Esempi in Python per Ring.ideal

Esempio n. 1

File: syz.py Progetto: rjolly/jas

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


#Katsura equations for N = 3:

#r = Ring( "Rat(u0,u1,u2,u3) L" );
#print "Ring: " + str(r);
#print;

ps = """
(
 u3*u3 + u2*u2 + u1*u1 + u0*u0 + u1*u1 + u2*u2 + u3*u3 - u0,
 u3*0 + u2*u3 + u1*u2 + u0*u1 + u1*u0 + u2*u1 + u3*u2 - u1,
 u3*0 + u2*0 + u1*u3 + u0*u2 + u1*u1 + u2*u0 + u3*u1 - u2,

Esempio n. 2

r = Ring( "IntFunc(a, c, b) (y2, y1, z1, z2, x) G" );
print "Ring: " + str(r);
print;

[one,a,c,b,y2,y1,z1,z2,x] = r.gens();

p1 = x + 2 * y1 * z1 + 3 * a * y1**2 + 5 * y1**4 + 2 * c * y1;
p2 = x + 2 * y2 * z2 + 3 * a * y2**2 + 5 * y2**4 + 2 * c * y2;
p3 = 2 * z2 + 6 * a * y2 + 20 * y2**3 + 2 * c; 
p4 = 3 * z1**2 + y1**2 + b;
p5 = 3 * z2**2 + y2**2 + b; 

F = [p1,p2,p3,p4,p5];

g = r.ideal( list=F );
print "Ideal: " + str(g);
print;

rg = g.GB();
rg = g.GB();
rg = g.GB();
rg = g.GB();
print "GB:", rg;
print;

bg = rg.isGB();
print "isGB:", bg;
print;

p7 = ( x + 1 ) / ( x**2 - x + 1 );

Esempio n. 3

from jas import Ideal

from edu.jas.gb import Katsura

# katsura examples

knum = 4
tnum = 2

k = Katsura(knum)
r = Ring(k.varList("Rat", "G"))
#r = Ring.new( k.varList("Mod 23","G") );
print "Ring: " + str(r)
print

ps = k.polyList()

f = r.ideal(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

Esempio n. 4

File: mark.py Progetto: lukaszzdanikowski/randoop

# mark, d-gb diplom example

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

ps = """
( 
 ( z + x y**2 + 4 x**2 + 1 ),
 ( y**2 z + 2 x + 1 ),
 ( x**2 z + y**2 + x )
) 
""";

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

from edu.jas.ring import EGroebnerBaseSeq;
from edu.jas.ring import DGroebnerBaseSeq;

egbs = EGroebnerBaseSeq();
dgbs = DGroebnerBaseSeq();

#startLog();

eg = egbs.GB( f.list );
rg = r.ideal(list=eg);
print "seq e-GB:", rg;
print "is e-GB:", egbs.isGB(eg);

Esempio n. 5

# Frist polynomial produces a different e-GB.
# Second polynomial reproduces the e-GB with the second polynomial.

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

ps = """
( 
 ( y**6 + x**4 y**4 - x**2 y**4 - y**4 - x**4 y**2 + 2 x**2 y**2 + x**6 - x**4 ),
 ( 2 x**3 y**4 - x y**4 - 2 x**3 y**2 + 2 x y**2 + 3 x**5 - 2 x** 3 ),
 ( 3 y**5 + 2 x**4 y**3 - 2 x**2 y**3 - 2 y**3 - x**4 y + 2 x**2 y )
) 
"""

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

from edu.jas.ring import EGroebnerBaseSeq
from edu.jas.ring import DGroebnerBaseSeq

egbs = EGroebnerBaseSeq()
dgbs = DGroebnerBaseSeq()

#startLog();

eg = egbs.GB(f.list)
rg = r.ideal(list=eg)
print "seq e-GB:", rg
print "is e-GB:", egbs.isGB(eg)

Esempio n. 6

File: preimage.py Progetto: rjolly/jas

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 = r.ideal( 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);

Esempio n. 7

File: trinks_s.py Progetto: zourzouvillys/java-algebra-system

f1 = 45 * P + 35 * S - 165 * B - 36
f2 = 35 * P + 40 * Z + 25 * T - 27 * S
f3 = 15 * W + 25 * S * P + 30 * Z - 18 * T - 165 * B**2
f4 = -9 * W + 15 * T * P + 20 * S * Z
f5 = P * W + 2 * T * Z - 11 * B**3
f6 = 99 * W - 11 * B * S + 3 * B**2
f7 = 10000 * B**2 + 6600 * B + 2673
#all ok:
#f7 = f7 + e * f6**0;
#f7 = f7 + 5959345574908321469098512640906154241024000000**2 * f6;
#f7 = f7 + 35555./332 * f1;

F = [f1, f2, f3, f4, f5, f6, f7]
#F = [ f1, f2, f3, f4, f5, f6 ];
#print "F = ", [ str(f) for f in F ];
I = r.ideal("", list=F)
print "Ideal: " + str(I)
print

#sys.exit();

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

terminate()
sys.exit()

ps = """
( 
 ( 45 P + 35 S - 165 B - 36 ), 

Esempio n. 8

# ideal elimination example

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

ps1 = """
(
 ( x^2 - 2 ),
 ( y^2 - 3 ),
 ( z^3 - x * y )
)
""";

F1 = r.ideal( ps1 );
print "Ideal: " + str(F1);
print;

e = Ring( "Rat(z) G" );
print "Ring: " + str(e);
print;

#startLog();

rg1 = F1.eliminateRing(e);
print "rg1 = ", rg1;
print;

rg2 = rg1.intersectRing(e);
print "rg2 = ", rg2;

Esempio n. 9

File: trinks_s.py Progetto: lukaszzdanikowski/randoop

f1 = 45 * P + 35 * S - 165 * B - 36;
f2 = 35 * P + 40 * Z + 25 * T - 27 * S;
f3 = 15 * W + 25 * S * P + 30 * Z - 18 * T - 165 * B**2;
f4 = - 9 * W + 15 * T * P + 20 * S * Z;
f5 = P * W + 2 * T * Z - 11 * B**3;
f6 = 99 * W - 11 *B * S + 3 * B**2;
f7 = 10000.0 * B**2 + 6600 * B + 2673;
#all ok:
#f7 = f7 + e * f6**0;
#f7 = f7 + 5959345574908321469098512640906154241024000000**2 * f6;
#f7 = f7 + 35555./332 * f1;

F = [ f1, f2, f3, f4, f5, f6, f7 ];
#F = [ f1, f2, f3, f4, f5, f6 ]; 
#print "F = ", [ str(f) for f in F ];
I = r.ideal( "", list=F );
print "Ideal: " + str(I);
print;

#sys.exit();

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

terminate();
sys.exit();

ps = """
( 
 ( 45 P + 35 S - 165 B - 36 ), 

Esempio n. 10

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

startLog()

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

#sys.exit();

Esempio n. 11

File: logic.py Progetto: Eeeeddddy/gittest

ks = """
(
 ( a^2 - a ),
 ( f^2 - f ),
 ( p^2 - p ),
 ( u^2 - u )
)
"""

ps = """
(
 ( p f + p ),
 ( p u + p + u + 1 ),
 ( a + u + 1 ),
 ( a + p + 1 )
)
"""

k = r.ideal(ks)
p = r.ideal(ps)

f = k.sum(p)

print "Ideal: " + str(f)
print

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

Esempio n. 12

File: rose_part.py Progetto: rjolly/jas

 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 = r.ideal( pp );
print "Ideal: " + str(f);
print;

startLog();

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

#sys.exit();

Esempio n. 13

File: preimage.py Progetto: zourzouvillys/java-algebra-system

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 = r.ideal(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()

Esempio n. 14

(
 ( x - 1 ),
 ( y - 1 ),
 ( z - 1 )
)
""";

ps2 = """
(
 ( x - 2 ),
 ( y - 3 ),
 ( z - 3 )
)
""";

F1 = r.ideal( ps1 );
#print "Ideal: " + str(F1);
#print;

F2 = r.ideal( ps2 );
#print "Ideal: " + str(F2);
#print;

#startLog();

rg1 = F1.GB();
print "rg1 = ", rg1;
print;

rg2 = F2.GB();
print "rg2 = ", rg2;

Esempio n. 15

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

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

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

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

Esempio n. 16

File: intprog.py Progetto: rjolly/jas

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

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


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

fp = r.ideal( pf );

Esempio n. 17

 ( a^2 - a ),
 ( f^2 - f ),
 ( p^2 - p ),
 ( u^2 - u )
)
""";

ps = """
(
 ( p f + p ),
 ( p u + p + u + 1 ),
 ( a + u + 1 ),
 ( a + p + 1 )
)
""";


k = r.ideal( ks );
p = r.ideal( ps );

f = k.sum( p );

print "Ideal: " + str(f);
print;

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

Esempio n. 18

File: trinks_s.py Progetto: rjolly/jas

f1 = 45 * P + 35 * S - 165 * B - 36
f2 = 35 * P + 40 * Z + 25 * T - 27 * S
f3 = 15 * W + 25 * S * P + 30 * Z - 18 * T - 165 * B ** 2
f4 = -9 * W + 15 * T * P + 20 * S * Z
f5 = P * W + 2 * T * Z - 11 * B ** 3
f6 = 99 * W - 11 * B * S + 3 * B ** 2
f7 = 10000 * B ** 2 + 6600 * B + 2673
# all ok:
# f7 = f7 + e * f6**0;
# f7 = f7 + 5959345574908321469098512640906154241024000000**2 * f6;
# f7 = f7 + 35555./332 * f1;

F = [f1, f2, f3, f4, f5, f6, f7]
# F = [ f1, f2, f3, f4, f5, f6 ];
# print "F = ", [ str(f) for f in F ];
I = r.ideal("", list=F)
print "Ideal: " + str(I)
print

# sys.exit();

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

terminate()
sys.exit()

ps = """
( 
 ( 45 P + 35 S - 165 B - 36 ),