print;
ps9 = ps8 - c;
print "ps9:", ps9;
print;
# conversion from polynomials
pr = Ring("Q(y) L");
print "pr:", pr;
print;
[yp] = pr.gens();
one = pr.one();
p1 = one;
p2 = one - yp;
ps1 = psr.from(p1);
ps2 = psr.from(p2);
# rational function as power series:
ps3 = ps1 / ps2;
print "p1:", p1;
print "p2:", p2;
print "ps1:", ps1;
print "ps2:", ps2;
print "ps3:", ps3;
print;
from jas import startLog
from jas import terminate
# hermite polynomial example
# H(0) = 1
# H(1) = 2 * x
# H(n) = 2 * x * H(n-1) - 2 * (n-1) * H(n-2)
r = Ring( "Z(x) L" );
print "Ring: " + str(r);
print;
# sage like: with generators for the polynomial ring
[x] = r.gens();
one = r.one();
x2 = 2 * x;
N = 10;
H = [one,x2];
for n in range(2,N):
h = x2 * H[n-1] - 2 * (n-1) * H[n-2];
H.append( h );
for n in range(0,N):
print "H[%s] = %s" % (n,H[n]);
print;
#sys.exit();
c = CC((2, ), (3, ))
print "c:", c
print "c^5:", c**5 + c.one()
print
c = CC((2, ), rn)
print "c:", c
print
r = Ring("Q(x,y) L")
print "Ring: " + str(r)
print
# sage like: with generators for the polynomial ring
[x, y] = r.gens()
one = r.one()
zero = r.zero()
try:
f = RF()
except:
f = None
print "f: " + str(f)
d = x**2 + 5 * x - 6
f = RF(d)
print "f: " + str(f)
n = d * d + y + 1
f = RF(d, n)
print "f: " + str(f)
