On Monday, February 5, 2018 at 9:11:44 AM UTC, Patrick Reichert wrote: > > I want to submit an *error report* for SAGE 7.0 and 8.0: > > The division of two polynomials in an ideal causes an *kernel death* > after one hour of computation. > Singular performs the calculation in about *one second*. > > It's worth noting that Sage's "quotient ring" does not seem to wrap singular directly (although internally it probably does depend on it via calling reduce)
*SAGE source code:* > > Q.<E,F,X,Y> = QQ['E', 'F', 'X', 'Y']; > > i1 = F^4+(E^3+E^2-E+2)*F^3+(E^3-3*E+1)*F^2-(E^4+2*E)*F+E^3+E^2; > > i2 = Y^2+(E^3+E^2*(3*F+2)-E*(F^2-2*F-1)-F*(F^2+3*F+1))*X*Y+(F*(E+1)*(E-F > )*(E+F+1)^2*(E^2+E-F)*(E^2+E*F+E-F^2-F))*Y-X^3-(F*(E+1)*(E-F)*(E+F+1)*(E^2 > +E-F))*X^2; > > J = Q.ideal(i1, i2); > > R.<e,f,x,y> = QuotientRing(Q, J); > > poly1 = x^4+(-e^2*f^4+e^4*f+2*e^3*f^2-e*f^4-2*e*f^3+2*f^4+2*e^2*f-6*e*f^2+ > f^3+5*e^2-5*e*f+11*f^2-17*e+18*f+16)*x^3+(-2*e^3-2*e^2*f+e*f^2+f^3-3*e^2+2 > *f^2-e+f)*x^2*y+(-6*e^2*f^5+11*e*f^6-3*f^7+3*e^6-6*e^5*f+17*e^4*f^2-69*e^2 > *f^4+5*e*f^5+17*f^6-5*e^5+26*e^4*f+83*e^3*f^2-106*e^2*f^3-104*e*f^4+71*f^5 > -28*e^4+66*e^3*f+57*e^2*f^2-149*e*f^3+54*f^4-55*e^3+78*e^2*f+9*e*f^2-32*f^ > 3-35*e^2+70*e*f-35*f^2)*x^2+(-e^2*f^7-e^7*f-3*e^6*f^2-2*e^2*f^6-e*f^7-5*e^ > 6*f-e^5*f^2-6*e^2*f^5-6*e*f^6+2*f^7+3*e^5*f-2*e^4*f^2-2*e^2*f^4-15*e*f^5+2 > *f^6-2*e^5-7*e^4*f-4*e^3*f^2-9*e^2*f^3-4*e*f^4+3*e^4+20*e^3*f-43*e^2*f^2- > 21*e*f^3+28*f^4-e^3-32*e^2*f-61*e*f^2+61*f^3-22*e^2-53*e*f+59*f^2-16*e+16* > f)*x*y+(e^6+2*e^5*f+3*e^5-4*e^3*f^2-2*e^2*f^3+2*e*f^4+f^5+3*e^4-5*e^2*f^2+ > 2*f^4+3*e^3-3*e^2*f-e*f^2+4*f^3-3*e^2+e*f-9*f^2+17*e-18*f-16)*y^2+(11*e*f^ > 9-3*f^10-3*e^9-5*e^7*f^2-101*e^2*f^7+30*e*f^8+11*f^9-e^8-32*e^7*f-74*e^6*f > ^2-422*e^2*f^6-117*e*f^7+121*f^8+35*e^7-39*e^6*f-134*e^5*f^2-486*e^2*f^5- > 660*e*f^6+276*f^7+141*e^6-106*e^5*f-226*e^4*f^2+384*e^2*f^4-1019*e*f^5+36* > f^6+189*e^5-367*e^4*f-681*e^3*f^2+1382*e^2*f^3+130*e*f^4-884*f^5+61*e^4- > 1019*e^3*f+565*e^2*f^2+1914*e*f^3-1521*f^4-251*e^3-499*e^2*f+1751*e*f^2- > 1001*f^3-231*e^2+462*e*f-231*f^2)*y; > > poly2 = x+e^5*f+e^4*f^2-e^2*f^4+2*e^4*f+e^3*f^2-3*e^2*f^3+f^5+3*e^3*f-3*e^ > 2*f^2-3*e*f^3+3*f^4+e^3+e^2*f-5*e*f^2+3*f^3+e^2-2*e*f+f^2; > > print (poly1 / poly2); > > > I would not expect that this code would call reduce(poly1/poly2, J). poly2 doesn't represent a unit modulo J, so the division is problematic. It is the case that poly1 in (J+(poly2)), so there is some polynomial that can represent poly1/poly2. However, this would in general not be unique modulo J (poly2 could still be a zero divisor modulo J). The operation is still a useful one in practice, of course, so in might be worthwhile exposing tools that allow one to easily perform the relevant computation. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
