Python SolvPolyRing.ideal Exemples

Exemple #1

#is automatic: [one,x,y,z] = pcz.gens();

zrelations = [z, y,  y * z + x
             ];

print "zrelations: = " + str([ str(f) for f in zrelations ]);
print;

pz = SolvPolyRing(QQ(), "x,y,z", PolyRing.lex, zrelations);
print "SolvPolyRing: " + str(pz);
print;

#startLog();

fl = [ z**2 + y, y**2 + x];
ff = pz.ideal("",fl);
print "ideal ff: " + str(ff);
print;

ff = ff.twosidedGB();
print "ideal ff: " + str(ff);
print;


f0 = SRC(ff,z + x + y + 1);
print "f0 = " + str(f0);

#f1 = SRC(ff, z-y+1 );
#f1 = SRC(ff, y*z+1  );
f1 = SRC(ff, y*z+x+1  );
print "f1 = " + str(f1);

Exemple #2

print "relations: =", [str(f) for f in relations]
print

#rp = SolvPolyRing(QQ(), "a,b,e1,e2,e3", rel=relations);
rp = SolvPolyRing(QQ(), "a,b,e1,e2,e3", PolyRing.lex, relations)
print "SolvPolyRing: " + str(rp)
print

print "gens =", [str(f) for f in rp.gens()]
#[one,a,b,e1,e2,e3] = rp.gens();
#[one,I,J,K,a,b,e1,e2,e3] = rp.gens();

f1 = e1 * e3**3 + e2**10 - a
f2 = e1**3 * e2**2 + e3
f3 = e3**3 + e3**2 - b

F = [f1, f2, f3]
print "F =", [str(f) for f in F]
print

I = rp.ideal(list=F)
print "SolvableIdeal: " + str(I)
print

rgt = I.twosidedGB()
print "seq twosided GB:" + str(rgt)
print "isTwosidedGB: " + str(rgt.isTwosidedGB())
print
print "rgt: ", [str(f) for f in rgt.list]
print

Exemple #3

#print "monic(b) = " +str(bm);
#print

#exit(0);

f1 = x**2 + y**2 + z**2 + t**2 + 1
print "f1 = ", f1

f2 = t * x * f1
print "f2 = ", f2

F = [f1, f2]
print "F =", [str(f) for f in F]
print

I = pt.ideal(list=F)
print "SolvableIdeal: " + str(I)
print

#exit(0);

rgl = I.leftGB()
print "seq left GB:" + str(rgl)
print "isLeftGB: " + str(rgl.isLeftGB())
print

#rgr = I.rightGB();
#print "seq right GB:" + str(rgr);
#print "isRightGB: " + str(rgr.isRightGB());
#print;

Exemple #4

f1 = e1 * e3**3 + e2**10 - a;
f2 = e1**3 * e2**2 + e3;
f3 = e3**3 + e3**2 - b;

f4 = ( e3**2 * e2**3 + e1 )**3;

#print "f1 = ", f1;
#print "f2 = ", f2;
#print "f3 = ", f3;
#print "f4 = ", f4;

F = [ f1, f2, f3 ];
print "F =", [ str(f) for f in F ];
print

I = rp.ideal( list=F );
print "SolvableIdeal: " + str(I);
print;

rgl = I.leftGB();
print "seq left GB:" + str(rgl);
print "isLeftGB: " + str(rgl.isLeftGB());
print;

rgt = I.twosidedGB();
print "seq twosided GB:" + str(rgt);
print "isTwosidedGB: " + str(rgt.isTwosidedGB());
print;

rgr = I.rightGB();
print "seq right GB:" + str(rgr);

Exemple #5

#is automatic: [one,x,y,z] = pcz.gens();

zrelations = [z, y,  y * z + x
             ];

print "zrelations: = " + str([ str(f) for f in zrelations ]);
print;

pz = SolvPolyRing(QQ(), "x,y,z", PolyRing.lex, zrelations);
print "SolvPolyRing: " + str(pz);
print;

#startLog();

fl = [ z**2 + y, y**2 + x];
ff = pz.ideal("",fl);
print "ideal ff: " + str(ff);
print;

ff = ff.twosidedGB();
print "ideal ff: " + str(ff);
print;


f0 = SRC(ff,z + x + y + 1);
print "f0 = " + str(f0);

#f1 = SRC(ff, z-y+1 );
#f1 = SRC(ff, y*z+1  );
f1 = SRC(ff, y*z+x+1  );
print "f1 = " + str(f1);

Exemple #6

Fichier : solv_ore_syz.py Projet : zourzouvillys/java-algebra-system

rp = SolvPolyRing(QQ(), "x,y,z,t", PolyRing.lex, relations)
print "SolvPolyRing: " + str(rp)
print

print "gens =" + str([str(f) for f in rp.gens()])
#is automatic: one,x,y,z,t = rp.gens();

#f1 = x**2 + y**2 + z**2 + t**2 + 1;
#print "f1 = " +str(f1);

ff = [x, y, z, t**2 - 1]
print "ff = " + str([str(f) for f in ff])
print

ii = rp.ideal("", ff)
print "SolvableIdeal: " + str(ii)
print

rgl = ii.leftGB()
print "seq left GB: " + str(rgl)
print "isLeftGB: " + str(rgl.isLeftGB())
print

s = rgl.leftSyzygy()
print "syzygy: " + str(s)
print

t = rgl.isLeftSyzygy(s)
print "is syzygy: " + str(t)
print "is syzygy: " + str(s.isLeftSyzygy(rgl))

Exemple #7

Fichier : solv_ore_syz.py Projet : rjolly/jas

rp = SolvPolyRing(QQ(), "x,y,z,t", PolyRing.lex, relations);
print "SolvPolyRing: " + str(rp);
print;

print "gens =" + str([ str(f) for f in rp.gens() ]);
#is automatic: one,x,y,z,t = rp.gens();

#f1 = x**2 + y**2 + z**2 + t**2 + 1;
#print "f1 = " +str(f1);

ff = [ x, y, z, t**2 - 1 ];
print "ff = " + str([ str(f) for f in ff ]);
print

ii = rp.ideal( "", ff );
print "SolvableIdeal: " + str(ii);
print;


rgl = ii.leftGB();
print "seq left GB: " + str(rgl);
print "isLeftGB: " + str(rgl.isLeftGB());
print;

s = rgl.leftSyzygy();
print "syzygy: " + str(s);
print;

t = rgl.isLeftSyzygy(s);
print "is syzygy: " + str(t);

Exemple #8

Fichier : solv_ore_iter.py Projet : siwiwit/java-algebra-system

# print "monic(b) = " +str(bm);
# print

# exit(0);

f1 = x ** 2 + y ** 2 + z ** 2 + t ** 2 + 1
print "f1 = ", f1

f2 = t * x * f1
print "f2 = ", f2

F = [f1, f2]
print "F =", [str(f) for f in F]
print

I = pt.ideal(list=F)
print "SolvableIdeal: " + str(I)
print

# exit(0);

rgl = I.leftGB()
print "seq left GB:" + str(rgl)
print "isLeftGB: " + str(rgl.isLeftGB())
print

# rgr = I.rightGB();
# print "seq right GB:" + str(rgr);
# print "isRightGB: " + str(rgr.isRightGB());
# print;

Exemple #9

Fichier : solv_ore_iter_gb.py Projet : zourzouvillys/java-algebra-system

rm = PolyRing(rcs, "u,v,w", PolyRing.lex)
#is automatic: [one,x,y,z,t,u,v,w] = rm.gens();

mrel = [v, u, u * v + x, w, v, v * w + y, w, u, u * w - z]

print "mrel: = " + str([str(r) for r in mrel])
print

rs = SolvPolyRing(rcs, "u,v,w", PolyRing.lex, mrel)

#exit(0)

ff = [(w**2 - v * u) * v * w**2, (u**3 + t) * v * w**2,
      (v * u**2 - x * y) * v * w**2]
f = rs.ideal("", ff)
print "f: " + str(f)
print

#exit(0)
#startLog();

lf = f.leftGB()
print "lf: " + str(lf)
print

ff = [(w**2 - v * u) * w, (u**3 + t) * w, (v * u**2 - x * y) * w]
f = rs.ideal("", ff)
print "f: " + str(f)
print

Exemple #10

# 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)

Exemple #11

r = SolvPolyRing( PolyRing(ZZ(),"a, c, b",PolyRing.lex), "y2, y1, z1, z2, x",PolyRing.grad);
print "Ring: " + str(r);
print;

one,a,c,b,y2,y1,z1,z2,x = r.gens();

p1 = x + 2 * y1 * z1 + 3 * a * y1**2 + 5 * y1**4 + 2 * c * y1;
p2 = x + 2 * y2 * z2 + 3 * a * y2**2 + 5 * y2**4 + 2 * c * y2;
p3 = 2 * z2 + 6 * a * y2 + 20 * y2**3 + 2 * c; 
p4 = 3 * z1**2 + y1**2 + b;
p5 = 3 * z2**2 + y2**2 + b; 

F = [p1,p2,p3,p4,p5];

g = r.ideal( "", F );
print "Ideal: " + str(g);
print;

#startLog();

rg = g.leftGB();
print "GB: " + str(rg);
print;

bg = rg.isLeftGB();
print "isGB: " + str(bg);
print;

startLog();
terminate();

Exemple #12

zrelations = [z, y,  y * z + x
             ];

print "zrelations: = " + str([ str(f) for f in zrelations ]);
print;

pz = SolvPolyRing(QQ(), "x,y,z", PolyRing.lex, zrelations);
print "SolvPolyRing: " + str(pz);
print;

#startLog();

#fl = [ z**2 + y, y**2 + x];
fl = [ z**2 + y, x];
ff = pz.ideal("",fl);
print "ideal ff: " + str(ff);
print;

ff = ff.twosidedGB();
print "ideal ff: " + str(ff);
print;


f0 = SLR(ff,z + x + y + 1);
print "f0 = " + str(f0);

#f1 = SLR(ff, z-y+1 );
#f1 = SLR(ff, y*z+1  );
f1 = SLR(ff, y*z+x+1  );
print "f1 = " + str(f1);

Exemple #13

print "f1 = " + str(f1)
print "f2 = " + str(f2)

f3 = f1 * f2
print "f3 = " + str(f3)

f4 = f2 * f1
print "f4 = " + str(f4)

ff = [f4, f3]
print "ff = [" + str([str(f) for f in ff])
print

#exit(0);

ii = rp2.ideal("", ff)
print "SolvableIdeal: " + str(ii)
print

rgl = ii.leftGB()
print "seq left GB: " + str(rgl)
print "isLeftGB: " + str(rgl.isLeftGB())
print

rgr = ii.rightGB()
print "seq right GB: " + str(rgr)
print "isRightGB: " + str(rgr.isRightGB())
print

#startLog();

Exemple #14

Fichier : solv_module_ts.py Projet : rjolly/jas

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 ]
       ];

Exemple #15

Fichier : solv_loca_ore_iter.py Projet : rjolly/jas

zrelations = [z, y,  y * z + x
             ];

print "zrelations: = " + str([ str(f) for f in zrelations ]);
print;

pz = SolvPolyRing(QQ(), "x,y,z", PolyRing.lex, zrelations);
print "SolvPolyRing: " + str(pz);
print;

#startLog();

#fl = [ z**2 + y, y**2 + x];
fl = [ z**2 + y, x];
ff = pz.ideal("",fl);
print "ideal ff: " + str(ff);
print;

ff = ff.twosidedGB();
print "ideal ff: " + str(ff);
print;


f0 = SLC(ff,z + x + y + 1);
print "f0 = " + str(f0);

#f1 = SLC(ff, z-y+1 );
#f1 = SLC(ff, y*z+1  );
f1 = SLC(ff, y*z+x+1  );
print "f1 = " + str(f1);

Exemple #16

#f3 = (v - u)*f1;
#f3 = f1*(v - u);
f3 = v*f1*u;
#print "f3 = " + str(f3);

#ff = [ f3, f3 ];
ff = [ f1, f2, f3 ];
#ff = [ f1 ];
#ff = [ u ]; # isTwoSided ideal if uv = vu
#ff = [ v ]; # isTwoSided ideal if uv = vu
#ff = [ w ]; # no twoSided ideal
print "ff = " + str( [ str(r) for r in ff ] );
print

ii = pt.ideal( "", ff );
print "SolvableIdeal: " + str(ii);
print;

#syl = ii.leftSyzygy().leftGB();
#print "left syzygy: " + str(syl);
#print;

#syr = ii.rightSyzygy().rightGB();
#print "right syzygy: " + str(syr);
#print;


#exit(0);
#startLog();

Exemple #17

Fichier : weyl_iter.py Projet : rjolly/jas

print "f1 = " +str(f1);
print "f2 = " +str(f2);

f3 = f1 * f2;
print "f3 = " +str(f3);

f4 = f2 * f1;
print "f4 = " +str(f4);

ff = [ f4 , f3 ];
print "ff = [" + str([ str(f) for f in ff ]);
print

#exit(0);

ii = rp2.ideal( "", ff );
print "SolvableIdeal: " + str(ii);
print;


rgl = ii.leftGB();
print "seq left GB: " + str(rgl);
print "isLeftGB: " + str(rgl.isLeftGB());
print;

rgr = ii.rightGB();
print "seq right GB: " + str(rgr);
print "isRightGB: " + str(rgr.isRightGB());
print;

#startLog();

Exemple #18

Fichier : solv_loca_ore_iter.py Projet : zourzouvillys/java-algebra-system

#is automatic: [one,x,y,z] = pcz.gens();

zrelations = [z, y, y * z + x]

print "zrelations: = " + str([str(f) for f in zrelations])
print

pz = SolvPolyRing(QQ(), "x,y,z", PolyRing.lex, zrelations)
print "SolvPolyRing: " + str(pz)
print

#startLog();

#fl = [ z**2 + y, y**2 + x];
fl = [z**2 + y, x]
ff = pz.ideal("", fl)
print "ideal ff: " + str(ff)
print

ff = ff.twosidedGB()
print "ideal ff: " + str(ff)
print

f0 = SLC(ff, z + x + y + 1)
print "f0 = " + str(f0)

#f1 = SLC(ff, z-y+1 );
#f1 = SLC(ff, y*z+1  );
f1 = SLC(ff, y * z + x + 1)
print "f1 = " + str(f1)