Exemplos de SolvableRing em Python

Exemplo n.º 1

Arquivo: u_2_wa_1.py Projeto: rjolly/jas

 ( b ), ( a ), ( a b + %s a )
)
""";


ps = """
(
 ( a - X^%s ),
 ( b - D X + %s )
)
""";


for t in (2,3,5,7,11,13,17,19,23,27,31,37,43):
  #for t in (5,7):
  r1  = SolvableRing( rs1 % t );
  r1c = SolvableRing( rs1c );
  #print "SolvableRing: " + str(r1);
  #print "SolvableRing: " + str(r1c);
  #print;
  it = r1.ideal( ps % (t,t) );
  #print "SolvableIdeal: " + str(it);
  #print;
  # compute I_{\phi_t} \cap WA_1^opp
  x = it.leftGB();
  print "seq left x:", x;
  y = Ideal(x.pset).intersect(r1c.ring);
  len = y.list.size();
  print "seq left y: ", y;
  print "seq left y len: ", len;
  #print;

Exemplo n.º 2

Arquivo: wa_1.py Projeto: zourzouvillys/java-algebra-system

#

from jas import SolvableRing

# WA_1 example

rs = """
# solvable polynomials, Weyl algebra A_1:
Rat(p,t,x,d) G
RelationTable
(
 ( d ), ( x ), ( x d + 1 )
)
"""

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

ps = """
(
 ( x^7 ),
 ( x d + 7 )
)
"""

i7 = r.ideal(ps)
print "SolvableIdeal: " + str(i7)
print

i7rg = i7.leftGB()

Exemplo n.º 3

Arquivo: solvablepolynomial.py Projeto: lukaszzdanikowski/randoop

# WA_32 solvable polynomial example

rs = """
# solvable polynomials, Weyl algebra A_3,2:
#Rat(a,b,e1,e2,e3) G|3|
Quat(a,b,e1,e2,e3) G|3|
RelationTable
(
 ( e3 ), ( e1 ), ( e1 e3 - e1 ),
 ( e3 ), ( e2 ), ( e2 e3 - e2 )
)
""";

r = SolvableRing( rs );
print "SolvableRing: " + str(r);
print;

[a,b,e1,e2,e3] = r.gens();
print "gens =", [ str(f) for f in r.gens() ];

f1 = e1 * e3**3 + e2**10 - a;
f2 = e1**3 * e2**2 + e3;
f3 = e3**3 + e3**2 - b;

f4 = ( e3**2 * e2**3 + e1 )**3;

#print "f1 = ", f1;
#print "f2 = ", f2;
#print "f3 = ", f3;

Exemplo n.º 4

Arquivo: u_sl_2_f.py Projeto: Eeeeddddy/gittest

from jas import SolvableRing
from jas import SolvableIdeal

# U(sl_2_f) example

rs = """
# solvable polynomials, U(sl_2_f):
Rat(f,h) G
RelationTable
(
 ( h ), ( f ), ( f h - 2 f ) 
)
"""

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

ps = """
(
 ( h^2 + f^3 )
)
"""

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

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

Exemplo n.º 5

Arquivo: wa_32.py Projeto: rjolly/jas

from jas import startLog, terminate


# WA_32 example

rs = """
# solvable polynomials, Weyl algebra A_3,2:
Rat(a,b,e1,e2,e3) G
RelationTable
(
 ( e3 ), ( e1 ), ( e1 e3 - e1 ),
 ( e3 ), ( e2 ), ( e2 e3 - e2 )
)
""";

r = SolvableRing( rs );
print "SolvableRing: " + str(r);
print;


ps = """
(
 ( e1 e3^3 + e2^10 - a ),
 ( e1^3 e2^2 + e3 ),
 ( e3^3 + e3^2 - b )
)
""";

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

Exemplo n.º 6

RelationTable
(
 ( b ), ( a ), ( a b + %s a )
)
"""

ps = """
(
 ( a - X^%s ),
 ( b - D X + %s )
)
"""

for t in (2, 3, 5, 7, 11, 13, 17, 19, 23, 27, 31, 37, 43):
    #for t in (5,7):
    r1 = SolvableRing(rs1 % t)
    r1c = SolvableRing(rs1c)
    #print "SolvableRing: " + str(r1);
    #print "SolvableRing: " + str(r1c);
    #print;
    it = r1.ideal(ps % (t, t))
    #print "SolvableIdeal: " + str(it);
    #print;
    # compute I_{\phi_t} \cap WA_1^opp
    x = it.leftGB()
    print "seq left x:", x
    y = Ideal(x.pset).intersect(r1c.ring)
    len = y.list.size()
    print "seq left y: ", y
    print "seq left y len: ", len
    #print;

Exemplo n.º 7

#exit(0);


rs = """
# solvable polynomials, Weyl algebra A_3,2:
Rat(a,b,e1,e2,e3) L
#Quat(a,b,e1,e2,e3) G|3|
RelationTable
(
 ( e3 ), ( e1 ), ( e1 e3 - e1 ),
 ( e3 ), ( e2 ), ( e2 e3 - e2 )
)
""";

r = SolvableRing( rs );
print "SolvableRing: " + str(r);
print;

print "gens =", [ str(f) for f in r.gens() ];
#[one,a,b,e1,e2,e3] = r.gens();
#[one,I,J,K,a,b,e1,e2,e3] = r.gens();

fs1 = e1 * e3**3 + e2**10 - a;
fs2 = e1**3 * e2**2 + e3;
fs3 = e3**3 + e3**2 - b;

fs4 = ( e3**2 * e2**3 + e1 )**3;

#print "fs1 = ", fs1;
#print "fs2 = ", fs2;

Exemplo n.º 8

Arquivo: u_sl_2_wa_1.py Projeto: zourzouvillys/java-algebra-system

 ( h ), ( f ), ( f h - 2 f )
)
""";


ps = """
(
 ( e - X ),
 ( f + D^2 X ),
 ( h - 2 D X )
)
""";

startLog();

r1  = SolvableRing( rs1 );
r1c = SolvableRing( rs1c );
#print "SolvableRing: " + str(r1);
#print "SolvableRing: " + str(r1c);
print;
it = r1.ideal( ps );
print "SolvableIdeal: " + str(it);
print;
# compute I_{\phi_t} \cap WA_1^opp
x = it.leftGB();
print "seq left x:", x;
y = Ideal(x.pset).intersect(r1c.ring);
len = y.list.size();
print "seq left y: ", y;
print "seq left y len: ", len;
print;

Exemplo n.º 9

 ( x ), ( v ), ( - v x ),
 ( y ), ( v ), ( - v y ),
 ( z ), ( v ), ( - v z ),

 ( x ), ( w ), ( - w x ),
 ( y ), ( w ), ( - w y ),
 ( z ), ( w ), ( - w z ),

 ( y ), ( x ), ( - x y ),
 ( z ), ( x ), ( - x z ),

 ( z ), ( y ), ( - y z )
)
"""

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

# ( a b + c f + g h ),
# ( u v + w x + y z ),
# ( a v + w x + y z ),

ps = """
(
 ( a b + c f + g h ),
 ( u v + w x + y z ),
 ( a^2 ),
 ( b^2 ),
 ( c^2 ),
 ( f^2 ),

Exemplo n.º 10

(
 ( f ), ( e ), ( e f - h ),
 ( h ), ( e ), ( e h + 2 e ),
 ( h ), ( f ), ( f h - 2 f )
)
"""

ps = """
(
 ( e - X ),
 ( f + D^2 X ),
 ( h - 2 D X )
)
"""

r1 = SolvableRing(rs1)
r1c = SolvableRing(rs1c)
#print "SolvableRing: " + str(r1);
#print "SolvableRing: " + str(r1c);
print
it = SolvableIdeal(r1, ps)
print "SolvableIdeal: " + str(it)
print
# compute I_{\phi_t} \cap WA_1^opp
x = it.leftGB()
print "seq left x:", x
y = Ideal(x.pset).intersect(r1c.ring)
len = y.list.size()
print "seq left y: ", y
print "seq left y len: ", len
print

Exemplo n.º 11

Arquivo: solvablepolynomial.py Projeto: Eeeeddddy/gittest

from jas import SolvableIdeal

# WA_32 solvable polynomial example

rs = """
# solvable polynomials, Weyl algebra A_3,2:
#Rat(a,b,e1,e2,e3) G|3|
Quat(a,b,e1,e2,e3) G|3|
RelationTable
(
 ( e3 ), ( e1 ), ( e1 e3 - e1 ),
 ( e3 ), ( e2 ), ( e2 e3 - e2 )
)
"""

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

[a, b, e1, e2, e3] = r.gens()
print "gens =", [str(f) for f in r.gens()]

f1 = e1 * e3**3 + e2**10 - a
f2 = e1**3 * e2**2 + e3
f3 = e3**3 + e3**2 - b

f4 = (e3**2 * e2**3 + e1)**3

#print "f1 = ", f1;
#print "f2 = ", f2;
#print "f3 = ", f3;

Exemplo n.º 12

Arquivo: solvablepolynomial.py Projeto: zourzouvillys/java-algebra-system

#exit(0);


rs = """
# solvable polynomials, Weyl algebra A_3,2:
Rat(a,b,e1,e2,e3) L
#Quat(a,b,e1,e2,e3) G|3|
RelationTable
(
 ( e3 ), ( e1 ), ( e1 e3 - e1 ),
 ( e3 ), ( e2 ), ( e2 e3 - e2 )
)
""";

r = SolvableRing( rs );
print "SolvableRing: " + str(r);
print;

print "gens =", [ str(f) for f in r.gens() ];
#[one,a,b,e1,e2,e3] = r.gens();
#[one,I,J,K,a,b,e1,e2,e3] = r.gens();

fs1 = e1 * e3**3 + e2**10 - a;
fs2 = e1**3 * e2**2 + e3;
fs3 = e3**3 + e3**2 - b;

fs4 = ( e3**2 * e2**3 + e1 )**3;

#print "fs1 = ", fs1;
#print "fs2 = ", fs2;

Exemplo n.º 13

 ( b ), ( a ), ( a b + %s a )
)
""";


ps = """
(
 ( a - X^%s ),
 ( b - D X + %s )
)
""";


for t in (2,3,5,7,11,13,17,19,23,27,31,37,43):
  #for t in (5,7):
  r1  = SolvableRing( rs1 % t );
  r1c = SolvableRing( rs1c );
  #print "SolvableRing: " + str(r1);
  #print "SolvableRing: " + str(r1c);
  #print;
  it = SolvableIdeal( r1, ps % (t,t) );
  #print "SolvableIdeal: " + str(it);
  #print;
  # compute I_{\phi_t} \cap WA_1^opp
  x = it.leftGB();
  print "seq left x:", x;
  y = Ideal(x.pset).intersect(r1c.ring);
  len = y.list.size();
  print "seq left y: ", y;
  print "seq left y len: ", len;
  #print;

Exemplo n.º 14

Arquivo: wa_1.py Projeto: rjolly/jas

from jas import SolvableRing


# WA_1 example

rs = """
# solvable polynomials, Weyl algebra A_1:
Rat(p,t,x,d) G
RelationTable
(
 ( d ), ( x ), ( x d + 1 )
)
""";

r = SolvableRing( rs );
print "SolvableRing: " + str(r);
print;


ps = """
(
 ( x^7 ),
 ( x d + 7 )
)
""";

i7 = r.ideal( ps );
print "SolvableIdeal: " + str(i7);
print;