Nils, thank you very much for your answer. (1) You are right when you say that the division of polynomials can't always be done in ideals. In my special case I deal with meromorphic functions on the general elliptic curve with 17-torsion point P=(0,0) and basepoint O and know the divisors of all mentioned polynomials:
div(poly1) = 4[P] + 2[4P] + [-4P] + [-8P] - 8[O] div(poly2) = [4P] + [-4P] - 2[O] div(poly1 / poly2) = 4[P] + [4P] + [-8P] - 6[O] Using this divisor I know that the result of the division "poly1 / poly2" must be a polynomial in the ideal, since the only pole is the basepoint O. (2) In the Singular manual (https://www.singular.uni-kl.de/Manual/4-0-3/sing_150.htm#SEC189) I have found the information that I cannot use the operator "/" to divide polynomials, since "non divisible terms" will we discarded and set to zero. So I have repaired the calculation in Singular (see below). But my initial problem still exists: In Singular the calculation takes 10 seconds and the Sage kernel dies after one hour of calculation. *Fixed Singular source Code:* ring R = 0,(x,y,e,f),dp; poly 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; poly 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; ideal I = i1,i2; ideal J = std(I); poly 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 + 7 0*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 - 10 19*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; poly 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; poly t1 = lift(p2,p1)[1,1]; *Singular output:* t1; -ye9+5ye7f2-5ye8+7ye7f+15ye6f2+4ye2f6-2yef7+x2e6-10ye7-2x2e5f+14ye6f-x2e4f2+ 20ye5f2+26ye2f5+yef6-5yf7+3x2e5-11ye6-7x2e4f+22ye5f+3ye4f2+4x2e2f3-2x2ef4+ 49ye2f4+43yef5-22yf6+3x2e4+4ye5-12x2e3f-7ye4f+10x2e2f2-27ye3f2+4x2ef3+ 10ye2f3-5x2f4+91yef4-18yf5-x2e3+xye3+29ye4-5x2e2f+7xye2f+11ye3f+13x2ef2- 2xyef2-99ye2f2-7x2f3-2xyf3-4yef3+63yf4-2x2e2+3xye2+73ye3+4x2ef+6xyef-29ye2f- 2x2f2-7xyf2-161yef2+117yf3-2x3+2xye+53ye2-2xyf-106yef+53yf2+3y2 -- 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.
