Category : BASIC Source Code
Archive : UBAS830.ZIP
Filename : POLFACT2.UB
Output of file : POLFACT2.UB contained in archive : UBAS830.ZIP
POLFACT2 VER 2.0
$ ®ÂÂð
, ¨
3 (
h 2 " * Polynomial factorization modulo a prime *"
< " * gives irreducible factors explicitly *"
Ò F " * use x or X for a variable *"
P " * example : x^3+2*x^2+3*x+4 *"À
Z
%d ±"f(x)="Á W
2n U0Ñ""
Ix I Ѳ W Â"xX")
I U0ÝѼ W ÂI Þñ )Ý"_X"À W Ñ» W ÂI Ýñ Âå)Àñx
¦ U0Ñý U0Ý W )
» À"f(X)="Á U0
Ë AutoswÑð
Ùª õModP
´ À"--------------------------------------------"
A¾ AutoswP ÑÎAutosw)À AutoswÀñú
UÈ §"Mod P="ÁP
fÒ P Ñð¿
Ü À¯ ° P ÔðAutoswÑÞP Àñ¾
¤æ P ÖÑP )
Æð À"not a prime"À¤ÀõModP
àú " modulo "ÁP À
X ѳõPolfact2¡í( U0ÂP )
, Â X )Ñð" constant"ÀõModp
Fõ PrintPolyÖí( X )
U"õModp
^,
w6õ PrintPoly ( X )
@ºI Â W
J þ X Âñ )Òñ þ X Âñ )Á
ÈTI Ññ Â X )ñ
ê^ W Ñ"("Ýüþ X ÂI ))Ý")"
.h þ X ÂI Ýñ ) W ÝÑ"^"Ý»üþ X ÂI Ýñ )Ýñ )Âñ Âå)
Sr I ÔÂ X )Þñ W ÝÑ" * "
r| ²Æ ²ÆÝ W )ÒñO
~ W Á
À
¤
®
¾¸³õPolfact2 ( U0ÂP )
àºI ÂDeg U Ñð Ansѽ)
ó̤Z ²Û U0))
Ö²ÑP
6àI Ñð²Û U0)Àÿ U ÂI )Ñÿ U0ÂI )çP À
Qê ²Û U )Õð( Ans)
ôC Ñÿ U Â²Û U ))À AnsѽC )À U æÑC À RemoveConstFactor
ÆþõRemoveMultiFactor`î U# -> U# * MF#
Ï
þ get product of factors for each degree
&õMakeZPZí
(0DegÑñ
<:õ
DegreeLoop
VD X ѲÝÄ U  Z ))
N ²Û X ) AnsÝѳõ IrredFactor@î( X )
XÀ U èÑ X
·b ²Û U )Õñ åDegÝñ ñ
ÊlõRaiseZPZ»í
Öv Deg
ëõ
DegreeLoopx
ô
²Û U ) AnsÝÑ U
-õ
SortResult%î(& Ans)
6¨
T² get multiple factors
]¼
wÆ X ѽþ AnsÂñ ))
ÐI Ññ Â Ans)
®ÚE ÑðÀ Z Ñþ AnsÂI )
¿ä ²Û MF)
éîÀ MFç Z ÑðÀ MFèÑ Z À E À
ø X Ýѽ Z ÂE )
²Ñð
( X )
(
L* power of polynomial mod U#
U4
t>³õ PolyPower ( Z Â E )
HºI Â W
R E Ñð(ûñ ))
¬\ W Ñ Z
ÊfI ÑÂ E )Þñ ðÞñ
âp W Ñ W ïñ ç U
z ÃI Â E ) W Ñ W å Z ç U
( W )
(
I ¢ remove multiple factors
R ¬
m ¶õRemoveMultiFactor
| À MFÑ U
Ê DUÑ²Ü U )À ²Û DU)Ñð¶
Ô Ô DUÑð W Ñ U À U Ññ Àñ.À p æ½®
î Þ G ѲÝÄ U  DU))
è ²Û G )Ñð¶ À ½döȵ
2
òÀ U èÑ G À W Ñ G
^
ü À ½dö©ç p æöðÆè¾·
x
G ѲÝÄ U  W ))
W èÑ G
²Û G )Ñð
À
$ ²Û W )Õð¶ À p æöȵ
. G ÑðÀI Ñð²Û W )èP Àÿ G ÂI )Ñÿ W ÂI åP )À
" 8 U åÑ G À 1 澯߷
, BñÊ
3 L·
C V MFèÑ U
J `
S j
t t Get Irreducible Factors
~ find factors of Deg% degree
¢
¾ ³õ IrredFactor ( F )
ö ºI  G  U  PowNeg W  Z  Ansѽ) Tmp
¦ ²Û F )ÑDeg(½ F ))
& ° U Ñ F
9 º Tmpѽ F )
B Ä
h Î W ѳõRndPolyRí(ñ åDegÞñ )
· Ø P Ññ Z Ñ W ÀI Ññ DegÞñ À Z Ñ Z ïñ ç U À W ÝÑ Z À
á âÀ W ѳõWPDí( W ÂDeg)Ýûñ )
ò ì U Ñûñ )
öI Ññ Â Tmp)
"
F Ñþ TmpÂI )
5
F ÑðñZ
O
G ѲÝÄ F  W ))
w
ç ðÔ²Û G )Â²Û G )Ô²Û F )}
( À F èÑ G
À
2 À ²Û F )ÑDeg AnsÝÑ F À F Ñð U åÑ F
Ù
< Àþ TmpÂI )Ñ F
F À ²Û G )ÑDeg AnsÝÑ G TmpÝÑ G À U åÑ G
*PÀ U åÑ F
1Z
Ed U Ñûñ )
Sn( Ans)
\x
u³õRndPoly (Deg)
º W
DegÑñ ÝÜêåêåDeg)
± I ÑðDeg
Ϊÿ W ÂI )ÑÜêåP )
Õ´
â¾( W )
ëÈ
Ò Sort result
Ü
$æõ
SortResult (& X )
CðºI ÂJ  W  W1 W2
fú W Ñ X À X ѽþ W Âñ ))
I Ññ Â W )Þñ
£PtrÑI À W1Ñþ W ÂI )
¿J ÑI Ýñ Â W )
Ö" W2Ñþ W ÂJ )
, ³õPolycmplí( W1Â W2)ÒðPtrÑJ À W1Ñ W2
6
W@ X ÝÑ W1À PtrÖI W1Ñþ W ÂI )Àþ W ÂPtr)Ñ W1
^J
yT X ÝÑþ W ÂÂ W ))
^
h
¦r³õPolyCmp ( W1Â W2)
±|ºI
Ð ²Û W1)Ò²Û W2)(ñ )
ð ²Û W1)Ô²Û W2)(Þñ )
I Ñ²Û W1)ðÞñ
6¤ ÿ W1ÂI )Òÿ W2ÂI )À(ñ )
c® ÿ W1ÂI )Ôÿ W2ÂI )À(Þñ )
j¸
tÂ(ð)
}Ì
Ö MAKE Z^P-Z
à
«êõMakeZPZ
»ôºI Â W
âþ ²Û U )ÒP Z Ñ_XïP ÀñD
W ÑûðÂñ )À Z Ñûñ )
I ÑðÂP )Þñ
C ÃI ÂP ) Z Ñ Z å W ç U
[& W Ñ W ïñ ç U
b0
{: Z Ñ Z å W ç U
D W Ñ Z ÀZ ñ )Ñ Z
ÔNI Ññ ²Û U )À W Ñ W å Z ç U ÀZ I )Ñ W À
óX Z Ñ( Z ÞûðÂñ ))ç U
úb
l
2v MAKE Z^(P^deg)-Z from Z^(P^(deg-1))-Z
;
MõRaiseZPZ
]ºI Â W
u W Ñ Z ÝûðÂñ )
¨ Z Ñûÿ W Âð))
²I Ññ ²Û W )À Z ÝÑZ I )åÿ W ÂI )À
á¼ Z Ñ( Z ÞûðÂñ ))ç U
èÆ
ñÐ
Ú MAKE W#^((P^deg%-1)\2)
ä
4î³õWPD ( W ÂDeg)
NøºI ÂJ Â V Â X
| W ѳõ PolyPowerðí( W Â(P Þñ )èñ )
V Ñ W
¤I Ññ DegÞñ
» X Ñûÿ V Âð))
ñ*J Ññ ²Û V )À X ÝÑZ J )åÿ V ÂJ )À
4 V Ñ X
> W Ñ W å V ç U
H
-R( 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/