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, mathvariant = \"normal\", fence = \"false\", separator = \"false\", \+
stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mova
blelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace \+
= \"0.0em\", equality = \"false\"), Typesetting:-mi(\" Input a Liouvil
lian extension\", italic = \"true\", mathvariant = \"italic\"), Typese
tting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\"
, linebreak = \"newline\"), Typesetting:-mspace(height = \"0.0ex\", wi
dth = \"0.0em\", depth = \"0.0ex\", linebreak = \"auto\"), Typesetting
:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", lin
ebreak = \"newline\"), Typesetting:-mspace(height = \"0.0ex\", width =
 \"0.0em\", depth = \"0.0ex\", linebreak = \"auto\"), Typesetting:-mo(
\" \", mathvariant = \"normal\", fence = \"false\", separator = \"fals
e\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\",
 movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rs
pace = \"0.0em\", equality = \"false\"), Typesetting:-mi(\"K\", italic
 = \"true\", mathvariant = \"italic\"), Typesetting:-mo(\"&coloneq;\",
 mathvariant = \"normal\", fence = \"false\", separator = \"false\", s
tretchy = \"false\", symmetric = \"false\", largeop = \"false\", movab
lelimits = \"false\", accent = \"false\", lspace = \"0.2777778em\", rs
pace = \"0.2777778em\", equality = \"false\"), Typesetting:-mi(\"x\", \+
italic = \"true\", mathvariant = \"italic\"), Typesetting:-mo(\",\", m
athvariant = \"normal\", fence = \"false\", separator = \"true\", stre
tchy = \"false\", symmetric = \"false\", largeop = \"false\", movablel
imits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"
0.3333333em\", equality = \"false\"), Typesetting:-mfenced(Typesetting
:-mrow(Typesetting:-mi(\"t\", italic = \"true\", mathvariant = \"itali
c\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn(\"1\", ma
thvariant = \"normal\")), mathvariant = \"normal\", open = \"[\", clos
e = \"]\"), Typesetting:-mo(\",\", mathvariant = \"normal\", fence = \+
\"false\", separator = \"true\", stretchy = \"false\", symmetric = \"f
alse\", largeop = \"false\", movablelimits = \"false\", accent = \"fal
se\", lspace = \"0.0em\", rspace = \"0.3333333em\", equality = \"false
\"), Typesetting:-mi(\"t\", italic = \"true\", mathvariant = \"italic
\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn(\"2\", mat
hvariant = \"normal\")), mathvariant = \"normal\", open = \"[\", close
 = \"]\"), Typesetting:-mi(\"\")), mathvariant = \"normal\", open = \"
[\", close = \"]\"), Typesetting:-mo(\",\", mathvariant = \"normal\", \+
fence = \"false\", separator = \"true\", stretchy = \"false\", symmetr
ic = \"false\", largeop = \"false\", movablelimits = \"false\", accent
 = \"false\", lspace = \"0.0em\", rspace = \"0.3333333em\", equality =
 \"false\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfrac
(Typesetting:-mn(\"1\", mathvariant = \"normal\"), Typesetting:-mrow(T
ypesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\")), l
inethickness = \"1\", denomalign = \"center\", numalign = \"center\", \+
bevelled = \"false\"), Typesetting:-mo(\",\", mathvariant = \"normal\"
, fence = \"false\", separator = \"true\", stretchy = \"false\", symme
tric = \"false\", largeop = \"false\", movablelimits = \"false\", acce
nt = \"false\", lspace = \"0.0em\", rspace = \"0.3333333em\", equality
 = \"false\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(
\"\"), Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mi(\"t\", ita
lic = \"true\", mathvariant = \"italic\"), Typesetting:-msup(Typesetti
ng:-mfenced(Typesetting:-mrow(Typesetting:-mn(\"1\", mathvariant = \"n
ormal\")), mathvariant = \"normal\", open = \"[\", close = \"]\"), Typ
esetting:-mrow(Typesetting:-mn(\"2\", mathvariant = \"normal\")), supe
rscriptshift = \"0\")), Typesetting:-mrow(Typesetting:-mi(\"x\", itali
c = \"true\", mathvariant = \"italic\"), Typesetting:-mo(\"&sdot;\", m
athvariant = \"normal\", fence = \"false\", separator = \"false\", str
etchy = \"false\", symmetric = \"false\", largeop = \"false\", movable
limits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \+
\"0.0em\", equality = \"false\"), Typesetting:-mfenced(Typesetting:-mr
ow(Typesetting:-mi(\"t\", italic = \"true\", mathvariant = \"italic\")
, Typesetting:-msup(Typesetting:-mfenced(Typesetting:-mrow(Typesetting
:-mn(\"1\", mathvariant = \"normal\")), mathvariant = \"normal\", open
 = \"[\", close = \"]\"), Typesetting:-mrow(Typesetting:-mn(\"2\", mat
hvariant = \"normal\")), superscriptshift = \"0\"), Typesetting:-mo(\"
+\", mathvariant = \"normal\", fence = \"false\", separator = \"false
\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", \+
movablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em
\", rspace = \"0.2222222em\", equality = \"false\"), Typesetting:-mi(
\"t\", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mfen
ced(Typesetting:-mrow(Typesetting:-mn(\"1\", mathvariant = \"normal\")
), mathvariant = \"normal\", open = \"[\", close = \"]\"), Typesetting
:-mo(\"+\", mathvariant = \"normal\", fence = \"false\", separator = \+
\"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"fa
lse\", movablelimits = \"false\", accent = \"false\", lspace = \"0.222
2222em\", rspace = \"0.2222222em\", equality = \"false\"), Typesetting
:-mi(\"x\", italic = \"true\", mathvariant = \"italic\")), mathvariant
 = \"normal\")), linethickness = \"1\", denomalign = \"center\", numal
ign = \"center\", bevelled = \"false\")), mathvariant = \"normal\"), T
ypesetting:-mo(\"&sdot;\", mathvariant = \"normal\", fence = \"false\"
, separator = \"false\", stretchy = \"false\", symmetric = \"false\", \+
largeop = \"false\", movablelimits = \"false\", accent = \"false\", ls
pace = \"0.0em\", rspace = \"0.0em\", equality = \"false\"), Typesetti
ng:-mi(\"t\", italic = \"true\", mathvariant = \"italic\"), Typesettin
g:-mfenced(Typesetting:-mrow(Typesetting:-mn(\"2\", mathvariant = \"no
rmal\")), mathvariant = \"normal\", open = \"[\", close = \"]\")), mat
hvariant = \"normal\", open = \"[\", close = \"]\"), Typesetting:-mo(
\";\", mathvariant = \"normal\", fence = \"false\", separator = \"true
\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", \+
movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rsp
ace = \"0.2777778em\", equality = \"false\"), Typesetting:-mspace(heig
ht = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"ne
wline\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", d
epth = \"0.0ex\", linebreak = \"auto\"), Typesetting:-mspace(height = \+
\"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline
\"), Typesetting:-mo(\" \", mathvariant = \"normal\", fence = \"false
\", separator = \"false\", stretchy = \"false\", symmetric = \"false\"
, largeop = \"false\", movablelimits = \"false\", accent = \"false\", \+
lspace = \"0.0em\", rspace = \"0.0em\", equality = \"false\"), Typeset
ting:-mo(\"#\", mathvariant = \"normal\", fence = \"false\", separator
 = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \+
\"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0
.0em\", rspace = \"0.0em\", equality = \"false\"), Typesetting:-mi(\" \+
Check whether K has new constant \", italic = \"true\", mathvariant = \+
\"italic\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\"
, depth = \"0.0ex\", linebreak = \"newline\"), Typesetting:-mspace(hei
ght = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"a
uto\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", dep
th = \"0.0ex\", linebreak = \"newline\"), Typesetting:-mspace(height =
 \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newlin
e\"), Typesetting:-mo(\" \", mathvariant = \"normal\", fence = \"false
\", separator = \"false\", stretchy = \"false\", symmetric = \"false\"
, largeop = \"false\", movablelimits = \"false\", accent = \"false\", \+
lspace = \"0.0em\", rspace = \"0.0em\", equality = \"false\"), Typeset
ting:-mi(\"NoNewConst\", italic = \"true\", mathvariant = \"italic\"),
 Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"K\", italic \+
= \"true\", mathvariant = \"italic\")), mathvariant = \"normal\"), Typ
esetting:-mo(\";\", mathvariant = \"normal\", fence = \"false\", separ
ator = \"true\", stretchy = \"false\", symmetric = \"false\", largeop \+
= \"false\", movablelimits = \"false\", accent = \"false\", lspace = \+
\"0.0em\", rspace = \"0.2777778em\", equality = \"false\"), Typesettin
g:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", li
nebreak = \"newline\"), Typesetting:-mo(\" \", mathvariant = \"normal
\", fence = \"false\", separator = \"false\", stretchy = \"false\", sy
mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a
ccent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\", equality = \+
\"false\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6B
-I#moGF$6.Q\"~F'/%,mathvariantGQ'normalF'/%&fenceGQ&falseF'/%*separato
rGF4/%)stretchyGF4/%*symmetricGF4/%(largeopGF4/%.movablelimitsGF4/%'ac
centGF4/%'lspaceGQ&0.0emF'/%'rspaceGFC/%)equalityGF4-F,6.Q\"#F'F/F2F5F
7F9F;F=F?FAFDFF-I#miGF$6%Q?~Input~a~Liouvillian~extensionF'/%'italicGQ
%trueF'/F0Q'italicF'-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGFC/%&dep
thGFY/%*linebreakGQ(newlineF'-FU6&FWFZFfn/FinQ%autoF'FTF[oF+-FL6%Q\"KF
'FOFR-F,6.Q*&coloneq;F'F/F2F5F7F9F;F=F?/FBQ,0.2777778emF'/FEFfoFF-FL6%
Q\"xF'FOFR-F,6.Q\",F'F/F2/F6FQF7F9F;F=F?FA/FEQ,0.3333333emF'FF-I(mfenc
edGF$6&-F#6(-FL6%Q\"tF'FOFR-Fbp6&-F#6#-I#mnGF$6$Q\"1F'F/F//%%openGQ\"[
F'/%&closeGQ\"]F'F[pFfp-Fbp6&-F#6#-F^q6$Q\"2F'F/F/FaqFdq-FL6#Q!F'F/Faq
FdqF[p-Fbp6&-F#6(-I&mfracGF$6(F]q-F#6#Fho/%.linethicknessGF`q/%+denoma
lignGQ'centerF'/%)numalignGF^s/%)bevelledGF4F[p-Fbp6$-F#6$F^r-Ffr6(-F#
6$Ffp-I%msupGF$6%FipFiq/%1superscriptshiftGQ\"0F'-F#6%Fho-F,6.Q'&sdot;
F'F/F2F5F7F9F;F=F?FAFDFF-Fbp6$-F#6)FfpF[t-F,6.Q\"+F'F/F2F5F7F9F;F=F?/F
BQ,0.2222222emF'/FEF^uFFFfpFipFjtFhoF/FjrF\\sF_sFasF/FctFfpFgqF/FaqFdq
-F,6.Q\";F'F/F2F^pF7F9F;F=F?FAFgoFFFTF[oFTF+FH-FL6%QC~Check~whether~K~
has~new~constant~F'FOFRFTF[oFTFTF+-FL6%Q+NoNewConstF'FOFR-Fbp6$-F#6#F_
oF/F`uFTF+" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I\"KG6\"6%I\"xGF$7$&I\"tG
F$6#\"\"\"&F)6#\"\"#7$*$F&!\"\"**F(F.F&F1,(*$F(F.F+F&F+F(F+F1F,F+" }}
{PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }}}{EXCHG {PARA 0 "
> " 0 "" {XPPEDIT 19 1 "Typesetting:-mrow(Typesetting:-mo(\"#\", mathv
ariant = \"normal\", fence = \"false\", separator = \"false\", stretch
y = \"false\", symmetric = \"false\", largeop = \"false\", movablelimi
ts = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0
em\", equality = \"false\"), Typesetting:-mi(\" Set the global variabl
e \", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mspac
e(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak \+
= \"newline\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0e
m\", depth = \"0.0ex\", linebreak = \"auto\"), Typesetting:-mspace(hei
ght = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"n
ewline\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", \+
depth = \"0.0ex\", linebreak = \"newline\"), Typesetting:-mspace(heigh
t = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"new
line\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", de
pth = \"0.0ex\", linebreak = \"auto\"), Typesetting:-mi(\"SetTower\", \+
italic = \"true\", mathvariant = \"italic\"), Typesetting:-mfenced(Typ
esetting:-mrow(Typesetting:-mi(\"K\", italic = \"true\", mathvariant =
 \"italic\")), mathvariant = \"normal\"), Typesetting:-mo(\";\", mathv
ariant = \"normal\", fence = \"false\", separator = \"true\", stretchy
 = \"false\", symmetric = \"false\", largeop = \"false\", movablelimit
s = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.27
77778em\", equality = \"false\"), Typesetting:-mspace(height = \"0.0ex
\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Ty
pesetting:-mo(\" \", mathvariant = \"normal\", fence = \"false\", sepa
rator = \"false\", stretchy = \"false\", symmetric = \"false\", largeo
p = \"false\", movablelimits = \"false\", accent = \"false\", lspace =
 \"0.0em\", rspace = \"0.0em\", equality = \"false\"), Typesetting:-ms
pace(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebre
ak = \"newline\"), Typesetting:-mi(\"\"));" "-I%mrowG6#/I+modulenameG6
\"I,TypesettingGI(_syslibGF'61-I#moGF$6.Q\"#F'/%,mathvariantGQ'normalF
'/%&fenceGQ&falseF'/%*separatorGF4/%)stretchyGF4/%*symmetricGF4/%(larg
eopGF4/%.movablelimitsGF4/%'accentGF4/%'lspaceGQ&0.0emF'/%'rspaceGFC/%
)equalityGF4-I#miGF$6%Q:~Set~the~global~variable~F'/%'italicGQ%trueF'/
F0Q'italicF'-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGFC/%&depthGFV/%*
linebreakGQ(newlineF'-FR6&FTFWFY/FfnQ%autoF'FQFQFQFhn-FI6%Q)SetTowerF'
FLFO-I(mfencedGF$6$-F#6#-FI6%Q\"KF'FLFOF/-F,6.Q\";F'F/F2/F6FNF7F9F;F=F
?FA/FEQ,0.2777778emF'FFFQ-F,6.Q\"~F'F/F2F5F7F9F;F=F?FAFDFFFQ-FI6#Q!F'"
 }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "Typesetting:-mrow(Typesett
ing:-mo(\"#\", mathvariant = \"normal\", fence = \"false\", separator \+
= \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"
false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0
em\", rspace = \"0.0em\", equality = \"false\"), Typesetting:-mi(\" In
put an element of K\", italic = \"true\", mathvariant = \"italic\"), T
ypesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \"0.
0ex\", linebreak = \"newline\"), Typesetting:-mspace(height = \"0.0ex
\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"auto\"), Types
etting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex
\", linebreak = \"newline\"), Typesetting:-mspace(height = \"0.0ex\", \+
width = \"0.0em\", depth = \"0.0ex\", linebreak = \"auto\"), Typesetti
ng:-mo(\" \", mathvariant = \"normal\", fence = \"false\", separator =
 \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"f
alse\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0e
m\", rspace = \"0.0em\", equality = \"false\"), Typesetting:-mi(\"f\",
 italic = \"true\", mathvariant = \"italic\"), Typesetting:-mo(\"&colo
neq;\", mathvariant = \"normal\", fence = \"false\", separator = \"fal
se\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\"
, movablelimits = \"false\", accent = \"false\", lspace = \"0.2777778e
m\", rspace = \"0.2777778em\", equality = \"false\"), Typesetting:-mfr
ac(Typesetting:-mrow(Typesetting:-mi(\"t\", italic = \"true\", mathvar
iant = \"italic\"), Typesetting:-msup(Typesetting:-mfenced(Typesetting
:-mrow(Typesetting:-mn(\"2\", mathvariant = \"normal\")), mathvariant \+
= \"normal\", open = \"[\", close = \"]\"), Typesetting:-mrow(Typesett
ing:-mn(\"3\", mathvariant = \"normal\")), superscriptshift = \"0\")),
 Typesetting:-mrow(Typesetting:-mn(\"1\", mathvariant = \"normal\"), T
ypesetting:-mo(\"+\", mathvariant = \"normal\", fence = \"false\", sep
arator = \"false\", stretchy = \"false\", symmetric = \"false\", large
op = \"false\", movablelimits = \"false\", accent = \"false\", lspace \+
= \"0.2222222em\", rspace = \"0.2222222em\", equality = \"false\"), Ty
pesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\"), Typ
esetting:-mo(\"&sdot;\", mathvariant = \"normal\", fence = \"false\", \+
separator = \"false\", stretchy = \"false\", symmetric = \"false\", la
rgeop = \"false\", movablelimits = \"false\", accent = \"false\", lspa
ce = \"0.0em\", rspace = \"0.0em\", equality = \"false\"), Typesetting
:-mi(\"t\", italic = \"true\", mathvariant = \"italic\"), Typesetting:
-mfenced(Typesetting:-mrow(Typesetting:-mn(\"1\", mathvariant = \"norm
al\")), mathvariant = \"normal\", open = \"[\", close = \"]\")), linet
hickness = \"1\", denomalign = \"center\", numalign = \"center\", beve
lled = \"false\"), Typesetting:-mo(\"+\", mathvariant = \"normal\", fe
nce = \"false\", separator = \"false\", stretchy = \"false\", symmetri
c = \"false\", largeop = \"false\", movablelimits = \"false\", accent \+
= \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\", equal
ity = \"false\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-
mfrac(Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic
\"), Typesetting:-mrow(Typesetting:-mn(\"1\", mathvariant = \"normal\"
), Typesetting:-mo(\"+\", mathvariant = \"normal\", fence = \"false\",
 separator = \"false\", stretchy = \"false\", symmetric = \"false\", l
argeop = \"false\", movablelimits = \"false\", accent = \"false\", lsp
ace = \"0.2222222em\", rspace = \"0.2222222em\", equality = \"false\")
, Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\"))
, linethickness = \"1\", denomalign = \"center\", numalign = \"center
\", bevelled = \"false\")), mathvariant = \"normal\"), Typesetting:-mo
(\"&sdot;\", mathvariant = \"normal\", fence = \"false\", separator = \+
\"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"fa
lse\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em
\", rspace = \"0.0em\", equality = \"false\"), Typesetting:-mi(\"t\", \+
italic = \"true\", mathvariant = \"italic\"), Typesetting:-mfenced(Typ
esetting:-mrow(Typesetting:-mn(\"2\", mathvariant = \"normal\")), math
variant = \"normal\", open = \"[\", close = \"]\"), Typesetting:-mo(\"
;\", mathvariant = \"normal\", fence = \"false\", separator = \"true\"
, stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mo
vablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspac
e = \"0.2777778em\", equality = \"false\"), Typesetting:-mspace(height
 = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newl
ine\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", dep
th = \"0.0ex\", linebreak = \"auto\"), Typesetting:-mspace(height = \"
0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"
), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \+
\"0.0ex\", linebreak = \"auto\"), Typesetting:-mspace(height = \"0.0ex
\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Ty
pesetting:-mo(\" \", mathvariant = \"normal\", fence = \"false\", sepa
rator = \"false\", stretchy = \"false\", symmetric = \"false\", largeo
p = \"false\", movablelimits = \"false\", accent = \"false\", lspace =
 \"0.0em\", rspace = \"0.0em\", equality = \"false\"));" "-I%mrowG6#/I
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%'rspaceGFC/%)equalityGF4-I#miGF$6%Q7~Input~an~element~of~KF'/%'italic
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epthGFV/%*linebreakGQ(newlineF'-FR6&FTFWFY/FfnQ%autoF'FQFhn-F,6.Q\"~F'
F/F2F5F7F9F;F=F?FAFDFF-FI6%Q\"fF'FLFO-F,6.Q*&coloneq;F'F/F2F5F7F9F;F=F
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6%-I(mfencedGF$6&-F#6#-I#mnGF$6$Q\"2F'F/F//%%openGQ\"[F'/%&closeGQ\"]F
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Q\"+F'F/F2F5F7F9F;F=F?/FBQ,0.2222222emF'/FEFcrFF-FI6%Q\"xF'FLFO-F,6.Q'
&sdot;F'F/F2F5F7F9F;F=F?FAFDFFF]p-Fdp6&-F#6#F\\rF/F\\qF_q/%.linethickn
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F#6#-Fio6(Fer-F#6%F\\rF_rFerF_sFasFdsFfsF/FhrF]pFcp-F,6.Q\";F'F/F2/F6F
NF7F9F;F=F?FAFgoFFFQFhnFQFhnFQF\\o" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I
\"fG6\",&*&&I\"tGF$6#\"\"#\"\"$,&*&I\"xGF$\"\"\"&F(6#F/F/F/F/F/!\"\"F/
*(F.F/,&F/F/F.F/F2F'F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "T
ypesetting:-mrow(Typesetting:-mo(\" \", mathvariant = \"normal\", fenc
e = \"false\", separator = \"false\", stretchy = \"false\", symmetric \+
= \"false\", largeop = \"false\", movablelimits = \"false\", accent = \+
\"false\", lspace = \"0.0em\", rspace = \"0.0em\", equality = \"false
\"), Typesetting:-mo(\"#\", mathvariant = \"normal\", fence = \"false
\", separator = \"false\", stretchy = \"false\", symmetric = \"false\"
, largeop = \"false\", movablelimits = \"false\", accent = \"false\", \+
lspace = \"0.0em\", rspace = \"0.0em\", equality = \"false\"), Typeset
ting:-mi(\" Compute an R-pair of f for (K, ')\", italic = \"true\", ma
thvariant = \"italic\"), Typesetting:-mspace(height = \"0.0ex\", width
 = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Typesetting
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ebreak = \"auto\"), Typesetting:-mspace(height = \"0.0ex\", width = \"
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k = \"auto\"), Typesetting:-mi(\"u\", italic = \"true\", mathvariant =
 \"italic\"), Typesetting:-mo(\",\", mathvariant = \"normal\", fence =
 \"false\", separator = \"true\", stretchy = \"false\", symmetric = \"
false\", largeop = \"false\", movablelimits = \"false\", accent = \"fa
lse\", lspace = \"0.0em\", rspace = \"0.3333333em\", equality = \"fals
e\"), Typesetting:-mi(\"v\", italic = \"true\", mathvariant = \"italic
\"), Typesetting:-mo(\"&coloneq;\", mathvariant = \"normal\", fence = \+
\"false\", separator = \"false\", stretchy = \"false\", symmetric = \"
false\", largeop = \"false\", movablelimits = \"false\", accent = \"fa
lse\", lspace = \"0.2777778em\", rspace = \"0.2777778em\", equality = \+
\"false\"), Typesetting:-mi(\"ReductionPair\", italic = \"true\", math
variant = \"italic\"), Typesetting:-mfenced(Typesetting:-mrow(Typesett
ing:-mn(\"0\", mathvariant = \"normal\"), Typesetting:-mo(\",\", mathv
ariant = \"normal\", fence = \"false\", separator = \"true\", stretchy
 = \"false\", symmetric = \"false\", largeop = \"false\", movablelimit
s = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.33
33333em\", equality = \"false\"), Typesetting:-mi(\"f\", italic = \"tr
ue\", mathvariant = \"italic\")), mathvariant = \"normal\"), Typesetti
ng:-mo(\";\", mathvariant = \"normal\", fence = \"false\", separator =
 \"true\", stretchy = \"false\", symmetric = \"false\", largeop = \"fa
lse\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em
\", rspace = \"0.2777778em\", equality = \"false\"));" "-I%mrowG6#/I+m
odulenameG6\"I,TypesettingGI(_syslibGF'60-I#moGF$6.Q\"~F'/%,mathvarian
tGQ'normalF'/%&fenceGQ&falseF'/%*separatorGF4/%)stretchyGF4/%*symmetri
cGF4/%(largeopGF4/%.movablelimitsGF4/%'accentGF4/%'lspaceGQ&0.0emF'/%'
rspaceGFC/%)equalityGF4-F,6.Q\"#F'F/F2F5F7F9F;F=F?FAFDFF-I#miGF$6%QC~C
ompute~an~R-pair~of~f~for~(K,~')F'/%'italicGQ%trueF'/F0Q'italicF'-I'ms
paceGF$6&/%'heightGQ&0.0exF'/%&widthGFC/%&depthGFY/%*linebreakGQ(newli
neF'-FU6&FWFZFfn/FinQ%autoF'FTF[o-FL6%Q\"uF'FOFR-F,6.Q\",F'F/F2/F6FQF7
F9F;F=F?FA/FEQ,0.3333333emF'FF-FL6%Q\"vF'FOFR-F,6.Q*&coloneq;F'F/F2F5F
7F9F;F=F?/FBQ,0.2777778emF'/FEF_pFF-FL6%Q.ReductionPairF'FOFR-I(mfence
dGF$6$-F#6%-I#mnGF$6$Q\"0F'F/Fbo-FL6%Q\"fF'FOFRF/-F,6.Q\";F'F/F2FeoF7F
9F;F=F?FAF`pFF" }}{PARA 11 "" 1 "" {XPPMATH 20 ">6$I\"uG6\"I\"vGF%6$,$
*&,&I\"xGF%\"\"\"!\"#F,F,&I\"tGF%6#\"\"#F,#F,F1,$*.F.F,,B*(F+F1&F/6#F,
F1F.F1F1*&F+\"\"%F7F,F,*&F+\"\"$F7F1F,*&F+F<F.F1F1*(F+F1F7F,F.F1F1*(F+
F,F7F1F.F1F1*&F+F<F7F,!\"\"*&F+F1F7F1FA*&F+F1F.F1F1*&F+F,F7F<F1*(F+F,F
7F,F.F1F1*$F+F<F,*&F+F1F7F,F,*$F+F1FA*&F+F,F7F,FA*$F7F1F1F,,&FIF,F,F,F
A,&F,F,F+F,FAF+FA,(FJF,F+F,F7F,FAF2" }}}{EXCHG {PARA 0 "> " 0 "" 
{XPPEDIT 19 1 "Typesetting:-mrow(Typesetting:-mo(\"#\", mathvariant = \+
\"normal\", fence = \"false\", separator = \"false\", stretchy = \"fal
se\", symmetric = \"false\", largeop = \"false\", movablelimits = \"fa
lse\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\", equ
ality = \"false\"), Typesetting:-mi(\" Verify the result\", italic = \+
\"true\", mathvariant = \"italic\"), Typesetting:-mspace(height = \"0.
0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"),
 Typesetting:-mi(\"\"), Typesetting:-mo(\" \", mathvariant = \"normal
\", fence = \"false\", separator = \"false\", stretchy = \"false\", sy
mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a
ccent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\", equality = \+
\"false\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'
-I#moGF$6.Q\"#F'/%,mathvariantGQ'normalF'/%&fenceGQ&falseF'/%*separato
rGF4/%)stretchyGF4/%*symmetricGF4/%(largeopGF4/%.movablelimitsGF4/%'ac
centGF4/%'lspaceGQ&0.0emF'/%'rspaceGFC/%)equalityGF4-I#miGF$6%Q3~Verif
y~the~resultF'/%'italicGQ%trueF'/F0Q'italicF'-I'mspaceGF$6&/%'heightGQ
&0.0exF'/%&widthGFC/%&depthGFV/%*linebreakGQ(newlineF'-FI6#Q!F'-F,6.Q
\"~F'F/F2F5F7F9F;F=F?FAFDFF" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1
 "Typesetting:-mrow(Typesetting:-mi(\"normal\", italic = \"true\", mat
hvariant = \"italic\"), Typesetting:-mfenced(Typesetting:-mrow(Typeset
ting:-mi(\"f\", italic = \"true\", mathvariant = \"italic\"), Typesett
ing:-mo(\"&minus;\", mathvariant = \"normal\", fence = \"false\", sepa
rator = \"false\", stretchy = \"false\", symmetric = \"false\", largeo
p = \"false\", movablelimits = \"false\", accent = \"false\", lspace =
 \"0.2222222em\", rspace = \"0.2222222em\", equality = \"false\"), Typ
esetting:-mi(\"TowerDerivative\", italic = \"true\", mathvariant = \"i
talic\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"u\"
, italic = \"true\", mathvariant = \"italic\")), mathvariant = \"norma
l\"), Typesetting:-mo(\"&minus;\", mathvariant = \"normal\", fence = \+
\"false\", separator = \"false\", stretchy = \"false\", symmetric = \"
false\", largeop = \"false\", movablelimits = \"false\", accent = \"fa
lse\", lspace = \"0.2222222em\", rspace = \"0.2222222em\", equality = \+
\"false\"), Typesetting:-mi(\"v\", italic = \"true\", mathvariant = \"
italic\")), mathvariant = \"normal\"), Typesetting:-mo(\";\", mathvari
ant = \"normal\", fence = \"false\", separator = \"true\", stretchy = \+
\"false\", symmetric = \"false\", largeop = \"false\", movablelimits =
 \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.27777
78em\", equality = \"false\"), Typesetting:-mspace(height = \"0.0ex\",
 width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Types
etting:-mi(\"\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_sysli
bGF'6'-I#miGF$6%Q'normalF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-
I(mfencedGF$6$-F#6(-F,6%Q\"fF'F/F2-I#moGF$6.Q(&minus;F'/F3F./%&fenceGQ
&falseF'/%*separatorGFD/%)stretchyGFD/%*symmetricGFD/%(largeopGFD/%.mo
vablelimitsGFD/%'accentGFD/%'lspaceGQ,0.2222222emF'/%'rspaceGFS/%)equa
lityGFD-F,6%Q0TowerDerivativeF'F/F2-F66$-F#6#-F,6%Q\"uF'F/F2FAF=-F,6%Q
\"vF'F/F2FA-F>6.Q\";F'FAFB/FFF1FGFIFKFMFO/FRQ&0.0emF'/FUQ,0.2777778emF
'FV-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGFdo/%&depthGF\\p/%*linebr
eakGQ(newlineF'-F,6#Q!F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "Typesetting:-mrow(Typesetting:
-mo(\"#\", mathvariant = \"normal\", fence = \"false\", separator = \"
false\", stretchy = \"false\", symmetric = \"false\", largeop = \"fals
e\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\"
, rspace = \"0.0em\", equality = \"false\"), Typesetting:-mi(\" Input \+
a Liouvillian extension \", italic = \"true\", mathvariant = \"italic
\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth \+
= \"0.0ex\", linebreak = \"newline\"), Typesetting:-mspace(height = \"
0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"auto\"), \+
Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \"0
.0ex\", linebreak = \"newline\"), Typesetting:-mspace(height = \"0.0ex
\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Ty
pesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0
ex\", linebreak = \"newline\"), Typesetting:-mi(\"F\", italic = \"true
\", mathvariant = \"italic\"), Typesetting:-mo(\" \", mathvariant = \"
normal\", fence = \"false\", separator = \"false\", stretchy = \"false
\", symmetric = \"false\", largeop = \"false\", movablelimits = \"fals
e\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\", equal
ity = \"false\"), Typesetting:-mo(\"&coloneq;\", mathvariant = \"norma
l\", fence = \"false\", separator = \"false\", stretchy = \"false\", s
ymmetric = \"false\", largeop = \"false\", movablelimits = \"false\", \+
accent = \"false\", lspace = \"0.2777778em\", rspace = \"0.2777778em\"
, equality = \"false\"), Typesetting:-mo(\" \", mathvariant = \"normal
\", fence = \"false\", separator = \"false\", stretchy = \"false\", sy
mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a
ccent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\", equality = \+
\"false\"), Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"
italic\"), Typesetting:-mo(\",\", mathvariant = \"normal\", fence = \"
false\", separator = \"true\", stretchy = \"false\", symmetric = \"fal
se\", largeop = \"false\", movablelimits = \"false\", accent = \"false
\", lspace = \"0.0em\", rspace = \"0.3333333em\", equality = \"false\"
), Typesetting:-mo(\" \", mathvariant = \"normal\", fence = \"false\",
 separator = \"false\", stretchy = \"false\", symmetric = \"false\", l
argeop = \"false\", movablelimits = \"false\", accent = \"false\", lsp
ace = \"0.0em\", rspace = \"0.0em\", equality = \"false\"), Typesettin
g:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"s\", italic = \"true\",
 mathvariant = \"italic\"), Typesetting:-mo(\",\", mathvariant = \"nor
mal\", fence = \"false\", separator = \"true\", stretchy = \"false\", \+
symmetric = \"false\", largeop = \"false\", movablelimits = \"false\",
 accent = \"false\", lspace = \"0.0em\", rspace = \"0.3333333em\", equ
ality = \"false\"), Typesetting:-mi(\"t\", italic = \"true\", mathvari
ant = \"italic\")), mathvariant = \"normal\", open = \"[\", close = \"
]\"), Typesetting:-mo(\",\", mathvariant = \"normal\", fence = \"false
\", separator = \"true\", stretchy = \"false\", symmetric = \"false\",
 largeop = \"false\", movablelimits = \"false\", accent = \"false\", l
space = \"0.0em\", rspace = \"0.3333333em\", equality = \"false\"), Ty
pesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"s\", italic = \+
\"true\", mathvariant = \"italic\"), Typesetting:-mo(\",\", mathvarian
t = \"normal\", fence = \"false\", separator = \"true\", stretchy = \"
false\", symmetric = \"false\", largeop = \"false\", movablelimits = \+
\"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.333333
3em\", equality = \"false\"), Typesetting:-mo(\" \", mathvariant = \"n
ormal\", fence = \"false\", separator = \"false\", stretchy = \"false
\", symmetric = \"false\", largeop = \"false\", movablelimits = \"fals
e\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\", equal
ity = \"false\"), Typesetting:-mfrac(Typesetting:-mfenced(Typesetting:
-mrow(Typesetting:-mn(\"1\", mathvariant = \"normal\"), Typesetting:-m
o(\"+\", mathvariant = \"normal\", fence = \"false\", separator = \"fa
lse\", stretchy = \"false\", symmetric = \"false\", largeop = \"false
\", movablelimits = \"false\", accent = \"false\", lspace = \"0.222222
2em\", rspace = \"0.2222222em\", equality = \"false\"), Typesetting:-m
fenced(Typesetting:-mrow(Typesetting:-mn(\"1\", mathvariant = \"normal
\"), Typesetting:-mo(\"&minus;\", mathvariant = \"normal\", fence = \"
false\", separator = \"false\", stretchy = \"false\", symmetric = \"fa
lse\", largeop = \"false\", movablelimits = \"false\", accent = \"fals
e\", lspace = \"0.2222222em\", rspace = \"0.2222222em\", equality = \"
false\"), Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"it
alic\")), mathvariant = \"normal\"), Typesetting:-mo(\"&sdot;\", mathv
ariant = \"normal\", fence = \"false\", separator = \"false\", stretch
y = \"false\", symmetric = \"false\", largeop = \"false\", movablelimi
ts = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0
em\", equality = \"false\"), Typesetting:-mi(\"s\", italic = \"true\",
 mathvariant = \"italic\")), mathvariant = \"normal\"), Typesetting:-m
row(Typesetting:-msup(Typesetting:-mfenced(Typesetting:-mrow(Typesetti
ng:-mn(\"1\", mathvariant = \"normal\"), Typesetting:-mo(\"+\", mathva
riant = \"normal\", fence = \"false\", separator = \"false\", stretchy
 = \"false\", symmetric = \"false\", largeop = \"false\", movablelimit
s = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \+
\"0.2222222em\", equality = \"false\"), Typesetting:-mi(\"s\", italic \+
= \"true\", mathvariant = \"italic\")), mathvariant = \"normal\"), Typ
esetting:-mrow(Typesetting:-mn(\"2\", mathvariant = \"normal\")), supe
rscriptshift = \"0\")), linethickness = \"1\", denomalign = \"center\"
, numalign = \"center\", bevelled = \"false\"), Typesetting:-mo(\"&sdo
t;\", mathvariant = \"normal\", fence = \"false\", separator = \"false
\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", \+
movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rsp
ace = \"0.0em\", equality = \"false\"), Typesetting:-mi(\"t\", italic \+
= \"true\", mathvariant = \"italic\")), mathvariant = \"normal\", open
 = \"[\", close = \"]\"), Typesetting:-mo(\";\", mathvariant = \"norma
l\", fence = \"false\", separator = \"true\", stretchy = \"false\", sy
mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a
ccent = \"false\", lspace = \"0.0em\", rspace = \"0.2777778em\", equal
ity = \"false\"), Typesetting:-mo(\" \", mathvariant = \"normal\", fen
ce = \"false\", separator = \"false\", stretchy = \"false\", symmetric
 = \"false\", largeop = \"false\", movablelimits = \"false\", accent =
 \"false\", lspace = \"0.0em\", rspace = \"0.0em\", equality = \"false
\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth \+
= \"0.0ex\", linebreak = \"newline\"), Typesetting:-mspace(height = \"
0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"auto\"), \+
Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \"0
.0ex\", linebreak = \"newline\"), Typesetting:-mo(\"#\", mathvariant =
 \"normal\", fence = \"false\", separator = \"false\", stretchy = \"fa
lse\", symmetric = \"false\", largeop = \"false\", movablelimits = \"f
alse\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\", eq
uality = \"false\"), Typesetting:-mo(\" \", italic = \"true\", mathvar
iant = \"italic\", fence = \"false\", separator = \"false\", stretchy \+
= \"false\", symmetric = \"false\", largeop = \"false\", movablelimits
 = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em
\", equality = \"false\"), Typesetting:-mi(\"Check\", italic = \"true
\", mathvariant = \"italic\"), Typesetting:-mo(\" \", italic = \"true
\", mathvariant = \"italic\", fence = \"false\", separator = \"false\"
, stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mo
vablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspac
e = \"0.0em\", equality = \"false\"), Typesetting:-mi(\"whether\", ita
lic = \"true\", mathvariant = \"italic\"), Typesetting:-mo(\" \", ital
ic = \"true\", mathvariant = \"italic\", fence = \"false\", separator \+
= \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"
false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0
em\", rspace = \"0.0em\", equality = \"false\"), Typesetting:-mi(\"F\"
, italic = \"true\", mathvariant = \"italic\"), Typesetting:-mo(\" \",
 italic = \"true\", mathvariant = \"italic\", fence = \"false\", separ
ator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop
 = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \+
\"0.0em\", rspace = \"0.0em\", equality = \"false\"), Typesetting:-mi(
\"has\", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mo
(\" \", italic = \"true\", mathvariant = \"italic\", fence = \"false\"
, separator = \"false\", stretchy = \"false\", symmetric = \"false\", \+
largeop = \"false\", movablelimits = \"false\", accent = \"false\", ls
pace = \"0.0em\", rspace = \"0.0em\", equality = \"false\"), Typesetti
ng:-mi(\"new\", italic = \"true\", mathvariant = \"italic\"), Typesett
ing:-mo(\" \", italic = \"true\", mathvariant = \"italic\", fence = \"
false\", separator = \"false\", stretchy = \"false\", symmetric = \"fa
lse\", largeop = \"false\", movablelimits = \"false\", accent = \"fals
e\", lspace = \"0.0em\", rspace = \"0.0em\", equality = \"false\"), Ty
pesetting:-mi(\"constant\", italic = \"true\", mathvariant = \"italic
\"), Typesetting:-mo(\" \", italic = \"true\", mathvariant = \"italic
\", fence = \"false\", separator = \"false\", stretchy = \"false\", sy
mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a
ccent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\", equality = \+
\"false\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\",
 depth = \"0.0ex\", linebreak = \"newline\"), Typesetting:-mspace(heig
ht = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"au
to\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", dept
h = \"0.0ex\", linebreak = \"newline\"), Typesetting:-mspace(height = \+
\"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline
\"), Typesetting:-mo(\" \", mathvariant = \"normal\", fence = \"false
\", separator = \"false\", stretchy = \"false\", symmetric = \"false\"
, largeop = \"false\", movablelimits = \"false\", accent = \"false\", \+
lspace = \"0.0em\", rspace = \"0.0em\", equality = \"false\"), Typeset
ting:-mi(\"NoNewConst\", italic = \"true\", mathvariant = \"italic\"),
 Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"F\", italic \+
= \"true\", mathvariant = \"italic\")), mathvariant = \"normal\"), Typ
esetting:-mo(\";\", mathvariant = \"normal\", fence = \"false\", separ
ator = \"true\", stretchy = \"false\", symmetric = \"false\", largeop \+
= \"false\", movablelimits = \"false\", accent = \"false\", lspace = \+
\"0.0em\", rspace = \"0.2777778em\", equality = \"false\"));" "-I%mrow
G6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6N-I#moGF$6.Q\"#F'/%,mat
hvariantGQ'normalF'/%&fenceGQ&falseF'/%*separatorGF4/%)stretchyGF4/%*s
ymmetricGF4/%(largeopGF4/%.movablelimitsGF4/%'accentGF4/%'lspaceGQ&0.0
emF'/%'rspaceGFC/%)equalityGF4-I#miGF$6%Q@~Input~a~Liouvillian~extensi
on~F'/%'italicGQ%trueF'/F0Q'italicF'-I'mspaceGF$6&/%'heightGQ&0.0exF'/
%&widthGFC/%&depthGFV/%*linebreakGQ(newlineF'-FR6&FTFWFY/FfnQ%autoF'FQ
FQFQ-FI6%Q\"FF'FLFO-F,6.Q\"~F'F/F2F5F7F9F;F=F?FAFDFF-F,6.Q*&coloneq;F'
F/F2F5F7F9F;F=F?/FBQ,0.2777778emF'/FEFfoFFF_o-FI6%Q\"xF'FLFO-F,6.Q\",F
'F/F2/F6FNF7F9F;F=F?FA/FEQ,0.3333333emF'FFF_o-I(mfencedGF$6&-F#6%-FI6%
Q\"sF'FLFOF[p-FI6%Q\"tF'FLFOF//%%openGQ\"[F'/%&closeGQ\"]F'F[p-Fbp6&-F
#6(FfpF[pF_o-I&mfracGF$6(-Fbp6$-F#6'-I#mnGF$6$Q\"1F'F/-F,6.Q\"+F'F/F2F
5F7F9F;F=F?/FBQ,0.2222222emF'/FEFerFF-Fbp6$-F#6%F]r-F,6.Q(&minus;F'F/F
2F5F7F9F;F=F?FdrFfrFFFhoF/-F,6.Q'&sdot;F'F/F2F5F7F9F;F=F?FAFDFFFfpF/-F
#6#-I%msupGF$6%-Fbp6$-F#6%F]rFarFfpF/-F#6#-F^r6$Q\"2F'F//%1superscript
shiftGQ\"0F'/%.linethicknessGF`r/%+denomalignGQ'centerF'/%)numalignGFf
t/%)bevelledGF4F^sFipF/F\\qF_q-F,6.Q\";F'F/F2F^pF7F9F;F=F?FAFgoFFF_oFQ
FhnFQF+-F,6/FaoFLFOF2F5F7F9F;F=F?FAFDFF-FI6%Q&CheckF'FLFOF^u-FI6%Q(whe
therF'FLFOF^uF\\oF^u-FI6%Q$hasF'FLFOF^u-FI6%Q$newF'FLFOF^u-FI6%Q)const
antF'FLFOF^uFQFhnFQFQF_o-FI6%Q+NoNewConstF'FLFO-Fbp6$-F#6#F\\oF/F[u" }
}{PARA 11 "" 1 "" {XPPMATH 20 ">I\"FG6\"6%I\"xGF$7$I\"sGF$I\"tGF$7$F(*
(,&\"\"\"F-*&,&F-F-F&!\"\"F-F(F-F-F-,&F-F-F(F-!\"#F)F-" }}{PARA 11 "" 
1 "" {XPPMATH 20 "I%trueG%*protectedG" }}}{EXCHG {PARA 11 "" 1 "" 
{XPPMATH 20 "%#%?G" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "Typeset
ting:-mrow(Typesetting:-mo(\"#\", mathvariant = \"normal\", fence = \"
false\", separator = \"false\", stretchy = \"false\", symmetric = \"fa
lse\", largeop = \"false\", movablelimits = \"false\", accent = \"fals
e\", lspace = \"0.0em\", rspace = \"0.0em\", equality = \"false\"), Ty
pesetting:-mi(\" Set the global variable \", italic = \"true\", mathva
riant = \"italic\"), Typesetting:-mspace(height = \"0.0ex\", width = \+
\"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Typesetting:-m
space(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebr
eak = \"auto\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0
em\", depth = \"0.0ex\", linebreak = \"newline\"), Typesetting:-mspace
(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak =
 \"newline\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em
\", depth = \"0.0ex\", linebreak = \"newline\"), Typesetting:-mspace(h
eight = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \+
\"auto\"), Typesetting:-mi(\"SetTower\", italic = \"true\", mathvarian
t = \"italic\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-m
i(\"F\", italic = \"true\", mathvariant = \"italic\")), mathvariant = \+
\"normal\"), Typesetting:-mo(\";\", mathvariant = \"normal\", fence = \+
\"false\", separator = \"true\", stretchy = \"false\", symmetric = \"f
alse\", largeop = \"false\", movablelimits = \"false\", accent = \"fal
se\", lspace = \"0.0em\", rspace = \"0.2777778em\", equality = \"false
\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth \+
= \"0.0ex\", linebreak = \"newline\"), Typesetting:-mo(\" \", mathvari
ant = \"normal\", fence = \"false\", separator = \"false\", stretchy =
 \"false\", symmetric = \"false\", largeop = \"false\", movablelimits \+
= \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em
\", equality = \"false\"), Typesetting:-mspace(height = \"0.0ex\", wid
th = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Typesetti
ng:-mi(\"\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'
61-I#moGF$6.Q\"#F'/%,mathvariantGQ'normalF'/%&fenceGQ&falseF'/%*separa
torGF4/%)stretchyGF4/%*symmetricGF4/%(largeopGF4/%.movablelimitsGF4/%'
accentGF4/%'lspaceGQ&0.0emF'/%'rspaceGFC/%)equalityGF4-I#miGF$6%Q:~Set
~the~global~variable~F'/%'italicGQ%trueF'/F0Q'italicF'-I'mspaceGF$6&/%
'heightGQ&0.0exF'/%&widthGFC/%&depthGFV/%*linebreakGQ(newlineF'-FR6&FT
FWFY/FfnQ%autoF'FQFQFQFhn-FI6%Q)SetTowerF'FLFO-I(mfencedGF$6$-F#6#-FI6
%Q\"FF'FLFOF/-F,6.Q\";F'F/F2/F6FNF7F9F;F=F?FA/FEQ,0.2777778emF'FFFQ-F,
6.Q\"~F'F/F2F5F7F9F;F=F?FAFDFFFQ-FI6#Q!F'" }}}{EXCHG {PARA 0 "> " 0 ""
 {XPPEDIT 19 1 "Typesetting:-mrow(Typesetting:-mo(\" \", mathvariant =
 \"normal\", fence = \"false\", separator = \"false\", stretchy = \"fa
lse\", symmetric = \"false\", largeop = \"false\", movablelimits = \"f
alse\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\", eq
uality = \"false\"), Typesetting:-mo(\"#\", mathvariant = \"normal\", \+
fence = \"false\", separator = \"false\", stretchy = \"false\", symmet
ric = \"false\", largeop = \"false\", movablelimits = \"false\", accen
t = \"false\", lspace = \"0.0em\", rspace = \"0.0em\", equality = \"fa
lse\"), Typesetting:-mi(\" Input an element of F\", italic = \"true\",
 mathvariant = \"italic\"), Typesetting:-mspace(height = \"0.0ex\", wi
dth = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Typesett
ing:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", \+
linebreak = \"auto\"), Typesetting:-mspace(height = \"0.0ex\", width =
 \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Typesetting:-
mo(\" \", mathvariant = \"normal\", fence = \"false\", separator = \"f
alse\", stretchy = \"false\", symmetric = \"false\", largeop = \"false
\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\",
 rspace = \"0.0em\", equality = \"false\"), Typesetting:-mi(\"g\", ita
lic = \"true\", mathvariant = \"italic\"), Typesetting:-mo(\" \", math
variant = \"normal\", fence = \"false\", separator = \"false\", stretc
hy = \"false\", symmetric = \"false\", largeop = \"false\", movablelim
its = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.
0em\", equality = \"false\"), Typesetting:-mo(\"&coloneq;\", mathvaria
nt = \"normal\", fence = \"false\", separator = \"false\", stretchy = \+
\"false\", symmetric = \"false\", largeop = \"false\", movablelimits =
 \"false\", accent = \"false\", lspace = \"0.2777778em\", rspace = \"0
.2777778em\", equality = \"false\"), Typesetting:-mfrac(Typesetting:-m
row(Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\"
), Typesetting:-mo(\"&sdot;\", mathvariant = \"normal\", fence = \"fal
se\", separator = \"false\", stretchy = \"false\", symmetric = \"false
\", largeop = \"false\", movablelimits = \"false\", accent = \"false\"
, lspace = \"0.0em\", rspace = \"0.0em\", equality = \"false\"), Types
etting:-mi(\"t\", italic = \"true\", mathvariant = \"italic\")), Types
etting:-mrow(Typesetting:-mn(\"1\", mathvariant = \"normal\"), Typeset
ting:-mo(\"+\", mathvariant = \"normal\", fence = \"false\", separator
 = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \+
\"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0
.2222222em\", rspace = \"0.2222222em\", equality = \"false\"), Typeset
ting:-mi(\"s\", italic = \"true\", mathvariant = \"italic\")), linethi
ckness = \"1\", denomalign = \"center\", numalign = \"center\", bevell
ed = \"false\"), Typesetting:-mo(\";\", mathvariant = \"normal\", fenc
e = \"false\", separator = \"true\", stretchy = \"false\", symmetric =
 \"false\", largeop = \"false\", movablelimits = \"false\", accent = \+
\"false\", lspace = \"0.0em\", rspace = \"0.2777778em\", equality = \"
false\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6.-I
#moGF$6.Q\"~F'/%,mathvariantGQ'normalF'/%&fenceGQ&falseF'/%*separatorG
F4/%)stretchyGF4/%*symmetricGF4/%(largeopGF4/%.movablelimitsGF4/%'acce
ntGF4/%'lspaceGQ&0.0emF'/%'rspaceGFC/%)equalityGF4-F,6.Q\"#F'F/F2F5F7F
9F;F=F?FAFDFF-I#miGF$6%Q7~Input~an~element~of~FF'/%'italicGQ%trueF'/F0
Q'italicF'-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGFC/%&depthGFY/%*li
nebreakGQ(newlineF'-FU6&FWFZFfn/FinQ%autoF'FTF+-FL6%Q\"gF'FOFRF+-F,6.Q
*&coloneq;F'F/F2F5F7F9F;F=F?/FBQ,0.2777778emF'/FEFfoFF-I&mfracGF$6(-F#
6%-FL6%Q\"xF'FOFR-F,6.Q'&sdot;F'F/F2F5F7F9F;F=F?FAFDFF-FL6%Q\"tF'FOFR-
F#6%-I#mnGF$6$Q\"1F'F/-F,6.Q\"+F'F/F2F5F7F9F;F=F?/FBQ,0.2222222emF'/FE
F`qFF-FL6%Q\"sF'FOFR/%.linethicknessGF[q/%+denomalignGQ'centerF'/%)num
alignGFiq/%)bevelledGF4-F,6.Q\";F'F/F2/F6FQF7F9F;F=F?FAFgoFF" }}{PARA 
11 "" 1 "" {XPPMATH 20 ">I\"gG6\"*(I\"xGF$\"\"\"I\"tGF$F',&F'F'I\"sGF$
F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "Typesetting:-mrow(
Typesetting:-mo(\" \", mathvariant = \"normal\", fence = \"false\", se
parator = \"false\", stretchy = \"false\", symmetric = \"false\", larg
eop = \"false\", movablelimits = \"false\", accent = \"false\", lspace
 = \"0.0em\", rspace = \"0.0em\", equality = \"false\"), Typesetting:-
mo(\"#\", mathvariant = \"normal\", fence = \"false\", separator = \"f
alse\", stretchy = \"false\", symmetric = \"false\", largeop = \"false
\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\",
 rspace = \"0.0em\", equality = \"false\"), Typesetting:-mi(\" Compute
 an R-pair of g for (F, ')\", italic = \"true\", mathvariant = \"itali
c\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth
 = \"0.0ex\", linebreak = \"newline\"), Typesetting:-mspace(height = \+
\"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"auto\")
, Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \+
\"0.0ex\", linebreak = \"newline\"), Typesetting:-mspace(height = \"0.
0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"),
 Typesetting:-mi(\"u\", italic = \"true\", mathvariant = \"italic\"), \+
Typesetting:-mo(\",\", mathvariant = \"normal\", fence = \"false\", se
parator = \"true\", stretchy = \"false\", symmetric = \"false\", large
op = \"false\", movablelimits = \"false\", accent = \"false\", lspace \+
= \"0.0em\", rspace = \"0.3333333em\", equality = \"false\"), Typesett
ing:-mi(\"v\", italic = \"true\", mathvariant = \"italic\"), Typesetti
ng:-mo(\"&coloneq;\", mathvariant = \"normal\", fence = \"false\", sep
arator = \"false\", stretchy = \"false\", symmetric = \"false\", large
op = \"false\", movablelimits = \"false\", accent = \"false\", lspace \+
= \"0.2777778em\", rspace = \"0.2777778em\", equality = \"false\"), Ty
pesetting:-mo(\" \", mathvariant = \"normal\", fence = \"false\", sepa
rator = \"false\", stretchy = \"false\", symmetric = \"false\", largeo
p = \"false\", movablelimits = \"false\", accent = \"false\", lspace =
 \"0.0em\", rspace = \"0.0em\", equality = \"false\"), Typesetting:-mi
(\"ReductionPair\", italic = \"true\", mathvariant = \"italic\"), Type
setting:-mfenced(Typesetting:-mrow(Typesetting:-mn(\"0\", mathvariant \+
= \"normal\"), Typesetting:-mo(\",\", mathvariant = \"normal\", fence \+
= \"false\", separator = \"true\", stretchy = \"false\", symmetric = \+
\"false\", largeop = \"false\", movablelimits = \"false\", accent = \"
false\", lspace = \"0.0em\", rspace = \"0.3333333em\", equality = \"fa
lse\"), Typesetting:-mi(\"g\", italic = \"true\", mathvariant = \"ital
ic\")), mathvariant = \"normal\"), Typesetting:-mo(\";\", mathvariant \+
= \"normal\", fence = \"false\", separator = \"true\", stretchy = \"fa
lse\", symmetric = \"false\", largeop = \"false\", movablelimits = \"f
alse\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.2777778em
\", equality = \"false\"), Typesetting:-mspace(height = \"0.0ex\", wid
th = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Typesetti
ng:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", l
inebreak = \"auto\"), Typesetting:-mi(\"\"));" "-I%mrowG6#/I+modulenam
eG6\"I,TypesettingGI(_syslibGF'64-I#moGF$6.Q\"~F'/%,mathvariantGQ'norm
alF'/%&fenceGQ&falseF'/%*separatorGF4/%)stretchyGF4/%*symmetricGF4/%(l
argeopGF4/%.movablelimitsGF4/%'accentGF4/%'lspaceGQ&0.0emF'/%'rspaceGF
C/%)equalityGF4-F,6.Q\"#F'F/F2F5F7F9F;F=F?FAFDFF-I#miGF$6%QC~Compute~a
n~R-pair~of~g~for~(F,~')F'/%'italicGQ%trueF'/F0Q'italicF'-I'mspaceGF$6
&/%'heightGQ&0.0exF'/%&widthGFC/%&depthGFY/%*linebreakGQ(newlineF'-FU6
&FWFZFfn/FinQ%autoF'FTFT-FL6%Q\"uF'FOFR-F,6.Q\",F'F/F2/F6FQF7F9F;F=F?F
A/FEQ,0.3333333emF'FF-FL6%Q\"vF'FOFR-F,6.Q*&coloneq;F'F/F2F5F7F9F;F=F?
/FBQ,0.2777778emF'/FEF_pFFF+-FL6%Q.ReductionPairF'FOFR-I(mfencedGF$6$-
F#6%-I#mnGF$6$Q\"0F'F/Fbo-FL6%Q\"gF'FOFRF/-F,6.Q\";F'F/F2FeoF7F9F;F=F?
FAF`pFFFTF[o-FL6#Q!F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">6$I\"uG6\"I\"v
GF%6$,$*(,&\"\"\"F+I\"sGF%F+F+F,!\"\"I\"tGF%F+F-\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {XPPEDIT 19 1 "Typesetting:-mrow(Typesetting:-mo(\" \+
\", mathvariant = \"normal\", fence = \"false\", separator = \"false\"
, stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mo
vablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspac
e = \"0.0em\", equality = \"false\"), Typesetting:-mo(\"#\", mathvaria
nt = \"normal\", fence = \"false\", separator = \"false\", stretchy = \+
\"false\", symmetric = \"false\", largeop = \"false\", movablelimits =
 \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"
, equality = \"false\"), Typesetting:-mi(\" Verify the result\", itali
c = \"true\", mathvariant = \"italic\"), Typesetting:-mspace(height = \+
\"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline
\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth \+
= \"0.0ex\", linebreak = \"auto\"), Typesetting:-mspace(height = \"0.0
ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), \+
Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \"0
.0ex\", linebreak = \"auto\"), Typesetting:-mi(\"normal\", italic = \"
true\", mathvariant = \"italic\"), Typesetting:-mfenced(Typesetting:-m
row(Typesetting:-mi(\"g\", italic = \"true\", mathvariant = \"italic\"
), Typesetting:-mo(\"&minus;\", mathvariant = \"normal\", fence = \"fa
lse\", separator = \"false\", stretchy = \"false\", symmetric = \"fals
e\", largeop = \"false\", movablelimits = \"false\", accent = \"false
\", lspace = \"0.2222222em\", rspace = \"0.2222222em\", equality = \"f
alse\"), Typesetting:-mi(\"TowerDerivative\", italic = \"true\", mathv
ariant = \"italic\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetti
ng:-mi(\"u\", italic = \"true\", mathvariant = \"italic\")), mathvaria
nt = \"normal\"), Typesetting:-mo(\"&minus;\", mathvariant = \"normal
\", fence = \"false\", separator = \"false\", stretchy = \"false\", sy
mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a
ccent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\",
 equality = \"false\"), Typesetting:-mi(\"v\", italic = \"true\", math
variant = \"italic\")), mathvariant = \"normal\"), Typesetting:-mo(\";
\", mathvariant = \"normal\", fence = \"false\", separator = \"true\",
 stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mov
ablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace
 = \"0.2777778em\", equality = \"false\"));" "-I%mrowG6#/I+modulenameG
6\"I,TypesettingGI(_syslibGF'6,-I#moGF$6.Q\"~F'/%,mathvariantGQ'normal
F'/%&fenceGQ&falseF'/%*separatorGF4/%)stretchyGF4/%*symmetricGF4/%(lar
geopGF4/%.movablelimitsGF4/%'accentGF4/%'lspaceGQ&0.0emF'/%'rspaceGFC/
%)equalityGF4-F,6.Q\"#F'F/F2F5F7F9F;F=F?FAFDFF-I#miGF$6%Q3~Verify~the~
resultF'/%'italicGQ%trueF'/F0Q'italicF'-I'mspaceGF$6&/%'heightGQ&0.0ex
F'/%&widthGFC/%&depthGFY/%*linebreakGQ(newlineF'-FU6&FWFZFfn/FinQ%auto
F'FTF[o-FL6%F1FOFR-I(mfencedGF$6$-F#6(-FL6%Q\"gF'FOFR-F,6.Q(&minus;F'F
/F2F5F7F9F;F=F?/FBQ,0.2222222emF'/FEF]pFF-FL6%Q0TowerDerivativeF'FOFR-
Fbo6$-F#6#-FL6%Q\"uF'FOFRF/Fio-FL6%Q\"vF'FOFRF/-F,6.Q\";F'F/F2/F6FQF7F
9F;F=F?FA/FEQ,0.2777778emF'FF" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" 
}}}{EXCHG {PARA 11 "" 1 "" {XPPMATH 20 "%#%?G" }}}}
{MARK "0 0 0" 0 }{VIEWOPTS 1 0 0 94 100 1803 1 1 1 1 }{PAGENUMBERS 0 
1 2 33 1 1 }