Python Ideal Exemples

Exemple #1

print "Ring: " + str(r);
print;


ps = """
( 
 ( z1^3 z2   z3^2 - w1 ),
 ( z1^2 z2^2 z3   - w2 ),
 ( z1   z2^3 z3   - w3 ),
 ( z1             - w4 ),
 ( z2             - w5 ),
 ( z3             - w6 )
) 
""";

f = Ideal( r, ps );
print "Ideal: " + str(f);
print;

rg = f.GB();
print "seq Output:", rg;
print;


pf = """
( 
 ( z1^45 z2^21 z3^18 )
) 
""";

fp = Ideal( r, pf );

Exemple #2

 ( U4^4 - 20/7 A46^2 ), 
 ( A46^2 U3^4 + 7/10 A46 U3^4 + 7/48 U3^4 - 50/27 A46^2 - 35/27 A46 - 49/216 ), 
 ( A46^5 U4^3 + 7/5 A46^4 U4^3 + 609/1000 A46^3 
 U4^3 + 49/1250 A46^2 U4^3 - 27391/800000 A46 U4^3 
 - 1029/160000 U4^3 + 3/7 A46^5 U3 U4^2 + 3/5 A46^6 
 U3 U4^2 + 63/200 A46^3 U3 U4^2 + 147/2000 A46^2 
 U3 U4^2 + 4137/800000 A46 U3 U4^2 - 7/20 A46^4 
 U3^2 U4 - 77/125 A46^3 U3^2 U4 - 23863/60000 A46^2 
 U3^2 U4 - 1078/9375 A46 U3^2 U4 - 24353/1920000 
  U3^2 U4 - 3/20 A46^4 U3^3 - 21/100 A46^3 U3^3 
 - 91/800 A46^2 U3^3 - 5887/200000 A46 U3^3 
 - 343/128000 U3^3 ) 
) 
""";

f = Ideal( r, ps );
print "Ideal: " + str(f);
print;

fi = f.toInteger();
print "Ideal: " + str(fi);
print;
#                    "1152921504606846883"
mf = ModIntegerRing( str(2**60-93), True );
#mf = ModIntegerRing( str(19), True );
fm = fi.toModular( mf );
print "Ideal: " + str(fm);

#sys.exit();

rm = fm.GB();

Exemple #3

Fichier : katsura.py Projet : Eeeeddddy/gittest

#r = Ring( "Mod 1152921504606846883 (B,S,T,Z,P,W) L" ); # 2^60-93
#r = Ring( "Quat(B,S,T,Z,P,W) L" );
#r = Ring( "Z(B,S,T,Z,P,W) L" );
#r = Ring( "C(B,S,T,Z,P,W) L" );
#r = Ring( "Rat(B,S,T,Z,P,W) L" );
#print "Ring: " + str(r);
#print;

k = Katsura(knum)
r = Ring(k.varList("Rat", "G"))
print "Ring: " + str(r)
print

ps = k.polyList()

f = Ideal(r, ps)
print "Ideal: " + str(f)
print

rg = f.parGB(tnum)
for th in range(tnum, 0, -1):
    rg = f.parGB(th)
    #print "par Output:", rg;
    #print;

rg = f.GB()
#print "seq Output:", rg;
print

# rg = f.distGB(2);
#print "dist Output:", rg;

Exemple #4

#r = Ring( "Mod 1152921504606846883 (B,S,T,Z,P,W) L" ); # 2^60-93
#r = Ring( "Quat(B,S,T,Z,P,W) L" );
#r = Ring( "Z(B,S,T,Z,P,W) L" );
#r = Ring( "C(B,S,T,Z,P,W) L" );
#r = Ring( "Rat(B,S,T,Z,P,W) L" );
#print "Ring: " + str(r);
#print;

k = Katsura(knum);
r = Ring( k.varList("Rat","G") );
print "Ring: " + str(r);
print;

ps = k.polyList();

f = Ideal( r, ps );
print "Ideal: " + str(f);
print;

rg = f.parGB(tnum);
for th in range(tnum,0,-1):
   rg = f.parGB(th);
   #print "par Output:", rg;
   #print;

rg = f.GB();
#print "seq Output:", rg;
print;


# rg = f.distGB(2);

Exemple #5

print "------- RC(PolyRing(QQ(),\"a,b,c\",PolyRing.lex)) ---------";
r = PolyRing(QQ(),"a,b,c",PolyRing.lex);
print "r = " + str(r);
[pone,pa,pb,pc] = r.gens();
print "pone   = " + str(pone);
print "pa     = " + str(pa);
print "pb     = " + str(pb);
print "pc     = " + str(pc);
g1 = pa**2 - 2;
print "g1 = " + str(g1);
g2 = pb**3 - 2;
print "g2 = " + str(g2);
g3 = pc**2 - pa*pb;
print "g3 = " + str(g3);
F = Ideal(r,list=[g1,g2,g3]);
print "F = " + str(F);
rc = RC(F);
print "rc.factory() = " + str(rc.factory());
[one,a,b,c] = rc.gens();
print "one   = " + str(one);
print "a     = " + str(a);
print "b     = " + str(b);
print "c     = " + str(c);
r1 = a*b + c;
print "r1 = " + str(r1);
r2 = r1*r1*r1 - r1*r1 + one;
print "r2 = " + str(r2);
r3 = r2**3 - r1 + one;
print "r3 = " + str(r3);
r4 = ( -120 * a * b**2 * c + 606 * b**2 * c + 1917 * a * b * c + 400 * b * c - 132 * a * c - 673 * c + 432 * a * b**2 + 2130 * b**2 + 1436 * a * b - 72 * b + 100 * a - 1950 );

Exemple #6

 ( U4^4 - 20/7 A46^2 ), 
 ( A46^2 U3^4 + 7/10 A46 U3^4 + 7/48 U3^4 - 50/27 A46^2 - 35/27 A46 - 49/216 ), 
 ( A46^5 U4^3 + 7/5 A46^4 U4^3 + 609/1000 A46^3 
 U4^3 + 49/1250 A46^2 U4^3 - 27391/800000 A46 U4^3 
 - 1029/160000 U4^3 + 3/7 A46^5 U3 U4^2 + 3/5 A46^6 
 U3 U4^2 + 63/200 A46^3 U3 U4^2 + 147/2000 A46^2 
 U3 U4^2 + 4137/800000 A46 U3 U4^2 - 7/20 A46^4 
 U3^2 U4 - 77/125 A46^3 U3^2 U4 - 23863/60000 A46^2 
 U3^2 U4 - 1078/9375 A46 U3^2 U4 - 24353/1920000 
  U3^2 U4 - 3/20 A46^4 U3^3 - 21/100 A46^3 U3^3 
 - 91/800 A46^2 U3^3 - 5887/200000 A46 U3^3 
 - 343/128000 U3^3 ) 
) 
""";

f = Ideal( r, ps );
print "Ideal: " + str(f);
print;

startLog();

o = f.optimize();
print "optimized Ideal: " + str(o);
print;

#rg = f.GB();
#print "Output:", rg;
#print;

org = o.GB();
print "opt Output:", org;

Exemple #7

Fichier : syzy3.py Projet : Eeeeddddy/gittest

from jas import Ideal

# ? example

r = Ring("Rat(x,y,z) L")
print "Ring: " + str(r)
print

ps = """
( 
 ( z^3 - y ),
 ( y z - x ),
 ( y^3 - x^2 z ),
 ( x z^2 - y^2 )
) 
"""

f = Ideal(r, ps)
print "Ideal: " + str(f)
print

from edu.jas.module import SyzygyAbstract
from edu.jas.vector import ModuleList
from edu.jas.module import ModGroebnerBaseAbstract

R = SyzygyAbstract().resolution(f.pset)

for i in range(0, R.size()):
    print "\n %s. resolution" % (i + 1)
    print "\n ", R[i]

Exemple #8

print "------- RC(PolyRing(QQ(),\"a,b,c\",PolyRing.lex)) ---------"
r = PolyRing(QQ(), "a,b,c", PolyRing.lex)
print "r = " + str(r)
[pone, pa, pb, pc] = r.gens()
print "pone   = " + str(pone)
print "pa     = " + str(pa)
print "pb     = " + str(pb)
print "pc     = " + str(pc)
g1 = pa**2 - 2
print "g1 = " + str(g1)
g2 = pb**3 - 2
print "g2 = " + str(g2)
g3 = pc**2 - pa * pb
print "g3 = " + str(g3)
F = Ideal(r, list=[g1, g2, g3])
print "F = " + str(F)
rc = RC(F)
print "rc.factory() = " + str(rc.factory())
[one, a, b, c] = rc.gens()
print "one   = " + str(one)
print "a     = " + str(a)
print "b     = " + str(b)
print "c     = " + str(c)
r1 = a * b + c
print "r1 = " + str(r1)
r2 = r1 * r1 * r1 - r1 * r1 + one
print "r2 = " + str(r2)
r3 = r2**3 - r1 + one
print "r3 = " + str(r3)
r4 = (-120 * a * b**2 * c + 606 * b**2 * c + 1917 * a * b * c + 400 * b * c -

Exemple #9

Fichier : rose_part.py Projet : Eeeeddddy/gittest

 U3 U4^2 + 4137/800000 A46 U3 U4^2 - 7/20 A46^4 
 U3^2 U4 - 77/125 A46^3 U3^2 U4 - 23863/60000 A46^2 
 U3^2 U4 - 1078/9375 A46 U3^2 U4 - 24353/1920000 
  U3^2 U4 - 3/20 A46^4 U3^3 - 21/100 A46^3 U3^3 
 - 91/800 A46^2 U3^3 - 5887/200000 A46 U3^3 
 - 343/128000 U3^3 ) 
) 
"""

pp1 = """
 ( 20 A46 + 7 ),
"""

pp2 = """
 ( 5480334637123239936000000000000000000 A46^32 + 23330567455181792870400000000000000000 A46^31 - 22260410953422455439360000000000000000 A46^30 - 379039147753503876710400000000000000000 A46^29 - 1305289515920841108357120000000000000000 A46^28 - 2661894008686715272062566400000000000000 A46^27 - 3732109213267597335472373760000000000000 A46^26 - 3719328899522099347074318336000000000000 A46^25 - 2513175000419852400394764288000000000000 A46^24 - 801907472074794268996141056000000000000 A46^23 + 559468735767998648283977220096000000000 A46^22 + 1161692745234469227508358814105600000000 A46^21 + 1115120737963786660933876454522880000000 A46^20 + 754183677763034219243933188227072000000 A46^19 + 366205139138005719200006792439398400000 A46^18 + 95407136698255889087520898673541120000 A46^17 - 35897763757636362165902256717692928000 A46^16 - 68696958358719191677546842722559590400 A46^15 - 55382563098545072682320366954843996160 A46^14 - 32223104574376823941781148035505979392 A46^13 - 14867126462105106300205537184606126080 A46^12 - 5596017809975575801376014016653721600 A46^11 - 1730893404306213749794640488178116608 A46^10 - 438698743729822786570094575456788480 A46^9 - 90199241991532353478039712103521280 A46^8 - 14778859703096558479650421488297984 A46^7 - 1874056025467134008603806670325120 A46^6 - 174876413639867324175892636604160 A46^5 - 10843113615171040141214782270464 A46^4 - 325577720150105105056746125600 A46^3 + 6040454553390756509792153750 A46^2 + 761038687880048862537750000 A46 + 13745464623924567359765625 ),
"""

pp = ps % pp1

f = Ideal(r, pp)
print "Ideal: " + str(f)
print

startLog()

rg = f.GB()
print "seq Output:", rg
print

#sys.exit();

Exemple #10

print;

ps = """
(
x1 + x2 + x3 + x4 + x5 + x6,
x1*x2 + x1*x6 + x2*x3 + x3*x4 + x4*x5 + x5*x6,
x1*x2*x3 + x1*x2*x6 + x1*x5*x6 + x2*x3*x4 + x3*x4*x5 + x4*x5*x6,
x1*x2*x3*x4 + x1*x2*x3*x6 + x1*x2*x5*x6 + x1*x4*x5*x6 + x2*x3*x4*x5 + x3*x4*x5*x6,
x1*x2*x3*x4*x5 + x1*x2*x3*x4*x6 + x1*x2*x3*x5*x6 + x1*x2*x4*x5*x6 + x1*x3*x4*x5*x6 + x2*x3*x4*x5*x6,
x1*x2*x3*x4*x5*x6 - 1
)
""";
#x1 + x2 + x3 + x4 + x5 + x6,
#x1*x2*x3*x4*x5*x6 - 1

f = Ideal( r, ps );
print "Ideal: " + str(f);
print;

startLog();

o = f.optimize();
print "optimized Ideal: " + str(o);
print;

rg = f.GB();
print "Output:", rg;
print;

#org = o.GB();
#print "opt Output:", org;

Exemple #11

# ? example

r = Ring("Rat(x,y,z) L")
print "Ring: " + str(r)
print

ps = """
( 
 ( z^3 - y ),
 ( y z - x ),
 ( y^3 - x^2 z ),
 ( x z^2 - y^2 )
) 
"""

f = Ideal(r, ps)
print "Ideal: " + str(f)
print

rg = f.GB()
print "seq Output:", rg
print

from edu.jas.module import SyzygyAbstract
from edu.jas.vector import ModuleList
from edu.jas.module import ModGroebnerBaseAbstract

s = SyzygyAbstract().zeroRelations(rg.list)
sl = ModuleList(rg.pset.ring, s)

print "syzygy:", sl

Exemple #12

 ( U4^4 - 20/7 A46^2 ), 
 ( A46^2 U3^4 + 7/10 A46 U3^4 + 7/48 U3^4 - 50/27 A46^2 - 35/27 A46 - 49/216 ), 
 ( A46^5 U4^3 + 7/5 A46^4 U4^3 + 609/1000 A46^3 
 U4^3 + 49/1250 A46^2 U4^3 - 27391/800000 A46 U4^3 
 - 1029/160000 U4^3 + 3/7 A46^5 U3 U4^2 + 3/5 A46^6 
 U3 U4^2 + 63/200 A46^3 U3 U4^2 + 147/2000 A46^2 
 U3 U4^2 + 4137/800000 A46 U3 U4^2 - 7/20 A46^4 
 U3^2 U4 - 77/125 A46^3 U3^2 U4 - 23863/60000 A46^2 
 U3^2 U4 - 1078/9375 A46 U3^2 U4 - 24353/1920000 
  U3^2 U4 - 3/20 A46^4 U3^3 - 21/100 A46^3 U3^3 
 - 91/800 A46^2 U3^3 - 5887/200000 A46 U3^3 
 - 343/128000 U3^3 ) 
) 
""";

f = Ideal( r, ps );
print "Ideal: " + str(f);
print;

#startLog();

rg = f.GB();
#print "seq Output:", rg;
#print;

#sys.exit();

rg = f.parNewGB(2);
#print "par-new Output:", rg;
#print;

Exemple #13

 ( U4^4 - 20/7 A46^2 ), 
 ( A46^2 U3^4 + 7/10 A46 U3^4 + 7/48 U3^4 - 50/27 A46^2 - 35/27 A46 - 49/216 ), 
 ( A46^5 U4^3 + 7/5 A46^4 U4^3 + 609/1000 A46^3 
 U4^3 + 49/1250 A46^2 U4^3 - 27391/800000 A46 U4^3 
 - 1029/160000 U4^3 + 3/7 A46^5 U3 U4^2 + 3/5 A46^6 
 U3 U4^2 + 63/200 A46^3 U3 U4^2 + 147/2000 A46^2 
 U3 U4^2 + 4137/800000 A46 U3 U4^2 - 7/20 A46^4 
 U3^2 U4 - 77/125 A46^3 U3^2 U4 - 23863/60000 A46^2 
 U3^2 U4 - 1078/9375 A46 U3^2 U4 - 24353/1920000 
  U3^2 U4 - 3/20 A46^4 U3^3 - 21/100 A46^3 U3^3 
 - 91/800 A46^2 U3^3 - 5887/200000 A46 U3^3 
 - 343/128000 U3^3 ) 
) 
"""

f = Ideal(r, ps)
print "Ideal: " + str(f)
print

startLog()

o = f.optimize()
print "optimized Ideal: " + str(o)
print

#rg = f.GB();
#print "Output:", rg;
#print;

org = o.GB()
print "opt Output:", org

Exemple #14

Fichier : rose.py Projet : Eeeeddddy/gittest

 ( U4^4 - 20/7 A46^2 ), 
 ( A46^2 U3^4 + 7/10 A46 U3^4 + 7/48 U3^4 - 50/27 A46^2 - 35/27 A46 - 49/216 ), 
 ( A46^5 U4^3 + 7/5 A46^4 U4^3 + 609/1000 A46^3 
 U4^3 + 49/1250 A46^2 U4^3 - 27391/800000 A46 U4^3 
 - 1029/160000 U4^3 + 3/7 A46^5 U3 U4^2 + 3/5 A46^6 
 U3 U4^2 + 63/200 A46^3 U3 U4^2 + 147/2000 A46^2 
 U3 U4^2 + 4137/800000 A46 U3 U4^2 - 7/20 A46^4 
 U3^2 U4 - 77/125 A46^3 U3^2 U4 - 23863/60000 A46^2 
 U3^2 U4 - 1078/9375 A46 U3^2 U4 - 24353/1920000 
  U3^2 U4 - 3/20 A46^4 U3^3 - 21/100 A46^3 U3^3 
 - 91/800 A46^2 U3^3 - 5887/200000 A46 U3^3 
 - 343/128000 U3^3 ) 
) 
""";

f = Ideal( r, ps );
print "Ideal: " + str(f);
print;

rg = f.GB();
#print "seq Output:", rg;
#print;

#sys.exit();

rg = f.parGB(2);
#print "par Output:", rg;
#print;

rg = f.parOldGB(2);
#print "par-old Output:", rg;

Exemple #15

Fichier : preimage.py Projet : Eeeeddddy/gittest

Rat(x1,x2,x3,y1,y2) G|3|
"""

ps = """
(
 ( y1 + y2 - 1 ),
 ( x1 - y1^2 - y1 - y2 ),
 ( x2 - y1 - y2^2 ),
 ( x3 - y1 y2 )
)
"""

r = Ring(rs)
print "Ring: " + str(r)

i = Ideal(r, ps)
print "Ideal: " + str(i)

g = i.GB()
print "seq GB:", g

rsi = """
# polynomial ring:
Rat(x1,x2,x3) G
"""

ri = Ring(rsi)
print "Ring: " + str(ri)

y = application.Ideal(g.pset).intersect(ri.ring)
len = y.list.size()

Exemple #16

Fichier : rose_modular.py Projet : Eeeeddddy/gittest

 ( U4^4 - 20/7 A46^2 ), 
 ( A46^2 U3^4 + 7/10 A46 U3^4 + 7/48 U3^4 - 50/27 A46^2 - 35/27 A46 - 49/216 ), 
 ( A46^5 U4^3 + 7/5 A46^4 U4^3 + 609/1000 A46^3 
 U4^3 + 49/1250 A46^2 U4^3 - 27391/800000 A46 U4^3 
 - 1029/160000 U4^3 + 3/7 A46^5 U3 U4^2 + 3/5 A46^6 
 U3 U4^2 + 63/200 A46^3 U3 U4^2 + 147/2000 A46^2 
 U3 U4^2 + 4137/800000 A46 U3 U4^2 - 7/20 A46^4 
 U3^2 U4 - 77/125 A46^3 U3^2 U4 - 23863/60000 A46^2 
 U3^2 U4 - 1078/9375 A46 U3^2 U4 - 24353/1920000 
  U3^2 U4 - 3/20 A46^4 U3^3 - 21/100 A46^3 U3^3 
 - 91/800 A46^2 U3^3 - 5887/200000 A46 U3^3 
 - 343/128000 U3^3 ) 
) 
"""

f = Ideal(r, ps)
print "Ideal: " + str(f)
print

fi = f.toInteger()
print "Ideal: " + str(fi)
print
#                    "1152921504606846883"
mf = ModIntegerRing(str(2**60 - 93), True)
#mf = ModIntegerRing( str(19), True );
fm = fi.toModular(mf)
print "Ideal: " + str(fm)

#sys.exit();

rm = fm.GB()

Exemple #17

Fichier : intprog.py Projet : Eeeeddddy/gittest

from jas import Ideal

r = Ring("Rat(w1,w2,w3,w4,z1,z2) W( (0,0,0,0,1,1),(1,1,2,2,0,0) )")
print "Ring: " + str(r)
print

ps = """
( 
 ( z1^4 z2^2 - w1 ),
 ( z1^5 z2^3 - w2 ),
 ( z1 - w3 ),
 ( z2 - w4 )
) 
"""

f = Ideal(r, ps)
print "Ideal: " + str(f)
print

rg = f.GB()
print "seq Output:", rg
print

pf = """
( 
 ( z1^37 z2^20 )
) 
"""

fp = Ideal(r, pf)
print "Ideal: " + str(fp)

Exemple #18

from jas import Ring
from jas import Ideal

# trinks 7 example

r = Ring("Rat(B,S,T,Z,P,W) L")

print "Ring: " + str(r)
print

ps = """
( 
 ( 45 P + 35 S - 165 B - 36 ), 
 ( 35 P + 40 Z + 25 T - 27 S ), 
 ( 15 W + 25 S P + 30 Z - 18 T - 165 B**2 ), 
 ( - 9 W + 15 T P + 20 S Z ), 
 ( P W + 2 T Z - 11 B**3 ), 
 ( 99 W - 11 B S + 3 B**2 ),
 ( B**2 + 33/50 B + 2673/10000 )
) 
"""

f = Ideal(r, ps)
print "Ideal: " + str(f)
print

g = f.GB()
print "Groebner base:", g
print