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#
# jython examples for jas.
# $Id$
#
from java.lang import System
from jas import SolvableRing, SolvPolyRing, PolyRing, SRF
from jas import QQ, startLog, SolvableModule, SolvableSubModule, terminate
# Ore extension solvable polynomial example, modules
rp = PolyRing(QQ(),"x,y,z,t",PolyRing.lex);
#is automatic: [one,x,y,z,t] = rp.gens();
trel = [ z, y, y * z + x,
t, y, y * t + y,
t, z, z * t - z
];
print "trel: = " + str([ str(f) for f in trel ]);
print;
rs = SolvPolyRing(QQ(),"x,y,z,t",PolyRing.lex,trel);
#exit(0)
f = rs.ideal("",[t**2 + z**2 + x**2 + y**2 + 1]);
print "f: " + str(f);
tf = f.twosidedGB();
print "t: " + str(tf);
print;
#exit(0)
r = SolvableModule("",rs);
print "SolvableModule: " + str(r);
print;
subm = [
[ 0, t**2 + z**2 + x**2 + y**2 + 1],
[ x**2 + y**2, z ]
];
m = SolvableSubModule( r, "", subm );
print "SolvableSubModule: " + str(m);
print;
#exit()
#startLog();
lg = m.leftGB();
print "seq left GB: " + str(lg);
print "is left GB: " + str(lg.isLeftGB());
print;
tg = m.twosidedGB();
print "seq twosided GB: " + str(tg);
print "is twosided GB: " + str(tg.isTwosidedGB());
print "is right GB: " + str(tg.isRightGB());
print;
#exit()
rg = m.rightGB();
print "seq right GB: " + str(rg);
print "is right GB: " + str(rg.isRightGB());
print;
# as quotients to coefficients
rq = SRF(rs);
rpq = PolyRing(rq,"v,w",PolyRing.lex);
print "PolyRing: rpq = " + str(rpq);
vrel = [ v, t, t * v + x,
w, t, t * w + y
];
print "vrel: = " + str([ str(f) for f in vrel ]);
print;
rsq = SolvPolyRing(rq,"v,w",PolyRing.lex,vrel);
print "SolvPolyRing: rsq = " + str(rsq);
print;
r = SolvableModule("",rsq);
print "SolvableModule: " + str(r);
print;
subm = [
[ 0, v + 1 ],
[ w + x, w - v ]
];
m = SolvableSubModule( r, "", subm );
print "SolvableSubModule: " + str(m);
print;
#startLog();
lg = m.leftGB();
print "seq left GB: " + str(lg);
print "is left GB: " + str(lg.isLeftGB());
print;
#exit();
#startLog();
tg = m.twosidedGB();
print "seq twosided GB: " + str(tg);
print "is twosided GB: " + str(tg.isTwosidedGB());
print "is right GB: " + str(tg.isRightGB());
print;
#exit()
rg = m.rightGB();
print "seq right GB: " + str(rg);
print "is right GB: " + str(rg.isRightGB());
print;
#startLog();
terminate();
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