leif wrote:
Dominique Laurain wrote:Thanks leif for your help.. Since some weeks, I have a strange ("final destination") feeling falling too much into deep software traps at office or at home...Work-around: Works in Sage 6.2 if you define f (i.e., u, v and w) "the right way":
Sorry, my bad, forget that... (I confused the windows and only *thought* I was using 6.2).
Not very surprisingly, my version behaves exactly the same in Sage 6.2. :-/ (as it just shortcuts f.polynomial(QQ).factor() to f.factor())
-leif
sage: R.<u,v,w>=QQ[] sage: f = 16*u^4*v^6*w^2 + 144*u^4*v^5*w^3 + 80*u^3*v^6*w^3 + 416*u^4*v^4*w^4 + 560*u^3*v^5*w^4 + 96*u^2*v^6*w^4 + 560*u^4*v^3*w^5 + 1296*u^3*v^4*w^5 + 368*u^2*v^5*w^5 + 16*u*v^6*w^5 + 384*u^4*v^2*w^6 + 1328*u^3*v^3*w^6 + 528*u^2*v^4*w^6 + 48*u*v^5*w^6 + 128*u^4*v*w^7 + 608*u^3*v^2*w^7 + 336*u^2*v^3*w^7 + 48*u*v^4*w^7 + 16*u^4*w^8 + 96*u^3*v*w^8 + 80*u^2*v^2*w^8 + 16*u*v^3*w^8 - 112*u^4*v^5*w^2 - 64*u^3*v^6*w^2 - 752*u^4*v^4*w^3 - 960*u^3*v^5*w^3 - 176*u^2*v^6*w^3 - 1648*u^4*v^3*w^4 - 3744*u^3*v^4*w^4 - 1344*u^2*v^5*w^4 - 64*u*v^6*w^4 - 1600*u^4*v^2*w^5 - 5744*u^3*v^3*w^5 - 3104*u^2*v^4*w^5 - 304*u*v^5*w^5 - 704*u^4*v*w^6 - 3840*u^3*v^2*w^6 - 3056*u^2*v^3*w^6 - 480*u*v^4*w^6 - 112*u^4*w^7 - 1008*u^3*v*w^7 - 1296*u^2*v^2*w^7 - 304*u*v^3*w^7 - 64*u^3*w^8 - 176*u^2*v*w^8 - 64*u*v^2*w^8 + 312*u^4*v^4*w^2 + 400*u^3*v^5*w^2 + 76*u^2*v^6*w^2 + 1540*u^4*v^3*w^3 + 3436*u^3*v^4*w^3 + 1360*u^2*v^5*w^3 + 72*u*v^6*w^3 + 2412*u^4*v^2*w^4 + 8788*u^3*v^3*w^4 + 5572*u^2*v^4*w^4 + 616*u*v^5*w^4 + 1500*u^4*v*w^5 + 8836*u^3*v^2*w^5 + 8524*u^2*v^3*w^5 + 1540*u*v^4*w^5 + 316*u^4*w^6 + 3484*u^3*v*w^6 + 5512*u^2*v^2*w^6 + 1548*u*v^3*w^6 + 400*u^3*w^7 + 1348*u^2*v*w^7 + 628*u*v^2*w^7 + 72*u^2*w^8 + 76*u*v*w^8 - 448*u^4*v^3*w^2 - 1004*u^3*v^4*w^2 - 420*u^2*v^5*w^2 - 24*u*v^6*w^2 - 1548*u^4*v^2*w^3 - 5672*u^3*v^3*w^3 - 3920*u^2*v^4*w^3 - 476*u*v^5*w^3 - 1544*u^4*v*w^4 - 9500*u^3*v^2*w^4 - 10280*u^2*v^3*w^4 - 2076*u*v^4*w^4 - 460*u^4*w^5 - 5696*u^3*v*w^5 - 10244*u^2*v^2*w^5 - 3280*u*v^3*w^5 - 1008*u^3*w^6 - 3884*u^2*v*w^6 - 2108*u*v^2*w^6 - 404*u^2*w^7 - 492*u*v*w^7 - 24*u*w^8 + 352*u^4*v^2*w^2 + 1304*u^3*v^3*w^2 + 952*u^2*v^4*w^2 + 124*u*v^5*w^2 + 764*u^4*v*w^3 + 4824*u^3*v^2*w^3 + 5604*u^2*v^3*w^3 + 1228*u*v^4*w^3 + 364*u^4*w^4 + 4836*u^3*v*w^4 + 9468*u^2*v^2*w^4 + 3332*u*v^3*w^4 + 1316*u^3*w^5 + 5568*u^2*v*w^5 + 3356*u*v^2*w^5 + 928*u^2*w^6 + 1252*u*v*w^6 + 124*u*w^7 - 144*u^4*v*w^2 - 928*u^3*v^2*w^2 - 1132*u^2*v^3*w^2 - 264*u*v^4*w^2 - 148*u^4*w^3 - 2056*u^3*v*w^3 - 4264*u^2*v^2*w^3 - 1608*u*v^3*w^3 - 940*u^3*w^4 - 4252*u^2*v*w^4 - 2764*u*v^2*w^4 - 1116*u^2*w^5 - 1624*u*v*w^5 - 264*u*w^6 + 24*u^4*w^2 + 344*u^3*v*w^2 + 744*u^2*v^2*w^2 + 296*u*v^3*w^2 + 348*u^3*w^3 + 1652*u^2*v*w^3 + 1136*u*v^2*w^3 + 740*u^2*w^4 + 1140*u*v*w^4 + 296*u*w^5 - 52*u^3*w^2 - 256*u^2*v*w^2 - 184*u*v^2*w^2 - 256*u^2*w^3 - 412*u*v*w^3 - 184*u*w^4 + 36*u^2*w^2 + 60*u*v*w^2 + 60*u*w^3 - 8*u*w^2 sage: f.factor() (4) * u * w^2 * (v + w - 1)^3 * (4*u^3*v^3 + 24*u^3*v^2*w + 20*u^2*v^3*w + 20*u^3*v*w^2 + 80*u^2*v^2*w^2 + 24*u*v^3*w^2 + 4*u^3*w^3 + 24*u^2*v*w^3 + 20*u*v^2*w^3 + 4*v^3*w^3 - 16*u^3*v^2 - 16*u^2*v^3 - 44*u^3*v*w - 132*u^2*v^2*w - 44*u*v^3*w - 16*u^3*w^2 - 132*u^2*v*w^2 - 132*u*v^2*w^2 - 16*v^3*w^2 - 16*u^2*w^3 - 44*u*v*w^3 - 16*v^2*w^3 + 18*u^3*v + 52*u^2*v^2 + 19*u*v^3 + 19*u^3*w + 151*u^2*v*w + 151*u*v^2*w + 18*v^3*w + 52*u^2*w^2 + 151*u*v*w^2 + 52*v^2*w^2 + 18*u*w^3 + 19*v*w^3 - 6*u^3 - 47*u^2*v - 48*u*v^2 - 6*v^3 - 48*u^2*w - 137*u*v*w - 47*v^2*w - 47*u*w^2 - 48*v*w^2 - 6*w^3 + 13*u^2 + 37*u*v + 13*v^2 + 37*u*w + 37*v*w + 13*w^2 - 9*u - 9*v - 9*w + 2) (In your definition, f(u,v,w)=..., f is just a symbolic expression in the first place. It's still of course a bug that your way currently does no longer work.) -leif
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