Python RF.factory示例

示例#1

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

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

示例#2

文件： factors_algeb_trans.py 项目： zourzouvillys/java-algebra-system

print "Q2    = " + str(Q2.factory());
[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;

示例#3

print "s2  = " + str(s2);
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);

示例#4

文件： all_rings.py 项目： siwiwit/java-algebra-system

print "s2  = " + str(s2);
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);

示例#5

文件： factors_mod_ins.py 项目： rjolly/jas

fu = (u**2+u+1)**p;
print "fu = ", fu;
print;

t = System.currentTimeMillis();
G = cr.squarefreeFactors(fu);
t = System.currentTimeMillis() - t;
#print "G = ", G; #.toScript();
print "factor time =", t, "milliseconds";
for h, i in G.iteritems():
    print "h**i = (", h, ")**" + str(i);
    h = h**i;
print;

qcr = RF(cr);
print "Ring qcr: " + str(qcr.factory());

#not ok#r = PolyRing(cr,"x",PolyRing.lex );
r = PolyRing(qcr,"x",PolyRing.lex );
print "Ring r: " + str(r);

#qr = RF(r);
#print "Ring qr: " + str(qr.factory());
print;

#[one,u,x] = r.gens();
print "one = " + str(one);
print "u   = " + str(u);
print "x   = " + str(x);

示例#6

fu = (u**2 + u + 1)**p
print "fu = ", fu
print

t = System.currentTimeMillis()
G = cr.squarefreeFactors(fu)
t = System.currentTimeMillis() - t
#print "G = ", G; #.toScript();
print "factor time =", t, "milliseconds"
for h, i in G.iteritems():
    print "h**i = (", h, ")**" + str(i)
    h = h**i
print

qcr = RF(cr)
print "Ring qcr: " + str(qcr.factory())

#not ok#r = PolyRing(cr,"x",PolyRing.lex );
r = PolyRing(qcr, "x", PolyRing.lex)
print "Ring r: " + str(r)

#qr = RF(r);
#print "Ring qr: " + str(qr.factory());
print

#[one,u,x] = r.gens();
print "one = " + str(one)
print "u   = " + str(u)
print "x   = " + str(x)

#f = x**3 - u;