Ejemplos de RF.gens en Python

Ejemplo n.º 1

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();
#print "ewx   = " + str(ewx);
print "ax    = " + str(ax);
print "wx    = " + str(wx);
print;

#rootx = wx**5 - 2; # not working
#rootx = wx**5 - 1/ax;
#rootx = wx**5 - ax;

Ejemplo n.º 2

Archivo: factors_algeb_trans_algeb_charp.py Proyecto: rjolly/jas

[one, w2] = Q2.gens()
# print "one   = " + str(one);
# print "w2    = " + str(w2);
print

Qp = PolyRing(Q2, "x", PolyRing.lex)
print "Qp    = " + str(Qp)
[ep, wp, ap] = Qp.gens()
# print "ep    = " + str(ep);
# print "wp    = " + str(wp);
# print "ap    = " + str(ap);
print

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

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

# rootx = wx**5 - ax;

Ejemplo n.º 3

Archivo: factors_algeb_trans.py Proyecto: zourzouvillys/java-algebra-system

[one,w2] = Q2.gens();
#print "one   = " + str(one);
#print "w2    = " + str(w2);
print;

Qp = PolyRing(Q2,"x",PolyRing.lex);
print "Qp    = " + str(Qp);
[ep,wp,ap] = Qp.gens();
#print "ep    = " + str(ep);
#print "wp    = " + str(wp);
#print "ap    = " + str(ap);
print;

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

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

rootx = wx**2 - ax;

Ejemplo n.º 4

Archivo: all_rings.py Proyecto: siwiwit/java-algebra-system

s3  = z**2 + ( 2 ) * y * z + ( 2 ) * x * z + y**2 + ( 2 ) * x * y + ( b**2 + 2 * a * b + a**2 + (4,5) * b + (4,5) * a + (4,25) ) * y + x**2 - ( c - (2,3) ) * x + ( (1,2) );
print "s3  = " + str(s3);
s4 = s1 + s2 - 2 * s3;
print "s4  = " + str(s4);
print "s4.factory() = " + str(s4.factory());
x = PolyRing(PolyRing(QQ(),"a, b, c",PolyRing.grad),"x, y, z",PolyRing.lex);
print "x = " + str(x);
print;


print "------- RF(PolyRing(ZZ(),\"a,b,c\",PolyRing.lex)) ---------";
r = PolyRing(ZZ(),"a,b,c",PolyRing.lex);
print "r = " + str(r);
rf = RF(r);
print "rf = " + str(rf.factory());
[one,a,b,c] = rf.gens();
print "one   = " + str(one);
print "a     = " + str(a);
print "b     = " + str(b);
print "c     = " + str(c);
q1 = a / b;
print "q1 = " + str(q1);
q2 = ( -2 * c**2 + 4 * b**2 + 4 * a**2 - 7 );
print "q2 = " + str(q2);
q3 = ( -7 * b + 4 * a + 12 );
print "q3 = " + str(q3);
q4 = q2 / q3;
print "q4 = " + str(q4);
q5 = ( 2 * c**2 - 4 * b**2 - 4 * a**2 + 7  ) / (7 * b - 4 * a - 12 );
print "q5 = " + str(q5);
q6 = q4 - q5;

Ejemplo n.º 5

s3  = z**2 + ( 2 ) * y * z + ( 2 ) * x * z + y**2 + ( 2 ) * x * y + ( b**2 + 2 * a * b + a**2 + (4,5) * b + (4,5) * a + (4,25) ) * y + x**2 - ( c - (2,3) ) * x + ( (1,2) );
print "s3  = " + str(s3);
s4 = s1 + s2 - 2 * s3;
print "s4  = " + str(s4);
print "s4.factory() = " + str(s4.factory());
x = PolyRing(PolyRing(QQ(),"a, b, c",PolyRing.grad),"x, y, z",PolyRing.lex);
print "x = " + str(x);
print;


print "------- RF(PolyRing(ZZ(),\"a,b,c\",PolyRing.lex)) ---------";
r = PolyRing(ZZ(),"a,b,c",PolyRing.lex);
print "r = " + str(r);
rf = RF(r);
print "rf = " + str(rf.factory());
[one,a,b,c] = rf.gens();
print "one   = " + str(one);
print "a     = " + str(a);
print "b     = " + str(b);
print "c     = " + str(c);
q1 = a / b;
print "q1 = " + str(q1);
q2 = ( -2 * c**2 + 4 * b**2 + 4 * a**2 - 7 );
print "q2 = " + str(q2);
q3 = ( -7 * b + 4 * a + 12 );
print "q3 = " + str(q3);
q4 = q2 / q3;
print "q4 = " + str(q4);
q5 = ( 2 * c**2 - 4 * b**2 - 4 * a**2 + 7  ) / (7 * b - 4 * a - 12 );
print "q5 = " + str(q5);
q6 = q4 - q5;

Ejemplo n.º 6

#

import sys

from java.lang import System

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

# elementary integration

r = PolyRing(QQ(), "x", PolyRing.lex)
print "r = " + str(r)
rf = RF(r)
print "rf = " + str(rf.factory())
[one, x] = rf.gens()
print "one   = " + str(one)
print "x     = " + str(x)
print

#f = 1 / ( 1 + x**2 );

#f = x**2 / ( x**2 + 1 );

#f = 1 / ( x**2 - 2 );
#f = 1 / ( x**3 - 2 );

#f = ( x + 3 ) / ( x**2- 3 * x - 40 );

f = (x**7 - 24 * x**4 - 4 * x**2 + 8 * x - 8) / (x**8 + 6 * x**6 + 12 * x**4 +
                                                 8 * x**2)

Ejemplo n.º 7

Archivo: factors_algebp_trans_charp.py Proyecto: zourzouvillys/java-algebra-system

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

# polynomial examples: factorization over Z_p(x)(sqrt{p}(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()
#print "ewx   = " + str(ewx);
print "ax    = " + str(ax)
print "wx    = " + str(wx)
print

#rootx = wx**5 - 2; # not working
#rootx = wx**5 - 1/ax;
#rootx = wx**5 - ax;

Ejemplo n.º 8

import sys

from java.lang import System

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

# elementary integration

r = PolyRing(QQ(),"x",PolyRing.lex);
print "r = " + str(r);
rf = RF(r);
print "rf = " + str(rf.factory());
[one,x] = rf.gens();
print "one   = " + str(one);
print "x     = " + str(x);
print;

#f = 1 / ( 1 + x**2 );

#f = x**2 / ( x**2 + 1 );

#f = 1 / ( x**2 - 2 );
#f = 1 / ( x**3 - 2 );

#f = ( x + 3 ) / ( x**2- 3 * x - 40 );

f = ( x**7 - 24 * x**4 - 4 * x**2 + 8 * x - 8 ) / ( x**8 + 6 * x**6 + 12 * x**4 + 8 * x**2 );

Ejemplo n.º 9

Archivo: radical-decomp_charp_ex816_algeb.py Proyecto: rjolly/jas

prime = 5;
cf = GF(prime);
#cf = QQ();

ca = PolyRing(cf,"t",PolyRing.lex);
print "ca = " + str(ca);
[ea,ta] = ca.gens();
print "ea   = " + str(ea);
print "ta   = " + str(ta);
print;

Qpt = RF(ca);
#print Qpt.gens();

[ea2,ta2] = Qpt.gens();
print "ea2  = " + str(ea2);
print "ta2  = " + str(ta2);
print;

cr = PolyRing(Qpt,"wpt",PolyRing.lex);
print "polynomial quotient ring: " + str(cr);

[et2,t,wpt] = cr.gens();
print "et2  = " + str(et2);
print "t    = " + str(t);
print "wpt  = " + str(wpt);
print;

root = wpt**prime - ta2;
af = AN(root,field=True);

Ejemplo n.º 10

Archivo: radical-decomp_charp_ex816_algeb.py Proyecto: zourzouvillys/java-algebra-system

prime = 5
cf = GF(prime)
#cf = QQ();

ca = PolyRing(cf, "t", PolyRing.lex)
print "ca = " + str(ca)
[ea, ta] = ca.gens()
print "ea   = " + str(ea)
print "ta   = " + str(ta)
print

Qpt = RF(ca)
#print Qpt.gens();

[ea2, ta2] = Qpt.gens()
print "ea2  = " + str(ea2)
print "ta2  = " + str(ta2)
print

cr = PolyRing(Qpt, "wpt", PolyRing.lex)
print "polynomial quotient ring: " + str(cr)

[et2, t, wpt] = cr.gens()
print "et2  = " + str(et2)
print "t    = " + str(t)
print "wpt  = " + str(wpt)
print

root = wpt**prime - ta2
af = AN(root, field=True)