Python jas.PolyRing类代码示例

 def testRingQQ(self):
     r = PolyRing( QQ(), "(t,x)", Order.INVLEX );
     self.assertEqual(str(r),'PolyRing(QQ(),"t,x",Order.INVLEX)');
     [one,x,t] = r.gens();
     self.assertTrue(one.isONE());
     self.assertTrue(len(x)==1);
     self.assertTrue(len(t)==1);
     #
     f = 11 * x**4 - 13 * t * x**2 - 11 * x**2 + 2 * t**2 + 11 * t;
     f = f**2 + f + 3;
     #print "f = " + str(f);
     self.assertEqual(str(f),'( 4 * x**4 - 52 * t**2 * x**3 + 44 * x**3 + 213 * t**4 * x**2 - 330 * t**2 * x**2 + 123 * x**2 - 286 * t**6 * x + 528 * t**4 * x - 255 * t**2 * x + 11 * x + 121 * t**8 - 242 * t**6 + 132 * t**4 - 11 * t**2 + 3 )');

 def testRingZM(self):
     r = PolyRing( GF(17), "(t,x)", Order.INVLEX );
     self.assertEqual(str(r),'PolyRing(GFI(17),"t,x",Order.INVLEX)');
     [one,x,t] = r.gens();
     self.assertTrue(one.isONE());
     self.assertTrue(len(x)==1);
     self.assertTrue(len(t)==1);
     #
     f = 11 * x**4 - 13 * t * x**2 - 11 * x**2 + 2 * t**2 + 11 * t;
     f = f**2 + f + 3;
     #print "f = " + str(f);
     self.assertEqual(str(f),'( 4 * x**4 + 16 * t**2 * x**3 + 10 * x**3 + 9 * t**4 * x**2 + 10 * t**2 * x**2 + 4 * x**2 + 3 * t**6 * x + t**4 * x + 11 * x + 2 * t**8 + 13 * t**6 + 13 * t**4 + 6 * t**2 + 3 )');

#
# jython examples for jas.
# $Id$
#

from java.lang import System
from java.lang import Integer

from jas import PolyRing, ZM, QQ
from jas import terminate
from jas import startLog

# polynomial examples: factorization over Z_p

r = PolyRing(ZM(1152921504606846883,field=True),"(x)",PolyRing.lex);
#r = PolyRing(ZM(19),"x",PolyRing.lex );
#r = PolyRing(ZM(23),"x",PolyRing.lex );

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

[one,x] = r.gens();


#f = x**4 - 1;
#f = x**3 + 1;
f = x**3 - x - 1;


print "f = ", f;
print;

## 3 z_1^2+y_1^2+b \&
## 3z_2^2+y_2^2+b \&
## \end{Equations}
## \end{PossoExample}


import sys;

from jas import Ring, PolyRing, QQ
from jas import startLog, terminate

# Hawes & Gibson example 2
# rational function coefficients

#r = Ring( "IntFunc(a, c, b) (y2, y1, z1, z2, x) G" );
r = PolyRing( PolyRing(QQ(),"a, c, b",PolyRing.lex), "y2, y1, z1, z2, x", PolyRing.grad );
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);

# $Id$
#

import sys;

from jas import Ring, PolyRing, Ideal
from jas import QQ, ZZ
from jas import startLog, terminate


# example: Algebraic Statistics
# Drton, Sturmfels, Sullivant, example 2.1.3


#r = PolyRing(QQ(),"l1,l2",PolyRing.grad);
r = PolyRing(QQ(),"l1,l2",PolyRing.lex);
print "Ring: " + str(r);
print;

print one,l1,l2;

u0 = 3; u1 = 5; u2 = 7; u12 = 11;

f1 = (u1+u12)*(l1+l2+2)*(l1+1)*(l1+l2+1)\
     + (u12)*l1*(l1+1)*(l1+l2+1)\
     - (u2+u12)*l1*(l1+l2+2)*(l1+l2+1)\
     - (u0+u1+u2+u12)*l1*(l1+l2+2)*(l1+1)  ;

f2 = (u2+u12)*(l1+l2+2)*(l2+1)*(l1+l2+1)\
     + (u12)*l2*(l2+1)*(l1+l2+1)\
     - (u1+u12)*l2*(l1+l2+2)*(l1+l2+1)\

#
# jython examples for jas.
# $Id$
#

import sys

from java.lang import System

from jas import PolyRing, Ideal
from jas import QQ, AN, RF
from jas import terminate, startLog

# polynomial examples: prime/primary decomposition in Q[w2,x,wx,y,z]

Q = PolyRing(QQ(), "w2,x,wx,y,z", PolyRing.lex)
print "Q     = " + str(Q)

[e, w2, x, wx, y, z] = Q.gens()
print "e     = " + str(e)
print "w2    = " + str(w2)
print "x     = " + str(x)
print "wx    = " + str(wx)
print "y     = " + str(y)
print "z     = " + str(z)
print

w1 = w2 ** 2 - 2
w2 = wx ** 2 - x
f1 = (y ** 2 - x) * (y ** 2 - 2)
# f1 = ( y**2 - x )**3 * ( y**2 - 2 )**2;

import sys

from java.lang import System
from java.lang import Integer

from jas import Ring
from jas import PolyRing
from jas import Ideal
from jas import ZM, QQ, AN, RF
from jas import terminate
from jas import startLog

# polynomial examples: factorization over Z_p(x)(sqrt3(x))[y]

Q = PolyRing(ZM(5),"x",PolyRing.lex);
print "Q     = " + str(Q);
[e,a] = Q.gens();
#print "e     = " + str(e);
print "a     = " + str(a);

Qr = RF(Q);
print "Qr    = " + str(Qr.factory());
[er,ar] = Qr.gens();
#print "er    = " + str(er);
#print "ar    = " + str(ar);
print;

Qwx = PolyRing(Qr,"wx",PolyRing.lex);
print "Qwx   = " + str(Qwx);
[ewx,ax,wx] = Qwx.gens();

#
# jython examples for jas.
# $Id$
#

import sys

from java.lang import System

from jas import Ring, PolyRing
from jas import QQ, AN
from jas import terminate, startLog

# polynomial examples: absolute factorization over Q(i)

Qr = PolyRing(QQ(), "i", PolyRing.lex)
print "Qr    = " + str(Qr)
[e, a] = Qr.gens()
print "e     = " + str(e)
print "a     = " + str(a)
print

imag = a ** 2 + 1
print "imag  = " + str(imag)
Qi = AN(imag, field=True)
print "Qi    = " + str(Qi.factory())
[one, i] = Qi.gens()
print "one   = " + str(one)
print "i     = " + str(i)
print

import sys;

from jas import Ring, PolyRing, RF, ZZ, QQ
from jas import startLog, terminate

from edu.jas.arith import ModIntegerRing

#startLog();

# Hawes & Gibson example 2
# rational function coefficients

#r = Ring( "RatFunc(a, c, b) (y2, y1, z1, z2, x) G" );
r = PolyRing( RF(PolyRing(ZZ(),"a, c, b",PolyRing.lex)), "y2, y1, z1, z2, x", PolyRing.grad );
print "Ring: " + str(r);
print;

ps = """
(
 ( x + 2 y1 z1 + { 3 a } y1^2 + 5 y1^4 + { 2 c } y1 ),
 ( x + 2 y2 z2 + { 3 a } y2^2 + 5 y2^4 + { 2 c } y2 ), 
 ( 2 z2 + { 6 a } y2 + 20 y2^3 + { 2 c } ), 
 ( 3 z1^2 + y1^2 + { b } ), 
 ( 3 z2^2 + y2^2 + { b } ) 
) 
""";

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

import sys;

from jas import QQ, Ring, PolyRing, Ideal
from jas import startLog, terminate


# trinks 6/7 example

#r = Ring( "Mod 19 (B,S,T,Z,P,W) L" );
#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" );
r = PolyRing( QQ(),"B,S,T,Z,P,W", PolyRing.lex);
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 ),
 ( 10000 B**2 + 6600 B + 2673 )
) 
""";

# jython examples for jas.
# $Id$
#

import sys;

from jas import Ring, PolyRing, Ideal
from jas import QQ, ZZ, RF
from jas import startLog, terminate


# example: Algebraic Statistics
# Drton, Sturmfels, Sullivant, example 2.1.3


r = PolyRing(RF(PolyRing(QQ(),"u0,u1,u2,u12",PolyRing.lex)),"l1,l2",PolyRing.grad);
print "Ring: " + str(r);
print;

print one,u0,u1,u2,u12,l1,l2;

f1 = (u1+u12)*(l1+l2+2)*(l1+1)*(l1+l2+1)\
     + (u12)*l1*(l1+1)*(l1+l2+1)\
     - (u2+u12)*l1*(l1+l2+2)*(l1+l2+1)\
     - (u0+u1+u2+u12)*l1*(l1+l2+2)*(l1+1)  ;

f2 = (u2+u12)*(l1+l2+2)*(l2+1)*(l1+l2+1)\
     + (u12)*l2*(l2+1)*(l1+l2+1)\
     - (u1+u12)*l2*(l1+l2+2)*(l1+l2+1)\
     - (u0+u1+u2+u12)*l2*(l1+l2+2)*(l2+1)  ;

#
# jython examples for jas.
# $Id$
#

from java.lang import System

from jas import PolyRing, ZM, GF
from jas import terminate, startLog

# system biology examples: GB in Z_2
# see: Informatik Spektrum, 2009, February,
# Laubenbacher, Sturmfels: Computer Algebra in der Systembiologie

r = PolyRing(GF(2),"M, B, A, L, P",PolyRing.lex);
print "PolyRing: " + str(r);
print;

#automatic: [one,M,B,A,L,P] = r.gens();

f1 = M - A;
f2 = B - M;
f3 = A - A - L * B - A * L * B;
f4 = P - M;
f5 = L - P - L - L * B - L * P - L * B * P;
## t1 = M - 1;
## t2 = B - 1;
## t3 = A - 1;
## t4 = L - 1;
## t5 = P - 1;
#

from jas import PolyRing, ZZ, QQ, ZM
from jas import terminate, startLog

from basic_sigbased_gb import sigbased_gb
from basic_sigbased_gb import ggv, ggv_first_implementation
from basic_sigbased_gb import coeff_free_sigbased_gb
from basic_sigbased_gb import arris_algorithm, min_size_mons
from basic_sigbased_gb import f5, f5z

from staggered_linear_basis import staglinbasis


#r = PolyRing( QQ(), "(B,S,T,Z,P,W)", PolyRing.lex );
#r = PolyRing( ZZ(), "(B,S,T,Z,P,W)", PolyRing.lex );
r = PolyRing( ZM(32003), "(B,S,T,Z,P,W)", PolyRing.lex );
#r = PolyRing( ZM(19), "(B,S,T,Z,P,W)", PolyRing.lex );
print "Ring: " + str(r);
print;

[one,B,S,T,Z,P,W] = r.gens();

p1 = 45 * P + 35 * S - 165 * B - 36; 
p2 = 35 * P + 40 * Z + 25 * T - 27 * S;
p3 = 15 * W + 25 * S * P + 30 * Z - 18 * T - 165 * B**2; 
p4 = -9 * W + 15 * T * P + 20 * S * Z; 
p5 = P * W + 2 * T * Z - 11 * B**3;
p6 = 99 * W - 11 * B * S + 3 * B**2;
p7 = 10000 * B**2 + 6600 * B + 2673;

F = [p1,p2,p3,p4,p5,p6,p7];

#
# jython examples for jas.
# $Id$
#

from java.lang import System

from jas import GF, PolyRing
from jas import terminate, startLog

# polynomial examples: factorization over Z_p

#r = Ring( "Mod 1152921504606846883 (x) L" );
#r = Ring( "Mod 19 (x) L" );
r = PolyRing( GF(19), "x", PolyRing.lex );
print "Ring: " + str(r);
print;

#[one,x] = r.gens();

#f = x**15 - 1;
#f = x * ( x + 1 )**2 * ( x**2 + x + 1 )**3;
#f = x**6 - 3 * x**5 + x**4 - 3 * x**3 - x**2 - 3 * x+ 1;
#f = x**(3*11*11) + 3 * x**(2*11*11) - x**(11*11);
#f = x**(3*11*11*11) + 3 * x**(2*11*11*11) - x**(11*11*11);
#f = (x**2+1)*(x-3)*(x-5)**3;
#f = x**4 + 1;
#f = x**12 + x**9 + x**6 + x**3 + 1;
#f = x**24 - 1;
#f = x**20 - 1;
#f = x**22 - 1;

# jython examples for jas.
# $Id$
#

from java.lang import System

from jas import Ring, PolyRing, QQ, ZZ, GF
from jas import terminate, startLog

# polynomial examples: gcd

#r = Ring( "Mod 1152921504606846883 (x,y,z) L" );
#r = Ring( "Rat(x,y,z) L" );
#r = Ring( "C(x,y,z) L" );
#r = Ring( "Z(x,y,z) L" );
r = PolyRing( QQ(), "x,y,z", PolyRing.lex );
print "Ring: " + str(r);
print;

#[one,x,y,z] = r.gens();

a = r.random();
b = r.random();
c = abs(r.random());
#c = 1; 
#a = 0;


print "a = ", a;
print "b = ", b;
print "c = ", c;