#
# jython examples for jas.
# $Id$
#
import sys
from java.lang import System
from jas import Ring, PolyRing, QQ, DD, EF
from jas import terminate, startLog
# polynomial examples: real root tower over Q
r = EF(QQ()).realExtend("q", "q^3 - 3", "[1,2]").realExtend(
"w", "w^2 - q", "[1,2]").realExtend("s", "s^5 - 2",
"[1,2]").polynomial("x").build()
print "Ring: " + str(r)
print
#automatic: [one,q,w,s,x] = r.gens();
print "one = " + str(one)
print "q = " + str(q)
print "w = " + str(w)
print "s = " + str(s)
print "x = " + str(x)
print
f = x**2 - w * s
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 QQ, AN, RF, EF
from jas import terminate
from jas import startLog
# polynomial examples: factorization over Q(sqrt(2))(x)(sqrt(x))[y]
Yr = EF(QQ()).extend("w2","w2^2 - 2").extend("x").extend("wx","wx^2 - x").polynomial("y").build();
#print "Yr = " + str(Yr);
#print
[one,w2,x,wx,y] = Yr.gens();
print "one = " + str(one);
print "w2 = " + str(w2);
print "x = " + str(x);
print "wx = " + str(wx);
print "y = " + str(y);
print;
f = ( y**2 - x ) * ( y**2 - 2 );
#f = ( y**2 - x )**2 * ( y**2 - 2 )**3;
#f = ( y**4 - x * 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 QQ, AN, RF, EF
from jas import terminate
from jas import startLog
# polynomial examples:
Yr = EF(QQ()).extend("x,y").extend("z", "z^2 + x^2 + y^2 - 1").build()
# print "Yr = " + str(Yr);
# print
[one, x, y, z] = Yr.gens()
print "one = " + str(one)
print "x = " + str(x)
print "y = " + str(y)
print "z = " + str(z)
print
f = (1 + z) * (1 - z)
# / ( x**2 + y**2 );
print "f = " + str(f)
print
#
# jython examples for jas.
# $Id$
#
import sys;
from java.lang import System
from jas import Ring, PolyRing, QQ, DD, EF
from jas import terminate, startLog
# polynomial examples: real root tower over Q
r = EF(QQ()).realExtend("q","q^3 - 3", "[1,2]").realExtend("w", "w^2 - q", "[1,2]").realExtend("s", "s^5 - 2", "[1,2]").polynomial("x").build();
print "Ring: " + str(r);
print;
#automatic: [one,q,w,s,x] = r.gens();
print "one = " + str(one);
print "q = " + str(q);
print "w = " + str(w);
print "s = " + str(s);
print "x = " + str(x);
print;
f = x**2 - w * s;
print "f = ", f;
print;
#
# jython examples for jas.
# $Id$
#
import sys
from java.lang import System
from jas import QQ, AN, RF, EF, Ring, PolyRing
from jas import terminate, startLog
# polynomial examples: factorization over Q(sqrt(2))(x)(sqrt(x))[y]
Yr = EF(QQ()).extend("w2","w2^2 - 2").extend("x").extend("wx","wx^2 - x").polynomial("y").build();
print "Yr = " + str(Yr);
print
#is automatic: [one,w2,x,wx,y] = Yr.gens();
print "one = " + str(one);
print "w2 = " + str(w2);
print "x = " + str(x);
print "wx = " + str(wx);
print "y = " + str(y);
print;
f = ( y**2 - x ) * ( y**2 - 2 );
#f = ( y**2 - x )**2 * ( y**2 - 2 )**3;
#f = ( y**4 - x * 2 );
#f = ( y**7 - x * 2 );
#
import sys;
from java.lang import System
from java.lang import Integer
from jas import Ring, PolyRing
from jas import QQ, DD, EF
from jas import terminate
from jas import startLog
# polynomial examples: real root tower over Q
r = EF(QQ()).realExtend("q","q^3 - 3", "[1,2]").realExtend("w", "w^2 - q", "[1,2]").realExtend("s", "s^5 - 2", "[1,2]").polynomial("x").build();
print "Ring: " + str(r);
print;
[one,q,w,s,x] = r.gens();
print "one = " + str(one);
print "q = " + str(q);
print "w = " + str(w);
print "s = " + str(s);
print "x = " + str(x);
print;
f = x**2 - w * s;
#
# jython examples for jas.
# $Id$
#
import sys;
from jas import PolyRing, Ideal, QQ, ZZ, EF, Mat
# matrix and polynomial examples:
# conditions for (non) commuting matrices
r = EF(QQ()).polynomial("a,b,c,d,e,f,g,h").build();
print "r = " + str(r);
#one, a, b, c, d, e, f, g, h = r.gens();
print "h = " + str(h);
print
x = Mat(r,2,2,[[a,b],[c,d]])
y = Mat(r,2,2,[[e,f],[g,h]])
print "x = " + str(x) + ", y = " + str(y) #+ ", x y = " + str(x*y)
print
com = x*y - y*x
print "commutator = " + str(com)
print
ff = r.ideal("", [ com[0][0], com[0][1], com[1][0], com[1][1] ] )
print "ff = " + str(ff)
print
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 QQ, AN, RF, EF
from jas import terminate
from jas import startLog
# polynomial examples:
Yr = EF(QQ()).extend("x,y").extend("z","z^2 + x^2 + y^2 - 1").build();
#print "Yr = " + str(Yr);
#print
[one,x,y,z] = Yr.gens();
print "one = " + str(one);
print "x = " + str(x);
print "y = " + str(y);
print "z = " + str(z);
print;
f = (1+z)*(1-z); # / ( x**2 + y**2 );
print "f = " + str(f);
print;
g = f / (1 - z);