT 1 0 26 " \+ r1:=expand(c1-q*d1);\n" }{MPLTEXT 1 0 26 " r2:=expand(c2-q*d2);\n" }{MPLTEXT 1 0 27 " c:=d; c1:=d1; c2:=d2;\n" }{MPLTEXT 1 0 27 " \+ d:=r; d1:=r1; d2:=r2;\n" }{MPLTEXT 1 0 7 " od;\n" }{MPLTEXT 1 0 19 " \+ if nargs<5 then\n" }{MPLTEXT 1 0 59 " s:=c1/sign(a)/sign(c); t:=c2 /sign(b)/sign(c); abs(c);\n" }{MPLTEXT 1 0 8 " else\n" }{MPLTEXT 1 0 33 " uc:=lcoeff(collect(c,x),x);\n" }{MPLTEXT 1 0 19 " if uc<>0 \+ then\n" }{MPLTEXT 1 0 51 " if ua<>0 then s:=c1/uc/ua else s:=c1/u c fi;\n" }{MPLTEXT 1 0 51 " if ub<>0 then t:=c2/uc/ub else s:=c2/ uc fi;\n" }{MPLTEXT 1 0 13 " c/uc;\n" }{MPLTEXT 1 0 10 " else \n" }{MPLTEXT 1 0 45 " if ua<>0 then s:=c1/ua else s:=c1 fi;\n" } {MPLTEXT 1 0 45 " if ub<>0 then t:=c2/ub else s:=c2 fi;\n" } {MPLTEXT 1 0 10 " c;\n" }{MPLTEXT 1 0 9 " fi;\n" }{MPLTEXT 1 0 7 " fi;\n" }{MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f *6'I\"aG6\"I\"bGF%I\"sGF%I\"tGF%I\"xGF%6/I\"cGF%I#c1GF%I#c2GF%I\"dGF%I #d1GF%I#d2GF%I\"qGF%I\"rGF%I#r1GF%I#r2GF%I#uaGF%I#ubGF%I#ucGF%F%F%C)@% 2%&nargsG\"\"&C$>F+-I$absG%*protectedG6#F$>F.-F@6#F&C&>F5-I'lcoeffGFA6 $-I(collectGF%6$F$F)F)@$0F5\"\"!>F+*&F$\"\"\"F5!\"\">F6-FI6$-FL6$F&F)F )@$0F6FP>F.*&F&FSF6FT>F,FS>F/FP>F-FP>F0FS?(F%FSFSF%0F.FPC,@%F:>F1-I%iq uoGFA6$F+F.>F1-I$quoGF%6%F+F.F)>F2-I'expandGFA6#,&F+FS*&F1FSF.FSFT>F3- Fjo6#,&F,FS*&F1FSF/FSFT>F4-Fjo6#,&F-FS*&F1FSF0FSFT>F+F.>F,F/>F-F0>F.F2 >F/F3>F0F4@%F:C%>F'*(F,FS-I%signGFAFBFT-Fcq6#F+FT>F(*(F-FS-FcqFEFTFdqF T-F@FeqC$>F7-FI6$-FL6$F+F)F)@%0F7FPC%@%FO>F'*(F,FSF7FTF5FT>F'*&F,FSF7F T@%Fen>F(*(F-FSF7FTF6FT>F'*&F-FSF7FT*&F+FSF7FTC%@%FO>F'*&F,FSF5FT>F'F, @%Fen>F(*&F-FSF6FT>F'F-F+F%F%F%" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 8 "E 2.8. P" }{TEXT 206 12 "\303\251lda." }{TEXT 206 1 " " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "debug(EEA);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I$EEAG6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "EEA(18,30,'s','t');" }}{PARA 9 "" 1 "" {TEXT 207 36 "\{--> ent er EEA, args = 18, 30, s, t" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#=" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"#I" }}{PARA 11 "" 1 "" {XPPMATH 20 "\" \"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#=" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#I" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#=" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#=" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "! \"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 9 "" 1 "" {TEXT 207 37 "<-- exit E EA (now at top level) = 6\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "s; t;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 8 "E 2.9. P" }{TEXT 206 12 "\303\251lda." }{TEXT 206 1 " " } }{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.10. P" }{TEXT 206 12 "\303\251lda." }{TEXT 206 1 " " }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.11. P" }{TEXT 206 12 "\303\251lda." } {TEXT 206 1 " " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "a:=3*x^3+x^2+x+5; b:=5*x^2-3*x+1;" }}{PARA 11 " " 1 "" {XPPMATH 20 ",**&\"\"$\"\"\")I\"xG6\"F$F%F%*$)F'\"\"#F%F%F'F%\" \"&F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&\"\"&\"\"\")I\"xG6\"\"\"#F% F%*&\"\"$F%F'F%!\"\"F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "q1:=3/5*x; r1:=expand(a-q1*b);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&# \"\"$\"\"&\"\"\"I\"xG6\"F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&#\"# 9\"\"&\"\"\")I\"xG6\"\"\"#F'F'*&#F+F&F'F)F'F'F&F'" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 31 "q2:=14/25; r2:=expand(r1-q2*b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "#\"#9\"#D" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&# \"#_\"#D\"\"\"I\"xG6\"F'F'#\"$6\"F&F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "q:=q1+q2; r:=r2; a=expand(q*b+r);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&#\"\"$\"\"&\"\"\"I\"xG6\"F'F'#\"#9\"#DF'" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&#\"#_\"#D\"\"\"I\"xG6\"F'F'#\"$6\"F&F'" }} {PARA 11 "" 1 "" {XPPMATH 20 "/,**&\"\"$\"\"\")I\"xG6\"F%F&F&*$)F(\"\" #F&F&F(F&\"\"&F&F#" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.12. P" }{TEXT 206 12 "\30 3\251lda." }{TEXT 206 1 " " }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" " %#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.13. P" }{TEXT 206 12 "\303\251lda." }{TEXT 206 1 " " }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.14. P" } {TEXT 206 12 "\303\251lda." }{TEXT 206 1 " " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "a:=48*x^3-84*x^2+ 42*x-36; b:=-4*x^3-10*x^2+44*x-30;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",* *&\"#[\"\"\")I\"xG6\"\"\"$F%F%*&\"#%)F%)F'\"\"#F%!\"\"*&\"#UF%F'F%F%\" #OF." }}{PARA 11 "" 1 "" {XPPMATH 20 ",**&\"\"%\"\"\")I\"xG6\"\"\"$F%! \"\"*&\"#5F%)F'\"\"#F%F**&\"#WF%F'F%F%\"#IF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Euclid(a,b,x);" }}{PARA 9 "" 1 "" {TEXT 207 74 " \{--> enter Euclid, args = 48*x^3-84*x^2+42*x-36, -4*x^3-10*x^2+44*x-3 0, x" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#[" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**$)I\"xG6\"\"\"$\"\"\"F(*&#\"\"(\"\"%F()F%\"\"#F(!\"\"* &#F+\"\")F(F%F(F(#F'F,F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"%" }} {PARA 11 "" 1 "" {XPPMATH 20 ",**$)I\"xG6\"\"\"$\"\"\"F(*&#\"\"&\"\"#F ()F%F,F(F(*&\"#6F(F%F(!\"\"#\"#:F,F(" }}{PARA 11 "" 1 "" {XPPMATH 20 " ,(#\"#L\"\"%!\"\"*&#\"# " 0 "" {MPLTEXT 1 0 19 "EEA(a,b,'s','t',x);" }}{PARA 9 "" 1 "" {TEXT 207 77 "\{--> enter EEA, args = 48*x^3-84*x^2+42*x-36, -4*x^ 3-10*x^2+44*x-30, s, t, x" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#[" }} {PARA 11 "" 1 "" {XPPMATH 20 ",**$)I\"xG6\"\"\"$\"\"\"F(*&#\"\"(\"\"%F ()F%\"\"#F(!\"\"*&#F+\"\")F(F%F(F(#F'F,F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**$)I\"xG6\"\"\"$ \"\"\"F(*&#\"\"&\"\"#F()F%F,F(F(*&\"#6F(F%F(!\"\"#\"#:F,F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" } }{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(#\"#L\"\"%!\"\"*&#\"# " 0 "" {MPLTEXT 1 0 22 "s; t; expand(s*a+t*b);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&#\" \"$\"$9#\"\"\"*&#\"#<\"%?kF&I\"xG6\"F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&#\"#r\"%S@\"\"\"*&#\"#<\"$N&F&I\"xG6\"F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&#\"\"$\"\"#!\"\"I\"xG6\"\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E \+ 2.16. P" }{TEXT 206 12 "\303\251lda." }{TEXT 206 1 " " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "p:=5*x^3 *y^2-x^2*y^4-3*x^2*y^2+7*x*y^2+2*x*y-2*x+4*y^4+5;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",2*(\"\"&\"\"\")I\"xG6\"\"\"$F%)I\"yGF(\"\"#F%F%*&)F'F,F% )F+\"\"%F%!\"\"*(F)F%F.F%F*F%F1*(\"\"(F%F'F%F*F%F%*(F,F%F'F%F+F%F%*&F, F%F'F%F1*&F0F%F/F%F%F$F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "sort(p,[y,x],plex);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",2*&)I\"yG6\"\" \"%\"\"\")I\"xGF&\"\"#F(!\"\"*&F'F(F$F(F(*(\"\"&F()F%F+F()F*\"\"$F(F(* (F2F(F0F(F)F(F,*(\"\"(F(F0F(F*F(F(*(F+F(F%F(F*F(F(*&F+F(F*F(F,F/F(" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "sort(p,[x,y],plex);" }} {PARA 11 "" 1 "" {XPPMATH 20 ",2*(\"\"&\"\"\")I\"xG6\"\"\"$F%)I\"yGF( \"\"#F%F%*&)F'F,F%)F+\"\"%F%!\"\"*(F)F%F.F%F*F%F1*(\"\"(F%F'F%F*F%F%*( F,F%F'F%F+F%F%*&F,F%F'F%F1*&F0F%F/F%F%F$F%" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.1 7. P" }{TEXT 206 12 "\303\251lda." }{TEXT 206 1 " " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "collect(p,[ x,y]);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,*(\"\"&\"\"\")I\"xG6\"\"\"$F %)I\"yGF(\"\"#F%F%*&,&*$)F+\"\"%F%!\"\"*&F)F%F*F%F2F%)F'F,F%F%*&,(*&F, F%F+F%F%F,F2*&\"\"(F%F*F%F%F%F'F%F%*&F1F%F0F%F%F$F%" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.18. P" }{TEXT 206 12 "\303\251lda." }{TEXT 206 1 " " }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "p:=collect(p,[x,y],`distributed`); lcoeff(p,[x,y],'t'); t;" }} {PARA 11 "" 1 "" {XPPMATH 20 ",2*(\"\"&\"\"\")I\"xG6\"\"\"$F%)I\"yGF( \"\"#F%F%*&)F'F,F%)F+\"\"%F%!\"\"*(F)F%F.F%F*F%F1*(\"\"(F%F'F%F*F%F%*( F,F%F'F%F+F%F%*&F,F%F'F%F1*&F0F%F/F%F%F$F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "*&)I\"xG6\"\"\"$\" \"\")I\"yGF%\"\"#F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "conv ert(t,list); map(x->op(2,x),%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$*$) I\"xG6\"\"\"$\"\"\"*$)I\"yGF&\"\"#F(" }}{PARA 11 "" 1 "" {XPPMATH 20 " 7$\"\"$\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "degree(p,\{ x,y\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "degree(p,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "degree(p,y);" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.1 9. P" }{TEXT 206 12 "\303\251lda." }{TEXT 206 1 " " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "a=expand((1 )*(2)*(3)*(2*x-3)*(4*x^2-x+2));\n" }{MPLTEXT 1 0 39 "b=expand((-1)*(2) *(2*x-3)*(x-1)*(x+5));" }}{PARA 11 "" 1 "" {XPPMATH 20 "/,**&\"#[\"\" \")I\"xG6\"\"\"$F&F&*&\"#%)F&)F(\"\"#F&!\"\"*&\"#UF&F(F&F&\"#OF/F#" }} {PARA 11 "" 1 "" {XPPMATH 20 "/,**&\"\"%\"\"\")I\"xG6\"\"\"$F&!\"\"*& \"#5F&)F(\"\"#F&F+*&\"#WF&F(F&F&\"#IF+F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "expand((2)*(2*x-3));" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&\"\"'!\"\"*&\"\"%\"\"\"I\"xG6\"F'F'" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.2 0. P" }{TEXT 206 12 "\303\251lda." }{TEXT 206 1 " " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "a=expand((4 8)*(x-3/2)*(x^2-1/4*x+1/2));\n" }{MPLTEXT 1 0 35 "b=expand((-4)*(x-3/2 )*(x-1)*(x+5));" }}{PARA 11 "" 1 "" {XPPMATH 20 "/,**&\"#[\"\"\")I\"xG 6\"\"\"$F&F&*&\"#%)F&)F(\"\"#F&!\"\"*&\"#UF&F(F&F&\"#OF/F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "/,**&\"\"%\"\"\")I\"xG6\"\"\"$F&!\"\"*&\"#5F&)F( \"\"#F&F+*&\"#WF&F(F&F&\"#IF+F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "x-3/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&#\"\"$\"\"#!\"\"I\"xG 6\"\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}} {SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.21. P" }{TEXT 206 12 "\303\25 1lda." }{TEXT 206 1 " " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "u:=proc(p,L,typ) local pp,uu;\n" } {MPLTEXT 1 0 51 " pp:=expand(p); pp:=collect(pp,L,`distributed`);\n" }{MPLTEXT 1 0 21 " uu:=lcoeff(pp,L);\n" }{MPLTEXT 1 0 29 " if uu=0 t hen return 1 fi;\n" }{MPLTEXT 1 0 45 " if typ='integer' then return s ign(uu) fi;\n" }{MPLTEXT 1 0 7 " uu;\n" }{MPLTEXT 1 0 4 "end;" }} {PARA 11 "" 1 "" {XPPMATH 20 "f*6%I\"pG6\"I\"LGF%I$typGF%6$I#ppGF%I#uu GF%F%F%C(>F)-I'expandG%*protectedG6#F$>F)-I(collectG6$F/I(_syslibGF%6% F)F&I,distributedGF%>F*-I'lcoeffGF/6$F)F&@$/F*\"\"!O\"\"\"@$/F'.I(inte gerGF/O-I%signGF/6#F*F*F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "cont:=proc(p,L,typ) local pp,uu,cL;\n" }{MPLTEXT 1 0 53 " if no ps(L)=1 and typ<>'integer' then return 1 fi;\n" }{MPLTEXT 1 0 19 " uu :=u(p,L,typ);\n" }{MPLTEXT 1 0 23 " pp:=simplify(p/uu);\n" }{MPLTEXT 1 0 25 " pp:=collect(pp,L[1]);\n" }{MPLTEXT 1 0 24 " cL:=coeffs(pp,L [1]);\n" }{MPLTEXT 1 0 41 " if nops(L)=1 then return igcd(cL) fi;\n" }{MPLTEXT 1 0 32 " GCD([cL],L[2..nops(L)],typ);\n" }{MPLTEXT 1 0 4 "e nd;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6%I\"pG6\"I\"LGF%I$typGF%6%I#pp GF%I#uuGF%I#cLGF%F%F%C)@$3/-I%nopsG%*protectedG6#F&\"\"\"0F'.I(integer GF2OF4>F*-I\"uGF%F#>F)-I)simplifyGF%6#*&F$F4F*!\"\">F)-I(collectG6$F2I (_syslibGF%6$F)&F&6#F4>F+-I'coeffsGF2FG@$F/O-I%igcdGF26#F+-I$GCDGF%6%7 #F+&F&6#;\"\"#F0F'F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "pp:=proc(p,L,typ) local uu,pp,c;\n" }{MPLTEXT 1 0 19 " uu:=u(p,L,typ );\n" }{MPLTEXT 1 0 23 " pp:=simplify(p/uu);\n" }{MPLTEXT 1 0 22 " c :=cont(pp,L,typ);\n" }{MPLTEXT 1 0 41 " if c=0 then 0 else simplify(p p/c) fi;\n" }{MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6 %I\"pG6\"I\"LGF%I$typGF%6%I#uuGF%I#ppGF%I\"cGF%F%F%C&>F)-I\"uGF%F#>F*- I)simplifyGF%6#*&F$\"\"\"F)!\"\">F+-I%contGF%6%F*F&F'@%/F+\"\"!F=-F26# *&F*F5F+F6F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "a;" }} {PARA 11 "" 1 "" {XPPMATH 20 ",**&\"#[\"\"\")I\"xG6\"\"\"$F%F%*&\"#%)F %)F'\"\"#F%!\"\"*&\"#UF%F'F%F%\"#OF." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "u(a,[x],'integer');" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "cont(a,[x],'integ er');" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "pp(a,[x],'integer');" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**&\"\")\"\"\")I\"xG6\"\"\"$F%F%*&\"#9F%)F'\"\"#F%!\"\"* &\"\"(F%F'F%F%\"\"'F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "u( a,[x],'rational');" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#[" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "cont(a,[x],'rational');" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "pp(a,[x],'rational');" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**$)I\"x G6\"\"\"$\"\"\"F(*&#\"\"(\"\"%F()F%\"\"#F(!\"\"*&#F+\"\")F(F%F(F(#F'F, F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "b;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**&\"\"%\"\"\")I\"xG6\"\"\"$F%!\"\"*&\"#5F%)F'\"\"#F%F* *&\"#WF%F'F%F%\"#IF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "u(b ,[x],'integer');" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "cont(b,[x],'integer');" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "pp(b,[x],'integer');" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**&\"\"#\" \"\")I\"xG6\"\"\"$F%F%*&\"\"&F%)F'F$F%F%*&\"#AF%F'F%!\"\"\"#:F%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "u(b,[x],'rational');" }} {PARA 11 "" 1 "" {XPPMATH 20 "!\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "cont(b,[x],'rational');" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "pp(b,[x],'rat ional');" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**$)I\"xG6\"\"\"$\"\"\"F(*& #\"\"&\"\"#F()F%F,F(F(*&\"#6F(F%F(!\"\"#\"#:F,F(" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 19 "A 2.3. Algoritmus. " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "pseudodiv:=proc(a,b,x,q,r) local l, beta,qq,aa,bb;\n" }{MPLTEXT 1 0 29 " aa:=collect(expand(a),x);\n" } {MPLTEXT 1 0 29 " bb:=collect(expand(b),x);\n" }{MPLTEXT 1 0 35 " l: =degree(aa,x)-degree(bb,x)+1;\n" }{MPLTEXT 1 0 9 " q:=0;\n" }{MPLTEXT 1 0 34 " if l<=0 then r:=aa; return fi;\n" }{MPLTEXT 1 0 23 " beta: =lcoeff(bb,x);\n" }{MPLTEXT 1 0 37 " aa:=collect(expand(aa*beta^l),x) ;\n" }{MPLTEXT 1 0 39 " while degree(aa,x)>=degree(bb,x) do\n" } {MPLTEXT 1 0 35 " l:=degree(aa,x)-degree(bb,x);\n" }{MPLTEXT 1 0 28 " qq:=lcoeff(aa,x)/beta;\n" }{MPLTEXT 1 0 14 " q:=q+qq;\n" } {MPLTEXT 1 0 42 " aa:=collect(expand(aa-qq*x^l*bb),x);\n" }{MPLTEXT 1 0 7 " od;\n" }{MPLTEXT 1 0 10 " r:=aa;\n" }{MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6'I\"aG6\"I\"bGF%I\"xGF%I\"qGF%I\"rG F%6'I\"lGF%I%betaGF%I#qqGF%I#aaGF%I#bbGF%F%F%C+>F.-I(collectG6$%*prote ctedGI(_syslibGF%6$-I'expandGF56#F$F'>F/-F36$-F96#F&F'>F+,(-I'degreeGF 56$F.F'\"\"\"-FC6$F/F'!\"\"FEFE>F(\"\"!@$1F+FJC$>F)F.OF%>F,-I'lcoeffGF 5FG>F.-F36$-F96#*&F.FE)F,F+FEF'?(F%FEFEF%1FFFBC&>F+,&FBFEFFFH>F-*&-FRF DFEF,FH>F(,&F(FEF-FE>F.-F36$-F96#,&F.FE*(F-FE)F'F+FEF/FEFHF'FNF%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "PrimitiveEuclidean:=proc( a,b,L,typ) local c,d,r,q,gamma;\n" }{MPLTEXT 1 0 35 " c:=pp(a,L,typ); d:=pp(b,L,typ);\n" }{MPLTEXT 1 0 17 " while d<>0 do\n" }{MPLTEXT 1 0 34 " pseudodiv(c,d,L[1],'q','r');\n" }{MPLTEXT 1 0 27 " c:=d; \+ d:=pp(r,L,typ);\n" }{MPLTEXT 1 0 7 " od;\n" }{MPLTEXT 1 0 21 " if no ps(L)=1 then\n" }{MPLTEXT 1 0 27 " if typ='integer' then\n" } {MPLTEXT 1 0 49 " gamma:=igcd(cont(a,L,typ),cont(b,L,typ));\n" } {MPLTEXT 1 0 23 " else gamma:=1 fi;\n" }{MPLTEXT 1 0 8 " else\n" } {MPLTEXT 1 0 79 " gamma:=PrimitiveEuclidean(cont(a,L,typ),cont(b,L, typ),L[2..nops(L)],typ);\n" }{MPLTEXT 1 0 16 " fi; gamma*c;\n" } {MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6&I\"aG6\"I\"b GF%I\"LGF%I$typGF%6'I\"cGF%I\"dGF%I\"rGF%I\"qGF%I&gammaG%*protectedGF% F%C'>F*-I#ppGF%6%F$F'F(>F+-F36%F&F'F(?(F%\"\"\"F9F%0F+\"\"!C%-I*pseudo divGF%6'F*F+&F'6#F9.F-.F,>F*F+>F+-F36%F,F'F(@%/-I%nopsGF/6#F'F9@%/F(.I (integerGF/>F.-I%igcdGF/6$-I%contGF%F4-FVF7>F.F9>F.-I3PrimitiveEuclide anGF%6&FUFW&F'6#;\"\"#FJF(*&F.F9F*F9F%F%F%" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 20 "GCD:=proc(P,L,typ)\n" }{MPLTEXT 1 0 34 " if nops(P )=0 then return 0 fi;\n" }{MPLTEXT 1 0 59 " if nops(P)=1 then return \+ expand(P[1]/u(P[1],L,typ)) fi;\n" }{MPLTEXT 1 0 53 " if nops(P)=2 the n PrimitiveEuclidean(op(P),L,typ)\n" }{MPLTEXT 1 0 79 " else GCD([Pri mitiveEuclidean(P[1],P[2],L,typ),op(P[3..nops(P)])],L,typ) fi;\n" } {MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6%I\"PG6\"I\"L GF%I$typGF%F%F%F%C%@$/-I%nopsG%*protectedG6#F$\"\"!OF/@$/F+\"\"\"O-I'e xpandGF-6#*&&F$6#F3F3-I\"uGF%6%F9F&F'!\"\"@%/F+\"\"#-I3PrimitiveEuclid eanGF%6%-I#opGF-F.F&F'-I$GCDGF%6%7$-FC6&F9&F$6#FAF&F'-FF6#&F$6#;\"\"$F +F&F'F%F%F%" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}} {SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.22. P" }{TEXT 206 12 "\303\25 1lda." }{TEXT 206 3 " \n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " debug(PrimitiveEuclidean);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I3Primitiv eEuclideanG6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Primitive Euclidean(a,b,[x],'integer');" }}{PARA 9 "" 1 "" {TEXT 207 97 "\{--> e nter PrimitiveEuclidean, args = 48*x^3-84*x^2+42*x-36, -4*x^3-10*x^2+4 4*x-30, [x], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**&\"\")\"\"\") I\"xG6\"\"\"$F%F%*&\"#9F%)F'\"\"#F%!\"\"*&\"\"(F%F'F%F%\"\"'F." }} {PARA 11 "" 1 "" {XPPMATH 20 ",**&\"\"#\"\"\")I\"xG6\"\"\"$F%F%*&\"\"& F%)F'F$F%F%*&\"#AF%F'F%!\"\"\"#:F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",( \"$K\"!\"\"*&\"#o\"\"\")I\"xG6\"\"\"#F'F$*&\"$!>F'F)F'F'" }}{PARA 11 " " 1 "" {XPPMATH 20 ",**&\"\"#\"\"\")I\"xG6\"\"\"$F%F%*&\"\"&F%)F'F$F%F %*&\"#AF%F'F%!\"\"\"#:F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(\"#m\"\"\" *&\"#MF$)I\"xG6\"\"\"#F$F$*&\"#&*F$F(F$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&\"%?k!\"\"*&\"%!G%\"\"\"I\"xG6\"F'F'" }}{PARA 11 "" 1 " " {XPPMATH 20 ",(\"#m\"\"\"*&\"#MF$)I\"xG6\"\"\"#F$F$*&\"#&*F$F(F$!\" \"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&\"\"$!\"\"*&\"\"#\"\"\"I\"xG6\"F 'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&\"\"$!\"\"*&\"\"#\"\"\"I\"xG6\"F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&\"\"'!\"\"*&\"\"%\"\"\"I\"xG6\"F'F'" }}{PARA 9 "" 1 "" {TEXT 207 57 "<-- exit PrimitiveEuclidean (now at top level) \+ = -6+4*x\}" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&\"\"'!\"\"*&\"\"%\"\"\"I \"xG6\"F'F'" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}} {SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.23. P" }{TEXT 206 12 "\303\25 1lda." }{TEXT 206 1 " " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "aa:=-30*x^3*y+90*x^2*y^2+15*x^2-60* x*y+45*y^2;\n" }{MPLTEXT 1 0 56 "bb:=100*x^2*y-140*x^2-250*x*y^2+350*x *y-150*y^3+210*y^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,*(\"#I\"\"\")I \"xG6\"\"\"$F%I\"yGF(F%!\"\"*(\"#!*F%)F'\"\"#F%)F*F/F%F%*&\"#:F%F.F%F% *(\"#gF%F'F%F*F%F+*&\"#XF%F0F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.*( \"$+\"\"\"\")I\"xG6\"\"\"#F%I\"yGF(F%F%*&\"$S\"F%F&F%!\"\"*(\"$]#F%F'F %)F*F)F%F-*(\"$]$F%F'F%F*F%F%*&\"$]\"F%)F*\"\"$F%F-*&\"$5#F%F0F%F%" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "aa:=collect(aa,[x,y]);" }} {PARA 11 "" 1 "" {XPPMATH 20 ",**(\"#I\"\"\")I\"xG6\"\"\"$F%I\"yGF(F%! \"\"*&,&*&\"#!*F%)F*\"\"#F%F%\"#:F%F%)F'F1F%F%*(\"#gF%F'F%F*F%F+*&\"#X F%F0F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "bb:=collect(bb, [x,y]);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**&,&*&\"$+\"\"\"\"I\"yG6\"F 'F'\"$S\"!\"\"F')I\"xGF)\"\"#F'F'*&,&*&\"$]#F')F(F.F'F+*&\"$]$F'F(F'F' F'F-F'F'*&\"$]\"F')F(\"\"$F'F+*&\"$5#F'F3F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "coeffs(aa,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 &,$*&\"#X\"\"\")I\"yG6\"\"\"#F&F&,$*&\"#gF&F(F&!\"\",$*&\"#IF&F(F&F.,& *&\"#!*F&F'F&F&\"#:F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "co effs(bb,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%,&*&\"$]\"\"\"\")I\"yG6 \"\"\"$F&!\"\"*&\"$5#F&)F(\"\"#F&F&,&*&\"$]#F&F.F&F+*&\"$]$F&F(F&F&,&* &\"$+\"F&F(F&F&\"$S\"F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 " debug(GCD):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "GCD([%%%],[y ],'integer');" }}{PARA 9 "" 1 "" {TEXT 207 71 "\{--> enter GCD, args = [45*y^2, -60*y, -30*y, 90*y^2+15], [y], integer" }}{PARA 9 "" 1 "" {TEXT 207 66 "\{--> enter PrimitiveEuclidean, args = 45*y^2, -60*y, [y ], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 "*$)I\"yG6\"\"\"#\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }}{PARA 11 " " 1 "" {XPPMATH 20 ",$*&\"#:\"\"\"I\"yG6\"F%F%" }}{PARA 9 "" 1 "" {TEXT 207 49 "<-- exit PrimitiveEuclidean (now in GCD) = 15*y\}" } {TEXT 207 64 "\n\{--> enter GCD, args = [15*y, -30*y, 90*y^2+15], [y], integer" }{TEXT 207 66 "\n\{--> enter PrimitiveEuclidean, args = 15*y , -30*y, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }}{PARA 11 " " 1 "" {XPPMATH 20 ",$*&\"#:\"\"\"I\"yG6\"F%F%" }}{PARA 9 "" 1 "" {TEXT 207 49 "<-- exit PrimitiveEuclidean (now in GCD) = 15*y\}" } {TEXT 207 57 "\n\{--> enter GCD, args = [15*y, 90*y^2+15], [y], intege r" }{TEXT 207 70 "\n\{--> enter PrimitiveEuclidean, args = 15*y, 90*y^ 2+15, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"'\"\"\")I\"yG6\"\"\"#F%F%F%F%" }} {PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"'\"\"\")I\"yG6\"\"\"#F%F%F%F%" } }{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }}{PARA 9 "" 1 "" {TEXT 207 47 "<-- exit PrimitiveE uclidean (now in GCD) = 15\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }} {PARA 9 "" 1 "" {TEXT 207 32 "<-- exit GCD (now in GCD) = 15\}" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }}{PARA 9 "" 1 "" {TEXT 207 32 "<- - exit GCD (now in GCD) = 15\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }}{PARA 9 "" 1 "" {TEXT 207 38 "<-- exit GCD (now at top level) = 15\} " }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "GCD([%%%],[y],'integer');" }}{PARA 9 "" 1 "" {TEXT 207 83 "\{--> enter GCD, args = [-150*y^3+210*y^2, -250*y^2+350*y, 100 *y-140], [y], integer" }}{PARA 9 "" 1 "" {TEXT 207 85 "\{--> enter Pri mitiveEuclidean, args = -150*y^3+210*y^2, -250*y^2+350*y, [y], integer " }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\")I\"yG6\"\"\"$F%F%*& \"\"(F%)F'\"\"#F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\" \")I\"yG6\"\"\"#F%F%*&\"\"(F%F'F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\")I\"yG6\"\"\"# F%F%*&\"\"(F%F'F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 ",& *&\"#]\"\"\")I\"yG6\"\"\"#F%F%*&\"#qF%F'F%!\"\"" }}{PARA 9 "" 1 "" {TEXT 207 56 "<-- exit PrimitiveEuclidean (now in GCD) = 50*y^2-70*y\} " }{TEXT 207 64 "\n\{--> enter GCD, args = [50*y^2-70*y, 100*y-140], [ y], integer" }{TEXT 207 77 "\n\{--> enter PrimitiveEuclidean, args = 5 0*y^2-70*y, 100*y-140, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 ", &*&\"\"&\"\"\")I\"yG6\"\"\"#F%F%*&\"\"(F%F'F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\"I\"yG6\"F%F%\"\"(!\"\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\"I \"yG6\"F%F%\"\"(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#] \"\"\"I\"yG6\"F%F%\"#q!\"\"" }}{PARA 9 "" 1 "" {TEXT 207 52 "<-- exit \+ PrimitiveEuclidean (now in GCD) = 50*y-70\}" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#]\"\"\"I\"yG6\"F%F%\"#q!\"\"" }}{PARA 9 "" 1 "" {TEXT 207 37 "<-- exit GCD (now in GCD) = 50*y-70\}" }}{PARA 11 "" 1 " " {XPPMATH 20 ",&*&\"#]\"\"\"I\"yG6\"F%F%\"#q!\"\"" }}{PARA 9 "" 1 "" {TEXT 207 43 "<-- exit GCD (now at top level) = 50*y-70\}" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#]\"\"\"I\"yG6\"F%F%\"#q!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "undebug(GCD);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I$GCDG6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "p p(aa,[x,y],'integer');" }}{PARA 9 "" 1 "" {TEXT 207 66 "\{--> enter Pr imitiveEuclidean, args = -45*y^2, 60*y, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 "*$)I\"yG6\"\"\"#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&\"#: \"\"\"I\"yG6\"F%F%" }}{PARA 9 "" 1 "" {TEXT 207 49 "<-- exit Primitive Euclidean (now in GCD) = 15*y\}" }{TEXT 207 65 "\n\{--> enter Primitiv eEuclidean, args = 15*y, 30*y, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "I \"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&\"#:\"\"\"I\"yG 6\"F%F%" }}{PARA 9 "" 1 "" {TEXT 207 49 "<-- exit PrimitiveEuclidean ( now in GCD) = 15*y\}" }{TEXT 207 71 "\n\{--> enter PrimitiveEuclidean, args = 15*y, -90*y^2-15, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"'\"\"\")I\"yG6\"\" \"#F%F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"'\"\"\")I\"yG6\" \"\"#F%F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" } }{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }}{PARA 11 " " 1 "" {XPPMATH 20 "\"#:" }}{PARA 9 "" 1 "" {TEXT 207 47 "<-- exit Pri mitiveEuclidean (now in GCD) = 15\}" }}{PARA 11 "" 1 "" {XPPMATH 20 ", ,*(\"\"#\"\"\")I\"xG6\"\"\"$F%I\"yGF(F%F%*(\"\"'F%)F'F$F%)F*F$F%!\"\"* $F-F%F/*(\"\"%F%F'F%F*F%F%*&F)F%F.F%F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "pp(bb,[x,y],'integer');" }}{PARA 9 "" 1 "" {TEXT 207 85 "\{--> enter PrimitiveEuclidean, args = -150*y^3+210*y^2, -250*y^2+ 350*y, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\")I \"yG6\"\"\"$F%F%*&\"\"(F%)F'\"\"#F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\")I\"yG6\"\"\"#F%F%*&\"\"(F%F'F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\" \"\")I\"yG6\"\"\"#F%F%*&\"\"(F%F'F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#]\"\"\")I\"yG6\"\"\"#F%F%*&\"#qF%F'F%!\"\"" }} {PARA 9 "" 1 "" {TEXT 207 56 "<-- exit PrimitiveEuclidean (now in GCD) = 50*y^2-70*y\}" }{TEXT 207 77 "\n\{--> enter PrimitiveEuclidean, arg s = 50*y^2-70*y, 100*y-140, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\")I\"yG6\"\"\"#F%F%*&\"\"(F%F'F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\"I\"yG6\"F%F%\"\"(!\"\"" }}{PARA 11 " " 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\" \"\"I\"yG6\"F%F%\"\"(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 ",& *&\"#]\"\"\"I\"yG6\"F%F%\"#q!\"\"" }}{PARA 9 "" 1 "" {TEXT 207 52 "<-- exit PrimitiveEuclidean (now in GCD) = 50*y-70\}" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&\"\"$\"\"\")I\"yG6\"\"\"#F%!\"\"*(\"\"&F%I\"xGF(F%F'F %F**&F)F%)F-F)F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "Primi tiveEuclidean(aa,bb,[x,y],'integer');" }}{PARA 9 "" 1 "" {TEXT 207 147 "\{--> enter PrimitiveEuclidean, args = -30*x^3*y+(90*y^2+15)*x^2- 60*x*y+45*y^2, (100*y-140)*x^2+(-250*y^2+350*y)*x-150*y^3+210*y^2, [x, y], integer" }}{PARA 9 "" 1 "" {TEXT 207 66 "\{--> enter PrimitiveEuc lidean, args = -45*y^2, 60*y, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 "*$)I\"yG6\"\"\"#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I \"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&\"#: \"\"\"I\"yG6\"F%F%" }}{PARA 9 "" 1 "" {TEXT 207 49 "<-- exit Primitive Euclidean (now in GCD) = 15*y\}" }{TEXT 207 65 "\n\{--> enter Primitiv eEuclidean, args = 15*y, 30*y, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "I \"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&\"#:\"\"\"I\"yG 6\"F%F%" }}{PARA 9 "" 1 "" {TEXT 207 49 "<-- exit PrimitiveEuclidean ( now in GCD) = 15*y\}" }{TEXT 207 71 "\n\{--> enter PrimitiveEuclidean, args = 15*y, -90*y^2-15, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"'\"\"\")I\"yG6\"\" \"#F%F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"'\"\"\")I\"yG6\" \"\"#F%F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" } }{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }}{PARA 11 " " 1 "" {XPPMATH 20 "\"#:" }}{PARA 9 "" 1 "" {TEXT 207 47 "<-- exit Pri mitiveEuclidean (now in GCD) = 15\}" }}{PARA 11 "" 1 "" {XPPMATH 20 ", ,*(\"\"#\"\"\")I\"xG6\"\"\"$F%I\"yGF(F%F%*(\"\"'F%)F'F$F%)F*F$F%!\"\"* $F-F%F/*(\"\"%F%F'F%F*F%F%*&F)F%F.F%F/" }}{PARA 9 "" 1 "" {TEXT 207 85 "\{--> enter PrimitiveEuclidean, args = -150*y^3+210*y^2, -250*y^2+ 350*y, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\")I \"yG6\"\"\"$F%F%*&\"\"(F%)F'\"\"#F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\")I\"yG6\"\"\"#F%F%*&\"\"(F%F'F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\" \"\")I\"yG6\"\"\"#F%F%*&\"\"(F%F'F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#]\"\"\")I\"yG6\"\"\"#F%F%*&\"#qF%F'F%!\"\"" }} {PARA 9 "" 1 "" {TEXT 207 56 "<-- exit PrimitiveEuclidean (now in GCD) = 50*y^2-70*y\}" }{TEXT 207 77 "\n\{--> enter PrimitiveEuclidean, arg s = 50*y^2-70*y, 100*y-140, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\")I\"yG6\"\"\"#F%F%*&\"\"(F%F'F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\"I\"yG6\"F%F%\"\"(!\"\"" }}{PARA 11 " " 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\" \"\"I\"yG6\"F%F%\"\"(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 ",& *&\"#]\"\"\"I\"yG6\"F%F%\"#q!\"\"" }}{PARA 9 "" 1 "" {TEXT 207 52 "<-- exit PrimitiveEuclidean (now in GCD) = 50*y-70\}" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&\"\"$\"\"\")I\"yG6\"\"\"#F%!\"\"*(\"\"&F%I\"xGF(F%F'F %F**&F)F%)F-F)F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&,&*&\"\"#\"\" \")I\"yG6\"\"\"$F'F'*&\"\"'F'F)F'F'F'I\"xGF*F'F'*&\"#=F')F)F&F'!\"\"*& F-F')F)\"\"%F'F2" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&\"\"$\"\"\")I\"y G6\"\"\"#F%!\"\"*(\"\"&F%I\"xGF(F%F'F%F**&F)F%)F-F)F%F%" }}{PARA 9 "" 1 "" {TEXT 207 77 "\{--> enter PrimitiveEuclidean, args = -18*y^2-6*y^ 4, 2*y^3+6*y, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"$ \"\"\")I\"yG6\"\"\"#F%F%*$)F'\"\"%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"yG6\"\"\"$\"\"\"F(*&F'F(F%F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"yG6\"\"\"$\"\"\"F(* &F'F(F%F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"#\"\"\")I \"yG6\"\"\"$F%F%*&\"\"'F%F'F%F%" }}{PARA 9 "" 1 "" {TEXT 207 54 "<-- e xit PrimitiveEuclidean (now in GCD) = 2*y^3+6*y\}" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"$\"\"\"I\"yG6\"F%!\"\"I\"xGF'F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"$\"\"\" I\"yG6\"F%!\"\"I\"xGF'F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 9 "" 1 "" {TEXT 207 66 "\{--> enter PrimitiveEuclidean, args = - 45*y^2, 60*y, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 "*$)I\"yG6 \"\"\"#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"#:" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&\"#:\"\"\"I\"yG6\"F%F%" }} {PARA 9 "" 1 "" {TEXT 207 49 "<-- exit PrimitiveEuclidean (now in GCD) = 15*y\}" }{TEXT 207 65 "\n\{--> enter PrimitiveEuclidean, args = 15* y, 30*y, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }}{PARA 11 " " 1 "" {XPPMATH 20 ",$*&\"#:\"\"\"I\"yG6\"F%F%" }}{PARA 9 "" 1 "" {TEXT 207 49 "<-- exit PrimitiveEuclidean (now in GCD) = 15*y\}" } {TEXT 207 71 "\n\{--> enter PrimitiveEuclidean, args = 15*y, -90*y^2-1 5, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"'\"\"\")I\"yG6\"\"\"#F%F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"'\"\"\")I\"yG6\"\"\"#F%F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\" \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"yG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" } }{PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"#:" }}{PARA 9 "" 1 "" {TEXT 207 47 "<-- exit PrimitiveEuclidean (now in GCD) = 15\}" }{TEXT 207 87 "\n\{--> enter PrimitiveEuclidean, args = -150*y^3+210*y^2, -250*y^2+350*y, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\")I\"yG6\"\"\"$F%F%*&\"\"(F%)F'\"\"#F%!\"\" " }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\")I\"yG6\"\"\"#F%F%*& \"\"(F%F'F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\")I\"yG6\"\"\"#F%F%*&\"\"(F%F'F%!\"\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#]\"\"\")I\"yG6\"\"\"# F%F%*&\"#qF%F'F%!\"\"" }}{PARA 9 "" 1 "" {TEXT 207 56 "<-- exit Primit iveEuclidean (now in GCD) = 50*y^2-70*y\}" }{TEXT 207 77 "\n\{--> ente r PrimitiveEuclidean, args = 50*y^2-70*y, 100*y-140, [y], integer" }} {PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\")I\"yG6\"\"\"#F%F%*&\"\"( F%F'F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\"I\"yG6\"F% F%\"\"(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 " " {XPPMATH 20 ",&*&\"\"&\"\"\"I\"yG6\"F%F%\"\"(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#]\"\"\"I\"yG6\"F%F%\"#q!\"\"" }}{PARA 9 "" 1 "" {TEXT 207 52 "<-- exit PrimitiveEuclidean (now in GCD) = 50*y -70\}" }{TEXT 207 66 "\n\{--> enter PrimitiveEuclidean, args = 15, 50* y-70, [y], integer" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\"I\"yG6\"F%F%\"\"(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"&\"\"\"I\"yG6\"F%F%\"\"(!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"&" }}{PARA 9 "" 1 "" {TEXT 207 61 "<-- exit P rimitiveEuclidean (now in PrimitiveEuclidean) = 5\}" }}{PARA 11 "" 1 " " {XPPMATH 20 "\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#:\"\"\"I \"yG6\"F%!\"\"*&\"\"&F%I\"xGF'F%F%" }}{PARA 9 "" 1 "" {TEXT 207 60 "<- - exit PrimitiveEuclidean (now at top level) = -15*y+5*x\}" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#:\"\"\"I\"yG6\"F%!\"\"*&\"\"&F%I\"xGF'F%F %" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.24. P" }{TEXT 206 12 "\303\251lda." } {TEXT 206 1 " " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "PrimitiveEuclidean(a,b,[x],'rational');" }} {PARA 9 "" 1 "" {TEXT 207 98 "\{--> enter PrimitiveEuclidean, args = 4 8*x^3-84*x^2+42*x-36, -4*x^3-10*x^2+44*x-30, [x], rational" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**$)I\"xG6\"\"\"$\"\"\"F(*&#\"\"(\"\"%F()F%\"\" #F(!\"\"*&#F+\"\")F(F%F(F(#F'F,F/" }}{PARA 11 "" 1 "" {XPPMATH 20 ",** $)I\"xG6\"\"\"$\"\"\"F(*&#\"\"&\"\"#F()F%F,F(F(*&\"#6F(F%F(!\"\"#\"#:F ,F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(#\"#L\"\"%!\"\"*&#\"# " 0 "" {MPLTEXT 1 0 36 "-2/4; 2/(-4); 100/(-200); -600/1200;" }}{PARA 11 "" 1 "" {XPPMATH 20 "#!\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "#!\"\"\" \"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "#!\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "#!\"\"\"\"#" }}}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.26. P" }{TEXT 206 12 "\303\251lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "a:=17/100*x^2-3/112*x+1/2; b:=5/9*x^2+4/5;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&#\"#<\"$+\"\"\"\")I\"xG6\"\"\"#F'F'*&#\"\"$\"$7\"F'F )F'!\"\"#F'F+F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&#\"\"&\"\"*\"\"\" )I\"xG6\"\"\"#F'F'#\"\"%F%F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "a/b;" }}{PARA 11 "" 1 "" {XPPMATH 20 "*&,(*&#\"#<\"$+\"\"\"\")I\" xG6\"\"\"#F(F(*&#\"\"$\"$7\"F(F*F(!\"\"#F(F,F(F(,&*&#\"\"&\"\"*F(F)F(F (#\"\"%F6F(F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "expand(a*2 5200)/expand(b*25200);" }}{PARA 11 "" 1 "" {XPPMATH 20 "*&,(*&\"%%G%\" \"\")I\"xG6\"\"\"#F&F&*&\"$v'F&F(F&!\"\"\"&+E\"F&F&,&*&\"&+S\"F&F'F&F& \"&g,#F&F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "expand(a*2520 0/14000)/expand(b*25200/14000);" }}{PARA 11 "" 1 "" {XPPMATH 20 "*&,(* &#\"$`\"\"$+&\"\"\")I\"xG6\"\"\"#F(F(*&#\"#F\"$g&F(F*F(!\"\"#\"\"*\"#5 F(F(,&*$F)F(F(#\"#O\"#DF(F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "normal(expand(a/b));" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(#\"\"*\" $g&\"\"\",(*&\"$w%F')I\"xG6\"\"\"#F'F'*&\"#vF'F,F'!\"\"\"%+9F'F',&*&\" #DF'F+F'F'\"#OF'F1F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "sim plify(a/b);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(#\"\"*\"$g&\"\"\",(*& \"$w%F')I\"xG6\"\"\"#F'F'*&\"#vF'F,F'!\"\"\"%+9F'F',&*&\"#DF'F+F'F'\"# OF'F1F'" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.27. P" }{TEXT 206 12 "\303\251lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "d:=series(1/(1-x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "+1I\"xG 6\"\"\"\"\"\"!F%F%F%\"\"#F%\"\"$F%\"\"%F%\"\"&-I\"OG%*protectedG6#F%\" \"'" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.28. P" }{TEXT 206 12 "\303\251lda." } }{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "series(1/d,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "+)I\"xG6\"\"\"\" \"\"!!\"\"F%-I\"OG%*protectedG6#F%\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.2 9. P" }{TEXT 206 12 "\303\251lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "with(powseries);" }}{PARA 11 "" 1 "" {XPPMATH 20 "77I(composeG6\"I(evalpowGF$I(inverseGF$I*multcon stGF$I)multiplyGF$I)negativeG%*protectedGI'powaddGF$I'powcosGF$I*powcr eateGF$I(powdiffGF$I'powexpGF$I'powintGF$I'powlogGF$I(powpolyGF$I'pows inGF$I)powsolveGF$I(powsqrtGF$I)quotientGF$I*reversionGF$I)subtractGF$ I(tpsformGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "c:='c'; pow create(c(n)=1,c(0)=2,c(1)=0,c(2)=0); tpsform(c,x,8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"cG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "+1I\"xG6\"\" \"#\"\"!\"\"\"\"\"$F'\"\"%F'\"\"&F'\"\"'F'\"\"(-I\"OG%*protectedG6#F' \"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "d:=powpoly(1-x,x); tpsform(d,x,8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I(powparmG6\"6$I #nnGF%I#t1GF%6#IaoCopyright~(c)~1990~by~the~University~of~Waterloo.~Al l~rights~reserved.GF%E\\s$\"\"!\"\"\"F-!\"\"I#_kGF%F,C$@%-I%typeG%*pro tectedG6$F$I(integerGF4C$>F'-%)procnameG6#F/@%30-I#opGF46$\"\"%-F@6#F: I%NULLGF4-I$hasGF46$7#-I(indicesGF46#F?F/C%>F(-I%subsGF46$/F/F$F'>-F:6 #%%argsG-I%evalGF46#F(OFWO.FTC$>FTFfnFen7%I(powpolyG6$F4/I+modulenameG F%I*powseriesG6$F4I(_syslibGF%,&F-F-I\"xGF%F.FboF%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "+'I\"xG6\"\"\"\"\"\"!!\"\"F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "e:=inverse(d); tpsform(e,x,8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I(powparmG6\"6$I#nnGF%I#t1GF%6#IaoCopyright~(c)~1 990~by~the~University~of~Waterloo.~All~rights~reserved.GF%E\\s#\"\"!\" \"\"I#_kGF%,$-I$sumGF%6$*&-I\"dGF%6#I\"jGF%F--I$ansGF%6#,&F.F-F7!\"\"F -/F7;F-F.FF'-%)procnameG6# F.@%30-I#opGFC6$\"\"%-FO6#FII%NULLGFC-I$hasGFC6$7#-I(indicesGFC6#FNF.C %>F(-I%subsGFC6$/F.F$F'>-FI6#%%argsG-I%evalGFC6#F(OF`oO.F]oC$>F]oFeoFd o7$I(inverseG6$FC/I+modulenameGF%I*powseriesG6$FCI(_syslibGF%F5F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "+5I\"xG6\"\"\"\"\"\"!F%F%F%\"\"#F%\" \"$F%\"\"%F%\"\"&F%\"\"'F%\"\"(-I\"OG%*protectedG6#F%\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "a:=multiply(e,c); tpsform(a,x,8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I(powparmG6\"6$I#nnGF%I#t1GF%6#Iao Copyright~(c)~1990~by~the~University~of~Waterloo.~All~rights~reserved. GF%E\\s\"I#_kGF%-I$sumG6$%*protectedGI(_syslibGF%6$*&-I\"eGF%6#I\"jGF% \"\"\"-I\"cGF%6#,&F,F8F7!\"\"F8/F7;\"\"!F,C$@%-I%typeGF06$F$I(integerG F0C$>F'-%)procnameG6#F,@%30-I#opGF06$\"\"%-FP6#FJI%NULLGF0-I$hasGF06$7 #-I(indicesGF06#FOF,C%>F(-I%subsGF06$/F,F$F'>-FJ6#%%argsG-I%evalGF06#F (OFaoO.F^oC$>F^oFfoFeo7%I)multiplyG6$F0/I+modulenameGF%I*powseriesGF/F 5F:F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "+5I\"xG6\"\"\"#\"\"!F%\"\" \"F%F%\"\"$F(\"\"%F)\"\"&F*\"\"'F+\"\"(F,-I\"OG%*protectedG6#F'\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "b:=multiply(a,e); tpsform (b,x,8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I(powparmG6\"6$I#nnGF%I# t1GF%6#IaoCopyright~(c)~1990~by~the~University~of~Waterloo.~All~rights ~reserved.GF%E\\s\"I#_kGF%-I$sumG6$%*protectedGI(_syslibGF%6$*&-I\"aGF %6#I\"jGF%\"\"\"-I\"eGF%6#,&F,F8F7!\"\"F8/F7;\"\"!F,C$@%-I%typeGF06$F$ I(integerGF0C$>F'-%)procnameG6#F,@%30-I#opGF06$\"\"%-FP6#FJI%NULLGF0-I $hasGF06$7#-I(indicesGF06#FOF,C%>F(-I%subsGF06$/F,F$F'>-FJ6#%%argsG-I% evalGF06#F(OFaoO.F^oC$>F^oFfoFeo7%I)multiplyG6$F0/I+modulenameGF%I*pow seriesGF/F5F:F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "+5I\"xG6\"\"\"#\" \"!\"\"%\"\"\"\"\"'F%\"\"*\"\"$\"#8F'\"#=\"\"&\"#CF)\"#J\"\"(-I\"OG%*p rotectedG6#F(\"\")" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.30. P" }{TEXT 206 12 "\30 3\251lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "b:=powlog(d); tpsform(b,x,8); a:=negative(b); tpsfor m(a,x,8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I(powparmG6\"6$I#nnGF%I #t1GF%6#IaoCopyright~(c)~1990~by~the~University~of~Waterloo.~All~right s~reserved.GF%E\\s#\"\"!F,I#_kGF%*&,&*&F-\"\"\"-I\"dGF%6#F-F1F1-I$sumG 6$%*protectedGI(_syslibGF%6$*(,&F-F1I\"iGF%!\"\"F1-I$ansGF%6#FF>F1F-F>C$@%-I%typeGF86$F$I(integerGF8C$>F'-%)proc nameGF4@%30-I#opGF86$\"\"%-FU6#FPI%NULLGF8-I$hasGF86$7#-I(indicesGF86# FTF-C%>F(-I%subsGF86$/F-F$F'>-FP6#%%argsG-I%evalGF86#F(OFfoO.FcoC$>Fco F[pFjo7$I'powlogG6$F8/I+modulenameGF%I*powseriesGF7F3F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "+3I\"xG6\"!\"\"\"\"\"#F%\"\"#F(#F%\"\"$F*#F%\" \"%F,#F%\"\"&F.#F%\"\"'F0#F%\"\"(F2-I\"OG%*protectedG6#F&\"\")" }} {PARA 11 "" 1 "" {XPPMATH 20 "f*6#I(powparmG6\"6$I#nnGF%I#t1GF%6#IaoCo pyright~(c)~1990~by~the~University~of~Waterloo.~All~rights~reserved.GF %E\\s\"I#_kGF%,$-I\"bGF%6#F,!\"\"C$@%-I%typeG%*protectedG6$F$I(integer GF6C$>F'-%)procnameGF0@%30-I#opGF66$\"\"%-FA6#FF(-I%subsGF66$/F,F$F'>-F<6#%%argsG-I%evalGF66#F( OFXO.FUC$>FUFgnFfn7$I)negativeG6$F6/I+modulenameGF%I*powseriesG6$F6I(_ syslibGF%F/F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "+3I\"xG6\"\"\"\"F%# F%\"\"#F'#F%\"\"$F)#F%\"\"%F+#F%\"\"&F-#F%\"\"'F/#F%\"\"(F1-I\"OG%*pro tectedG6#F%\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "c:=mult iply(a,e); tpsform(c,x,8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I(powp armG6\"6$I#nnGF%I#t1GF%6#IaoCopyright~(c)~1990~by~the~University~of~Wa terloo.~All~rights~reserved.GF%E\\s\"I#_kGF%-I$sumG6$%*protectedGI(_sy slibGF%6$*&-I\"aGF%6#I\"jGF%\"\"\"-I\"eGF%6#,&F,F8F7!\"\"F8/F7;\"\"!F, C$@%-I%typeGF06$F$I(integerGF0C$>F'-%)procnameG6#F,@%30-I#opGF06$\"\"% -FP6#FJI%NULLGF0-I$hasGF06$7#-I(indicesGF06#FOF,C%>F(-I%subsGF06$/F,F$ F'>-FJ6#%%argsG-I%evalGF06#F(OFaoO.F^oC$>F^oFfoFeo7%I)multiplyG6$F0/I+ modulenameGF%I*powseriesGF/F5F:F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "+3I\"xG6\"\"\"\"F%#\"\"$\"\"#F(#\"#6\"\"'F'#\"#D\"#7\"\"%#\"$P\"\"#g \"\"&#\"#\\\"#?F+#\"$j$\"$S\"\"\"(-I\"OG%*protectedG6#F%\"\")" }}} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 2.31. P" }{TEXT 206 12 "\303\251lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "c:='c '; powcreate(c(n)=1/2^(n-2),c(0)=0,c(1)=0); tpsform(c,x,8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"cG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "+1I \"xG6\"\"\"\"\"\"##F%F&\"\"$#F%\"\"%F*#F%\"\")\"\"&#F%\"#;\"\"'#F%\"#K \"\"(-I\"OG%*protectedG6#F%F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "a:=inverse(c);" }}{PARA 8 "" 1 "" {TEXT 208 61 "Error, (in powse ries:-inverse) inverse will have pole at zero" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "series(1/(x^2*(1-x/2)),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "+5I\"xG6\"\"\"\"!\"##F%\"\"#!\"\"#F%\"\"%\"\"!#F%\"\")F%# F%\"#;F(#F%\"#K\"\"$#F%\"#kF+#F%\"$G\"\"\"&-I\"OG%*protectedG6#F%\"\"' " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{PARA 0 "" 0 "" {TEXT 201 0 "" }}} {SECT 1 {PARA 3 "" 0 "" {TEXT 205 7 "3. Norm" }{TEXT 205 8 "\303\241" }{TEXT 205 6 "l form" }{TEXT 205 8 "\303\241" }{TEXT 205 12 "k, reprez ent" }{TEXT 205 18 "\303\241ci\303\263" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 13 "4. Aritmetika" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 4 "5 . K" }{TEXT 205 8 "\303\255" }{TEXT 205 9 "nai marad" }{TEXT 205 8 "\3 03\251" }{TEXT 205 3 "kol" }{TEXT 205 8 "\303\241" }{TEXT 205 1 "s" }} }{SECT 1 {PARA 3 "" 0 "" {TEXT 205 14 "6. Newton-iter" }{TEXT 205 8 " \303\241" }{TEXT 205 2 "ci" }{TEXT 205 8 "\303\263" }{TEXT 205 16 ", H ensel-felemel" }{TEXT 205 8 "\303\251" }{TEXT 205 1 "s" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 15 "7. Legnagyobb k" }{TEXT 205 8 "\303\266" }{TEXT 205 1 "z" }{TEXT 205 8 "\303\266" }{TEXT 205 6 "s oszt" }{TEXT 205 8 "\303\263" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 11 "8. Faktoriz " }{TEXT 205 8 "\303\241" }{TEXT 205 1 "l" }{TEXT 205 8 "\303\241" } {TEXT 205 1 "s" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 21 "9. Egyenletre ndszerek" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 6 "10. Gr" }{TEXT 205 27 "\303\266bner-b\303\241zisok" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 10 "11. Racion" }{TEXT 205 8 "\303\241" }{TEXT 205 5 "lis t" }{TEXT 205 8 "\303\266" }{TEXT 205 3 "rtf" }{TEXT 205 8 "\303\274" }{TEXT 205 3 "ggv" }{TEXT 205 8 "\303\251" }{TEXT 205 11 "nyek integr" }{TEXT 205 8 "\303\241" }{TEXT 205 1 "l" }{TEXT 205 8 "\303\241" }{TEXT 205 2 "sa" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 23 "12. A Risch-algoritmus ." }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }