Category : BASIC Source Code
Archive : UBAS830.ZIP
Filename : POLFACT.UB
Output of file : POLFACT.UB contained in archive : UBAS830.ZIP
J
POLFACT VER 2.02
"
P Polynomial Factorization in Z and Q
Y (
¢ 2 reference:D.E.Knuth The Art of Computer Programming, Chapter 4
« <
³ F ¨
º P
á Z " * polynomial factorization *"
d " * use x or X for a variable *"
2n " * example : x^3+2*x^2+3*x+4 *"À
Ex ±"f(x)="Á W
[ ú
 W )Ôñ ¿
h U0Ñ""
I Ѳ W Â"xX")
Å dI U0ÝѼ W ÂI Þñ )Ý"_X"À W Ñ» W ÂI Ýñ Âå)Àñ
ܪ U0Ñý U0Ý W )
ñ´ À"f(X)="Á U0
1¶ DenÑñ ÀI Ñð²Û U0)ÀDenѲãDen²Åÿ U0ÂI )))À
B¸ U0åÑDen
a¾ X ѳõPolFactô( U0Âð)
à þ X Âñ )Ñþ X Âñ )éDen
£È Àõ PrintPolyõ(& X )À
Ò ñx
¶Ü
Ðæ õ PrintPoly (& X )
àð ºI Â W
ú þ X Âñ )Öñ þ X Âñ )Á"* "Á
&I Ññ Â X )ñ
H W Ñ"("Ýüþ X ÂI ))Ý")"
+þ X ÂI Ýñ )Òñ W ÝÑ"^"Ý»üþ X ÂI Ýñ ))Âñ Âå)
±"PI ÔÂ X )Þñ W ÝÑ" * "
Ð, ²Æo²ÆÝ W )ÒñO
Ü6 W Á
å@À
ìJ
õT
^³õPolFact ( U0ÂTalksw)
9hºI ÂGoodDegÂDegÑ²Û U0)
rºP ÂP1ÂPaÂPbÂR ÂR1ÂGoodRÂHeightÂCfactor Gcdfactor Powerfactor
¯|º G  X  Ans Umem
ƺ
LimitwordsÑñ
à get const factor
ò G Ñ²Þ U0)
¤ U0ѳõ Primitiveö( U0)
(®CfactorÑ²Þ U0)
H¸ GcdfactorÑ G èCfactor
`Âÿ get power of X
uÌ PowerfactorÑð
ÖL²ß U0)Ñð
¤à PowerfactorÀ U0èÑ_X
ê
Þô} U0Ñûñ ) UmemÑûñ )À Ansѽ)Àñ¢
øþ get multi factor
UmemÑûñ )
I G ѳõ Primitiveö(²Ý³õGcdFô( U0Â²Ü U0)))åCfactor)
v ²Û G ) UmemåÑ G À U0èÑ G Àñ
&CfactorÑ²Þ U0)
05
Ç:f³õ
EisensteinUö( U0) Ansѽ U0)Àñ¢
öDI ÑðDegÀHeightÝÑÀÿ U0ÂI ))À
NHeightÝÑÀ²Þ U0))
?XPaÑÞñ
ÝàÌHeight)ïñ Âñ')ݲçñ2 )
ibPaÑÞPa)ÀCfactorçPaÑðñb
xlPbÑPa
¢vPbÑÞPb)ÀACfactorçPbÑðñv
±P ÑPb
ÛP ÑÞP )ÀzCfactorçP Ñðñ
GoodDegѳõGoodDegÌô(P ÂHeight)
GoodRÑDegèñ
?¨R ѳõBadnessõ( U0ÂP )
O² R Ôð
¼ÀP ÑÞP )À CfactorçP Ñðñ¼ ñ¨
°ÆOTalksw"For p="ÁP Á"Badness="ÁR
ÔÐsR Ññ Ansѽ U0)Àñ¢
ñÚR ÕGoodRèñ ñp
äP1ÑP
îI Ññ ²Û U0)èñ
Ýñ
1 øP1ÑÞP1)
S R1ѳõBadnessõ( U0ÂP1)
c 3R1Ôð
ÀP1ÑÞP1)À CfactorçP1Ñðñ ñ
Ä cTalksw"For p="ÁP1Á"Badness="ÁR1
ë *R1Ññ À Ansѽ U0)Àñ¢
þ 4ÓR1ÒR
4
>À PaÔP PaÑP1¯ ° PbÔP PbÑP1
Z
H R1ÕR P ÑP1ÀR ÑR1
w
RR ÔGoodRÀñp
~
\
f&
¬
pKTalksw"Use modulus"ÁP
Ï
z X ѳõPolfact3iõ( U0ÂP )
ö
Ansѳõ PolFactMain¤ö( U0 X )
õ
SortResultö(& Ans)
»
I ¢ X ѽ Gcdfactor)À set const factor
a ¬ set power of X
¶0 Powerfactor X Ýѽ_X Powerfactor)
© ÀI Ññ Â Ans)
É Ê X Ýѽþ AnsÂI )Âñ )
Ð Ô
î Þ UmemÑûñ )( X )
è set multiple factors
& òI Ññ Â X )ñ
F ü W Ñþ X ÂI )ÀJ Ññ
Z W Ñ_Xñ$
Umemç W Ñð UmemèÑ W À J Àñ
£ þ X ÂI Ýñ )ÑJ
Ä $ UmemÑûñ )À( X )
Ë .
ä 8"system error"ÀÀ¿
í B
ö L
V³õ PolFactMain ( U0Â X )
W
`ºI ÂJ ÂDegÂRaisedsw UsedGoodDegÂPeÂR ÂNewR
£
jº A  B  G  H  Sw U1 U2 V  W  W1 Y  Z  Ansѽ)
Ã
t¤V Â X ))ÂV1Â X ))
ñ
~ use global GoodDeg%,P,Height,Cfactor
I Ññ Â X )
& W Ñþ X ÂI )À V Ñð
MJ Ñð²Û W )À Z Ñÿ W ÂJ )
n¦
Z ÒP èñ Z ÞÑP
°ÿ V ÂJ )Ñ Z
º
Ä W Ñ V
¹Î V Ñ V åCfactorçP
ÙØõ ReductionÒõ(& V ÂP )
øâ V ѳõ Primitiveö( V )
=ì ³õTry,ô( V ) U0èÑ V À AnsÝÑ V ÀCfactorÑ²Þ U0)Àñ
WöV R )Ñ W À R
^
v
R Ñð( Ans)
R Ññ ( AnsÝ U0)
³ õ
RecalcGoodDegÊö(P )
¼(
Ð2 check main
Ù<
"FPeÑP ÀPe1ÑPeåP À ²ÛV ð))Òñ åGoodDegõ
CheckEisena
4PõLoopforP
BZ SwÑñ
Kd
inDegÑðÀI ÑðR Þñ
x ÃI  Sw)DegÝѲÛV I ))
¹ DegÕ UsedGoodDeg¶
è DegÒàGoodDegåñ Â²Û U0)èñ )¶
ü V ÑCfactor
ªI ÑðR Þñ
C´ ÃI  Sw) V Ñ V å²ßV I ))çPe
J¾
kÈ V ÒPeèñ V ÞÑPe
Ò V èÑÄ V ÂCfactorçPe)
¦Ü ²ß U0)ç V ¶
½æ V ÑûCfactor)
ÓðI ÑðR Þñ
ú ÃI Â Sw) V Ñ V åV I )çPe
(õ ReductionÂõ(& V ÂPe)
G V ѳõ Primitiveöõ( V )
i" ³õTry ô( V )õResetVK(
v,·À Sw
6 SwÓñ ïR Þñ
¼@ ²Û U0)Õñ åGoodDeg( AnsÝ U0)
÷J (²Û U0)Þ²ÛV R Þñ )))ÕGoodDeg( AnsÝ U0)
T UsedGoodDegÑGoodDeg
(^õ
CheckEisen
Th ³õ
EisensteinEö( U0)( AnsÝ U0)
]r
w| for higher power
RaisedswÑñ
Ø G Ñûñ )ÀJ ÑðR Þñ ñ À G Ѳà G ÂV J )ÂPe)À
ø¤õ ReductionÂõ(& G ÂPe)
>® H Ñûñ )ÀJ Ññ R Þñ ñ À H Ѳà H ÂV J )ÂPe)À
^¸õ ReductionÂõ(& H ÂPe)
¨ÂGHwordsÑ(²Û G )Ý²Û H )Ýñ )å((ÂCfactor)ÝÂPe)Ýñ )èñ )Ýñ
ËÌ if GHwords>Limitwords then
Ö :if Raisedsw%>1 then *LoopforP:else return(0):'giveup
à²ÑP
6ê V ѳõ TransPolyÜõ( G )
Uô W ѳõ TransPolyÜõ( H )
}þ A ѳõ
ModpolyModInväö( V Â W )
¥ B ѳõ
ModpolyModInväö( W Â V )
É ñ åGHwordsÕ
Limitwords
À W1ѳõ TransPolyÜõ(( U0ÞCfactorå G å H )èPe)æCfactor
6&À W1ѳõ Henselsub¨õ( G  H )
c0 X Ñ W1å B ç V À Y Ñ W1å A ç W
m:²Ñð
D U1ѳõ TransPolyÜõ( X )åPeÝ G
¿N U2ѳõ TransPolyÜõ( Y )åPeÝ H
àXõ ReductionÂõ(& U1ÂPe1)
bõ ReductionÂõ(& U2ÂPe1)
l
,v R Ññ V1ð)Ñ U1Àñ
FI ÑðR Þñ ñ
f G ÑV I )À H Ñûñ )
©J ÑðR Þñ ñ À J ÖI H Ѳà H ÂV J )ÂPe)
°
Шõ ReductionÂõ(& H ÂPe)
ݲ²ÑP
ü¼ V ѳõ TransPolyÜõ( G )
Æ W ѳõ TransPolyÜõ( H )
CÐ B ѳõ
ModpolyModInväö( W Â V )
Ú X ѳõ TransPolyÜõ(( U1Þ²à G  H ÂPe1))èPe)å B ç V
ä²Ñð
¾î X ѳõ TransPolyÜõ( X )åPeÝV I )
ßøõ ReductionÂõ(& X ÂPe1)
óV1I )Ñ X
ú
' R Õñ V1ñ )Ñ U2ÀñÀ
C*I Ññ R Þñ ñ
c4 G ÑV I )À H Ñûñ )
¨>J Ññ R Þñ ñ À J ÖI H Ѳà H ÂV J )ÂPe)
¯H
ÏRõ ReductionÂõ(& H ÂPe)
Ü\²ÑP
ûf V ѳõ TransPolyÜõ( G )
p W ѳõ TransPolyÜõ( H )
Bz B ѳõ
ModpolyModInväö( W Â V )
X ѳõ TransPolyÜõ(( U2Þ²à G  H ÂPe1))èPe)å B ç V
²Ñð
½ X ѳõ TransPolyÜõ( X )åPeÝV I )
Þ¢õ ReductionÂõ(& X ÂPe1)
ò¬V1I )Ñ X
ù¶
À¢V ðÃR Þñ )Ñ¢V1ðÃR Þñ )
bÊPeåÑP ÀPe1åÑP ÀGoodDegѳõGoodDeg¼ô(PeÂHeight)
|Ô TalkswÓñ )Á
½ÞÀÓñ
)Á"Use modulus"ÁPeÁ"valid for degree <="ÁGoodDeg
×è GoodDegÕñ ñ
ò RaisedswÑñ RaisedswÀñ õLoopforPX
ü
' õResetV
j U0èÑ V À AnsÝÑ V ÀCfactorÑ²Þ U0)À U0Ññ ( Ans)
õ
RecalcGoodDegÊö(Pe)
¢ $ TalkswÓñ )Á
ã . ÀÓñ
)Á"Use modulus"ÁPeÁ"valid for degree <="ÁGoodDeg
ñ 8 NewRÑð
B I ÑðR Þñ
< L ÃI Â Sw)ÑðV NewR)ÑV I )À NewR
C V
T ` R ÑNewR
j R Ññ ( AnsÝ U0) õLoopforPX
t
¼ ~ ³õPolymod ( X Â Y )À Y# must be monic
Ç ºI
ç I Ñ²Û X )²Û Y )Þñ
( X Ñ( X Þÿ X ÂI )å Y å_Xï(I Þ²Û Y )))ç(PeåP )
/ ¦
< ° ( X )
E º
d Ä ³õ Henselsub ( G Â H )
Î ºI ÂK Â V Â W ÂCfinv
¥ Ø CfinvÑÛCfactorÂP )
É â K Ñð²Û G )Ý²Û H )À W Ñð
ö ì I ÑßK Þ²Û H )Âð)à²Û G )ÂK )
& ö W ÝÑÿ G ÂI )åÿ H ÂK ÞI )çPe1
-
p
ÿ V ÂK )Ñ(ÿ U0ÂK )ÞCfactorå W çPe1)èPeåCfinv
w
( V )
(
® 2
³õGoodDeg (P ÂHeight)
¼ <
ºDegÑð
é F
,P Òñ åHeightå¸DegÂDegèñ )
õ P
Deg
þ Z
b,
d
(Deg)
n
2 x
õ
RecalcGoodDeg (P )
B
ºI Â W
o
I Ñð²Û U0)À W ÝÑÀÿ U0ÂI ))À
W ÝÑÀ²Þ U0))
W ÒHeight
Ø ª
HeightÑ W ÀGoodDegѳõGoodDeg¼ô(P ÂHeight)À
á ´
õ ¾
³õTry ( V )
!È
ºI Â WUÂ WV
'!Ò
Æ-²ß U0)ç²ß V )(ð)
D!Ü
ã-²Þ U0)ç²Þ V )(ð)
Q!æ
²ÑPa
!ð
WUѳõ TransPolyìõ( U0)À WVѳõ TransPolyìõ( V )
¦!ú
E. WUç WV²ÑðÀ(ð)
³! ²ÑPb
ì! WUѳõ TransPolyìõ( U0)À WVѳõ TransPolyìõ( V )
" §. WUç WV²ÑðÀ(ð)
"" ²Ñð
)", È. U0ç V (ð)
5"6 (ñ )
>"@
]"J õ Reduction (& W ÂP )
m"T ºI Â Z
"^ I Ñð²Û W )
º"h Z Ñÿ W ÂI )çP ÀY/ Z ÒP èñ Z ÞÑP
Ñ"r ÿ W ÂI )Ñ Z
Ø"|
ß"
è"
# ³õ TransPoly ( X )
#¤ ºI Â W
'#® I Ñð²Û X )
F#¸ ÿ W ÂI )Ñÿ X ÂI )
M#Â
Z#Ì ( W )
c#Ö
~#à ³õ
Eisenstein ( X )
³#ê ºI ÂJ ÂX ÂP ÂX  W  Z ÂModmemѲ
ã#ô I Ñðñ ÀX Ñ(I Ýñ )èñ À0£´X
$þ X ÑX À W ÑÀýü X )))
$ »0 W ÑðÀñÆ
1$ Ð0 W Ññ ñ¼
c$ P ÑÑ W )À1èþ0P Òñ ïñ ÂP Ñð}ñ¼
~$& 1²Þ X )çP Ñðñ:
$0 W èÑP À>1 W çP ñD
Æ$: W èÑP À W çP ñ ñ:
Ó$D ²ÑP
ò$N Z ѳõ Transpolyìõ( X )
%X X ÑX Ý_XÀ Z Ñýü Z ))
/%b J Ññ ²Û Z )Þñ
L%l ÿ Z ÂJ )Àñ¼
S%v
% Talksw"primarity by Eisenstein"Á
% À X " after X -> X"Á
º% À X ÔðüX )Á
Û% À "+"Á»üX )Âñ Âå)Á
õ%¨ À" with prime"ÁP
&² À²ÑModmemÀ(ñ )
&¼
-&Æ ²ÑModmemÀ(ð)
6&Ð
O&Ú ³õGcd ( X Â Y )
i&ä ºP Â G Â W Â Z
&î P ÑÎñݲçñè)
&ø ²ÑP
Ç&
W ѳõ TransPolyìõ( X )À Z ѳõ TransPolyìõ( Y )
'
¥3è3²Û W )Ô²Û X )Â²Û Z )Ô²Û Y )}P ÑÞP )Àñø
/'
²ÛÄ W  Z ))Ñð²ÑðÀ(ûñ ))
9'
²Ñð
r'*
X ѳõ Primitive ( X )À Y ѳõ Primitive ( Y )
'4
X Ñð( Y )
'>
Y Ñð( X )
Ã'H
²Û X )Ô²Û Y )¥ X Â Y
â'R
W Ñ²Þ X )À Z Ñ²Þ Y )
(\
G ÑÄ W  Z )À W èÑ G À Z èÑ G
+(f
W Öñ Y åÑ W
G(p
Z Öñ X åÑ Z
l(z
X ÞÑ Y å_Xï(²Û X )Þ²Û Y ))
(
X X ѳõ Primitive ( X )
(
ÀñH
»(
(³õ Primitive ( Y ))
Ä(¢
Þ(¬
³õ Primitive ( X )
î(¶
ºI Â G
)À
I Ñð²Û X )
6)Ê
G ÑÄ G Âÿ X ÂI ))ÀÕ5 G Ññ ÀñÞ
=)Ô
U)Þ
ô5²Þ X )Ôð´ G
n)è
6 G Ññ ( X )
)ò
( X è G )
)ü
)
°)³õPolfact3 ( U0ÂP )
â)ºI ÂDegÑ²Û U0) U  X  Z  Ansѽ)
ó)$¤Z Deg)
*.²ÑP
*8 X ÑÛ²Þ U0)ÂP )
S*BI ÑðDegÀÿ U ÂI )Ñÿ U0ÂI )å X çP À
u*L7²Û U )ÔDeg²ÑðÀ(½))
¢*VõRemoveMultiFactor÷A7U# -> U# * MF#
Ä*`c7²Û U )ÔDeg²ÑðÀ(½))
Í*j¤7
ü*t get product of factors for each degree
+~
+õMakeZPZ4õ
&+DegÑñ
:+õ
DegreeLoop
T+¦ X ѲÝÄ U  Z ))
+° ²Û X ) AnsÝѳõ IrredFactor¾ö( X )
+ºÀ U èÑ X
µ+Ä ²Û U )Õñ åDegÝñ ñö
È+ÎõRaiseZPZsõ
Ô+Ø Deg
é+âõ
DegreeLoop^7
ò+ì
,ö8²Û U ) AnsÝÑ U
+, õ
SortResultö(& Ans)
5,
²Ñð
C,( Ans)
L,
p,( power of polynomial mod U#
y,2
,<³õ PolyPower ( Z Â E )
¨,FºI Â W
Á,P`9 E Ñð(ûñ ))
Ð,Z W Ñ Z
î,dI ÑÂ E )Þñ ðÞñ
-n W Ñ W ïñ ç U
/-xÎ9ÃI Â E ) W Ñ W å Z ç U
6-
C-( W )
L-
m- remove multiple factors
v-ª
-´õRemoveMultiFactor
«-¾ºI  DU W  G
º-È MFÑ U
Ý-Ò DUÑ²Ü U )À|:²Û DU)Ñð¶
.ܶ: DUÑð W Ñ U À U Ññ Àñ6À p-th power poly
1.æ G ѲÝÄ U  DU))
V.ð ²Û G )Ñð¶<À no multiple
t.úÀ U èÑ G À W Ñ G
. À extract p-th power part
². G ѲÝÄ U  W ))
Â. W èÑ G
Ô." ²Û G )Ñð
û., ²Û W )Õð¶ À no p-th power
=/6 G ÑðÀI Ñð²Û W )èP Àÿ G ÂI )Ñÿ W ÂI åP )À
c/@ U åÑ G À restore 1-st power
m/JñÒ
t/T·
/^ MFèÑ U
/h
/r
µ/| Get Irreducible Factors
Ú/ find factors of Deg% degree
ã/
ÿ/³õ IrredFactor ( F )
10¤ºI  G  U  PowNeg W  Z  Ansѽ)
R0®ñ<²Û F )ÑDeg(½ F ))
a0¸ U Ñ F
t0 Tmpѽ F )
}0Ìÿÿ
£0Ö W ѳõRndPolyæô(ñ åDegÞñ )
É0à W ѳõWPD`ô( W ÂDeg)Ýûñ )
Ú0ê U Ñûñ )
ò0ôI Ññ Â Tmp)
1þ F Ñþ TmpÂI )
1¼= F ÑðñX
71 G ѲÝÄ F  W ))
_1 §>çý=ðÔ²Û G )Â²Û G )Ô²Û F )}
p1& À F èÑ G
¨10 À ²Û F )ÑDeg AnsÝÑ F À F ÑðG> U åÑ F
Á1: Àþ TmpÂI )Ñ F
þ1D À ²Û G )ÑDeg AnsÝÑ G > TmpÝÑ G À U åÑ G
2NÀ±> U åÑ F
2X
-2b = U Ñûñ )
;2l( Ans)
D2v
]2³õRndPoly (Deg)
h2º W
2DegÑñ ÝÜêåêåDeg)
2I ÑðDeg
¶2¨ÿ W ÂI )ÑÜêåP )
½2²
Ê2¼( W )
Ó2Æ
î2Ðõ
SortResult (& X )
3ÚºI ÂJ ÂPtr W  W1 W2
+3ä W Ñ X À X ѽ)
F3îI Ññ Â W )Þñ
h3øPtrÑI À W1Ñþ W ÂI )
3J ÑI Ýñ Â W )
3 W2Ñþ W ÂJ )
Ô3s@³õPolycmp õ(& W1Â& W2)ÒðPtrÑJ À W1Ñ W2
Û3
4* X ÝÑ W1À½@PtrÖI W1Ñþ W ÂI )Àþ W ÂPtr)Ñ W1
%44
@4> X ÝÑþ W ÂÂ W ))
G4H
P4R
o4\³õPolyCmp (& W1Â& W2)
z4fºI
4p8A²Û W1)Ò²Û W2)(ñ )
¹4zXA²Û W1)Ô²Û W2)(Þñ )
Ó4I Ñ²Û W1)ðÞñ
5¤AÀÿ W1ÂI ))ÒÀÿ W2ÂI ))À(ñ )
85×AÀÿ W1ÂI ))ÔÀÿ W2ÂI ))À(Þñ )
d5¢Bÿ W1ÂI )Òÿ W2ÂI )À(ñ )
5¬0Bÿ W1ÂI )Ôÿ W2ÂI )À(Þñ )
5¶
¢5À(ð)
«5Ê
Ç5ÔõBadness ( U0ÂP )
ñ5ÞºI ÂDeg DU G  U ÂBadness
6è¤Z ²Û U0))
6ò²ÑP
G6üI Ñð²Û U0)Àÿ U ÂI )Ñÿ U0ÂI )çP À
g6C²Û U )Ô²Û U0)(Þñ )
p6C
6 DUÑ²Ü U )À2C²Û DU)ÑðñL
ª6$IC DUÑð(Þñ )
Á6. G ÑÄ U Â DU)
Ù68xC²Û G )(Þñ )
â6BC
ô6LõMakeZPZ4õ
7VDegÑñ
7`«C
#7j G ÑÄ U Â Z )
>7t ²Û G ) U èÑ G
g7~I Ññ ²Û U )ÀZ I )çÑ U À
ª7À+D²Û G )ÑDeg Badness BadnessÝÑ(²Û G )èDeg)ïñ
Ï7D²Û U )Òñ åDegÝñ Deg
ã7ÀõRaiseZPZsõ
î7¦Àñj
8°¨D²Û U ) Badness
8º²Ñð
%8Ä(Badness)
.8Î
\8Ø polynomial inverse modulo polynomial
|8â A#=fnPolyModInv(X#,Y#)
8ì B#=(poly(1)-A#*X#)\Y#
¶8ö print A#*X#+B#*Y#
Û8 must set modulus in advance
þ8
³õ
ModpolyModInv ( X Â Y )
9º R Â Q Â A Â A1Â W
O9 è X Ñð Y Ñð}"illegal parameter"À
g9( A Ñûñ )À A1Ñð
p92
9< Q Ñ X è Y À R Ñ£À X Ñ Y À Y Ñ R
Ì9F W Ñ A1À A1Ñ A Þ Q å W À A Ñ W
Û9P R Ñð
þ9Z ²Û X )Öð"not coprime"À
:d A èÑ X
:n( A )
$:x
8: MAKE Z^P-Z
A:
R:õMakeZPZ
b: ºI Â W
:ª(G²Û U )ÒP Z Ñ_XïP Àñð
¨:´ W ÑûðÂñ )À Z Ñûñ )
Á:¾I ÑðÂP )Þñ
ê:ÈGÃI ÂP ) Z Ñ Z å W ç U
;Ò W Ñ W ïñ ç U
;Ü
";æ Z Ñ Z å W ç U
?;ð W Ñ Z ÀZ ñ )Ñ Z
{;úI Ññ ²Û U )À W Ñ W å Z ç U ÀZ I )Ñ W À
; Z Ñ( Z ÞûðÂñ ))ç U
¡;
ª;
Ä;" MAKE Z^(P^deg)-Z
Í;,
ß;6õRaiseZPZ
ï;@ºI Â W
q
¡< MAKE W#^((P^deg%-1)\2)
ª<
Ä<³õWPD ( W ÂDeg)
Þ<¤ºI ÂJ  V  X
=® W ѳõ PolyPower ö( W Â(P Þñ )èñ )
=¸ V Ñ W
4=ÂI Ññ DegÞñ
I=Ì X Ñû²ß V ))
=ÖJ Ññ ²Û V )À X ÝÑZ J )åÿ V ÂJ )À
=à V Ñ X
§=ê W Ñ W å V ç U
®=ô
»=þ( W )
Very nice! Thank you for this wonderful archive. I wonder why I found it only now. Long live the BBS file archives!
This is so awesome! 😀 I’d be cool if you could download an entire archive of this at once, though.
But one thing that puzzles me is the “mtswslnkmcjklsdlsbdmMICROSOFT” string. There is an article about it here. It is definitely worth a read: http://www.os2museum.com/wp/mtswslnk/