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Bug report: Kernel dies after 1 hour while dividing polynomials

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.

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^3-3E+1)F^2-(E^4+2E)*F+E^3+E^2;

i2 = Y^2+(E^3+E^2(3F+2)-E(F^2-2F-1)-F(F^2+3F+1))XY+(F(E+1)(E-F)(E+F+1)^2(E^2+E-F)(E^2+EF+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^2f^4+e^4f+2e^3f^2-ef^4-2ef^3+2f^4+2e^2f-6ef^2+f^3+5e^2-5ef+11f^2-17e+18f+16)x^3+(-2e^3-2e^2f+ef^2+f^3-3e^2+2f^2-e+f)x^2y+(-6e^2f^5+11ef^6-3f^7+3e^6-6e^5f+17e^4f^2-69e^2f^4+5ef^5+17f^6-5e^5+26e^4f+83e^3f^2-106e^2f^3-104ef^4+71f^5-28e^4+66e^3f+57e^2f^2-149ef^3+54f^4-55e^3+78e^2f+9ef^2-32f^3-35e^2+70ef-35f^2)x^2+(-e^2f^7-e^7f-3e^6f^2-2e^2f^6-ef^7-5e^6f-e^5f^2-6e^2f^5-6ef^6+2f^7+3e^5f-2e^4f^2-2e^2f^4-15ef^5+2f^6-2e^5-7e^4f-4e^3f^2-9e^2f^3-4ef^4+3e^4+20e^3f-43e^2f^2-21ef^3+28f^4-e^3-32e^2f-61ef^2+61f^3-22e^2-53ef+59f^2-16e+16f)xy+(e^6+2e^5f+3e^5-4e^3f^2-2e^2f^3+2ef^4+f^5+3e^4-5e^2f^2+2f^4+3e^3-3e^2f-ef^2+4f^3-3e^2+ef-9f^2+17e-18f-16)y^2+(11ef^9-3f^10-3e^9-5e^7f^2-101e^2f^7+30ef^8+11f^9-e^8-32e^7f-74e^6f^2-422e^2f^6-117ef^7+121f^8+35e^7-39e^6f-134e^5f^2-486e^2f^5-660ef^6+276f^7+141e^6-106e^5f-226e^4f^2+384e^2f^4-1019ef^5+36f^6+189e^5-367e^4f-681e^3f^2+1382e^2f^3+130ef^4-884f^5+61e^4-1019e^3f+565e^2f^2+1914ef^3-1521f^4-251e^3-499e^2f+1751ef^2-1001f^3-231e^2+462ef-231f^2)y;

poly2 = x+e^5f+e^4f^2-e^2f^4+2e^4f+e^3f^2-3e^2f^3+f^5+3e^3f-3e^2f^2-3ef^3+3f^4+e^3+e^2f-5ef^2+3f^3+e^2-2e*f+f^2;

print (poly1 / poly2);

Singular source code:

ring R = 0,(x,y,e,f),dp;

poly i1 = f^4+(e^3+e^2-e+2)f^3+(e^3-3e+1)f^2-(e^4+2e)*f+e^3+e^2;

poly i2 = y^2 + (e^3 + e^2(3f+2) - e(f^2-2f-1) - f(f^2+3f+1))xy + (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);

reduce((x^4 + (-e^2f^4 + e^4f + 2e^3f^2 - ef^4 - 2ef^3 + 2f^4 + 2e^2 f - 6ef^2 + f^3 + 5e^2 - 5ef + 11f^2 - 17e + 18f + 16)x^3 + (-2e^3 - 2 e^2f + ef^2 + f^3 - 3e^2 + 2f^2 - e + f)x^2y + (-6e^2f^5 + 11ef^6 - 3 *f^7 + 3e^6 - 6e^5f + 17e^4f^2 - 69e^2f^4 + 5ef^5 + 17f^6 - 5e^5 + 26 e^4f + 83e^3f^2 - 106e^2f^3 - 104ef^4 + 71f^5 - 28e^4 + 66e^3f + 57* e^2f^2 - 149ef^3 + 54f^4 - 55e^3 + 78e^2f + 9ef^2 - 32f^3 - 35e^2 + 7 0ef - 35f^2)x^2 + (-e^2f^7 - e^7f - 3e^6f^2 - 2e^2f^6 - ef^7 - 5e^6 f - e^5f^2 - 6e^2f^5 - 6ef^6 + 2f^7 + 3e^5f - 2e^4f^2 - 2e^2f^4 - 15 ef^5 + 2f^6 - 2e^5 - 7e^4f - 4e^3f^2 - 9e^2f^3 - 4ef^4 + 3e^4 + 20 e^3f - 43e^2f^2 - 21ef^3 + 28f^4 - e^3 - 32e^2f - 61ef^2 + 61f^3 - 22 *e^2 - 53ef + 59f^2 - 16e + 16f)xy + (e^6 + 2e^5f + 3e^5 - 4e^3f^2 - 2e^2f^3 + 2ef^4 + f^5 + 3e^4 - 5e^2f^2 + 2f^4 + 3e^3 - 3e^2f - ef^2 + 4f^3 - 3e^2 + ef - 9f^2 + 17e - 18f - 16)y^2 + (11ef^9 - 3f^10 - 3 e^9 - 5e^7f^2 - 101e^2f^7 + 30ef^8 + 11f^9 - e^8 - 32e^7f - 74e^6f^2
- 422
e^2f^6 - 117ef^7 + 121f^8 + 35e^7 - 39e^6f - 134e^5f^2 - 486e^2* f^5 - 660ef^6 + 276f^7 + 141e^6 - 106e^5f - 226e^4f^2 + 384e^2f^4 - 10 19ef^5 + 36f^6 + 189e^5 - 367e^4f - 681e^3f^2 + 1382e^2f^3 + 130ef^4 - 884f^5 + 61e^4 - 1019e^3f + 565e^2f^2 + 1914ef^3 - 1521f^4 - 251e^3 - 499e^2f + 1751ef^2 - 1001f^3 - 231e^2 + 462ef - 231f^2)y)/(x + e^5* f + e^4f^2 - e^2f^4 + 2e^4f + e^3f^2 - 3e^2f^3 + f^5 + 3e^3f - 3e^2f^ 2 - 3ef^3 + 3f^4 + e^3 + e^2f - 5ef^2 + 3f^3 + e^2 - 2ef + f^2), J);

Singular output:

15yef9-3yf10+23ye9-33ye7f2-93ye2f7+27yef8+15yf9-3x2e7+62ye8+6x2e6f-82ye7f-12x2e5f2-3xye5f2-147ye6f2-6x2e2f5+3xye2f5+15x2ef6-366ye2f6-3x2f7-120yef7+120yf8-6x2e6+2xye6+8ye7+21x2e5f-3xye5f-67ye6f-12x2e4f2-3xye4f2-121ye5f2-57x2e2f4+6xye2f4-6x2ef5-3xyef5-405ye2f5+21x2f6-513yef6+225yf7-18x2e5-xye5+97ye6+93x2e4f-4xye4f-233ye5f+3x3e2f2+9x2e3f2-12xye3f2-82ye4f2-93x2e2f3-45xye2f3-81x2ef4+12xyef4+138ye2f4+54x2f5+12xyf5-816yef5+57yf6-3x3e3-36x2e4+21xye4+44ye5+3x3e2f+120x2e3f+41xye3f-120ye4f-3x3ef2-36x2e2f2-49xye2f2-3y2e2f2-215ye3f2-90x2ef3-30xyef3+648ye2f3+39x2f4+33xyf4-277yef4-483yf5+6x3e2-43x2e3-6xye3+3y2e3-455ye4-6x3ef+78x2e2f-66xye2f-3y2e2f-485ye3f+15x3f2-10xyef2+3y2ef2+641ye2f2-27x2f3+33xyf3+1130yef3-1152yf4-18x3e-16x2e2-64xye2-6y2e2-832ye3+3x3f+83x2ef-66xyef+6y2ef-352ye2f-39x2f2+86xyf2-15y2f2+1830yef2-1140yf3+30x3-37x2e-27xye+18y2e-658ye2+26x2f+26xyf-3y2f+780yef-443yf2+2x2+9xy-29y2-11ye-221yf-318y

Bug report: Kernel dies after 1 hour while dividing polynomials

I want to submit an error report report for SAGE 7.0 and 8.0:

The division of two polynomials in an ideal causes an kernel death death after one hour of computation. Singular performs the calculation in about one second.second.

SAGE source code:

Q.<e,f,x,y>

Q.<E,F,X,Y> = QQ['E', 'F', 'X', 'Y']; 'Y'];

i1 = F^4+(E^3+E^2-E+2)F^3+(E^3-3E+1)F^2-(E^4+2E)*F+E^3+E^2; 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(3F+2)-E(F^2-2F-1)-F(F^2+3F+1))XY+(F(E+1)(E-F)(E+F+1)^2(E^2+E-F)(E^2+EF+E-F^2-F))Y-X^3-(F(E+1)(E-F)(E+F+1)(E^2+E-F))X^2; 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); i2);

R.<e,f,x,y> = QuotientRing(Q, J); J);

poly1 = x^4+(-e^2f^4+e^4f+2e^3f^2-ef^4-2ef^3+2f^4+2e^2f-6ef^2+f^3+5e^2-5ef+11f^2-17e+18f+16)x^3+(-2e^3-2e^2f+ef^2+f^3-3e^2+2f^2-e+f)x^2y+(-6e^2f^5+11ef^6-3f^7+3e^6-6e^5f+17e^4f^2-69e^2f^4+5ef^5+17f^6-5e^5+26e^4f+83e^3f^2-106e^2f^3-104ef^4+71f^5-28e^4+66e^3f+57e^2f^2-149ef^3+54f^4-55e^3+78e^2f+9ef^2-32f^3-35e^2+70ef-35f^2)x^2+(-e^2f^7-e^7f-3e^6f^2-2e^2f^6-ef^7-5e^6f-e^5f^2-6e^2f^5-6ef^6+2f^7+3e^5f-2e^4f^2-2e^2f^4-15ef^5+2f^6-2e^5-7e^4f-4e^3f^2-9e^2f^3-4ef^4+3e^4+20e^3f-43e^2f^2-21ef^3+28f^4-e^3-32e^2f-61ef^2+61f^3-22e^2-53ef+59f^2-16e+16f)xy+(e^6+2e^5f+3e^5-4e^3f^2-2e^2f^3+2ef^4+f^5+3e^4-5e^2f^2+2f^4+3e^3-3e^2f-ef^2+4f^3-3e^2+ef-9f^2+17e-18f-16)y^2+(11ef^9-3f^10-3e^9-5e^7f^2-101e^2f^7+30ef^8+11f^9-e^8-32e^7f-74e^6f^2-422e^2f^6-117ef^7+121f^8+35e^7-39e^6f-134e^5f^2-486e^2f^5-660ef^6+276f^7+141e^6-106e^5f-226e^4f^2+384e^2f^4-1019ef^5+36f^6+189e^5-367e^4f-681e^3f^2+1382e^2f^3+130ef^4-884f^5+61e^4-1019e^3f+565e^2f^2+1914ef^3-1521f^4-251e^3-499e^2f+1751ef^2-1001f^3-231e^2+462ef-231f^2)y; 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^5f+e^4f^2-e^2f^4+2e^4f+e^3f^2-3e^2f^3+f^5+3e^3f-3e^2f^2-3ef^3+3f^4+e^3+e^2f-5ef^2+3f^3+e^2-2e*f+f^2; 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);poly2);


Singular source code:

ring R = 0,(x,y,e,f),dp; 0,(x,y,e,f),dp;

poly i1 = f^4+(e^3+e^2-e+2)f^3+(e^3-3e+1)f^2-(e^4+2e)*f+e^3+e^2; 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(3f+2) - e(f^2-2f-1) - f(f^2+3f+1))xy 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; x^2;

ideal I = i1,i2;   ideal J = std(I);std(I);

reduce((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)/(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), J);


reduce((x^4 + (-e^2f^4 + e^4f + 2e^3f^2 - ef^4 - 2ef^3 + 2f^4 + 2e^2 f - 6ef^2 + f^3 + 5e^2 - 5ef + 11f^2 - 17e + 18f + 16)x^3 + (-2e^3 - 2 e^2f + ef^2 + f^3 - 3e^2 + 2f^2 - e + f)x^2y + (-6e^2f^5 + 11ef^6 - 3 *f^7 + 3e^6 - 6e^5f + 17e^4f^2 - 69e^2f^4 + 5ef^5 + 17f^6 - 5e^5 + 26 e^4f + 83e^3f^2 - 106e^2f^3 - 104ef^4 + 71f^5 - 28e^4 + 66e^3f + 57* e^2f^2 - 149ef^3 + 54f^4 - 55e^3 + 78e^2f + 9ef^2 - 32f^3 - 35e^2 + 7 0ef - 35f^2)x^2 + (-e^2f^7 - e^7f - 3e^6f^2 - 2e^2f^6 - ef^7 - 5e^6 f - e^5f^2 - 6e^2f^5 - 6ef^6 + 2f^7 + 3e^5f - 2e^4f^2 - 2e^2f^4 - 15 ef^5 + 2f^6 - 2e^5 - 7e^4f - 4e^3f^2 - 9e^2f^3 - 4ef^4 + 3e^4 + 20 e^3f - 43e^2f^2 - 21ef^3 + 28f^4 - e^3 - 32e^2f - 61ef^2 + 61f^3 - 22 *e^2 - 53ef + 59f^2 - 16e + 16f)xy + (e^6 + 2e^5f + 3e^5 - 4e^3f^2 - 2e^2f^3 + 2ef^4 + f^5 + 3e^4 - 5e^2f^2 + 2f^4 + 3e^3 - 3e^2f - ef^2 + 4f^3 - 3e^2 + ef - 9f^2 + 17e - 18f - 16)y^2 + (11ef^9 - 3f^10 - 3 e^9 - 5e^7f^2 - 101e^2f^7 + 30ef^8 + 11f^9 - e^8 - 32e^7f - 74e^6f^2
- 422
e^2f^6 - 117ef^7 + 121f^8 + 35e^7 - 39e^6f - 134e^5f^2 - 486e^2* f^5 - 660ef^6 + 276f^7 + 141e^6 - 106e^5f - 226e^4f^2 + 384e^2f^4 - 10 19ef^5 + 36f^6 + 189e^5 - 367e^4f - 681e^3f^2 + 1382e^2f^3 + 130ef^4 - 884f^5 + 61e^4 - 1019e^3f + 565e^2f^2 + 1914ef^3 - 1521f^4 - 251e^3 - 499e^2f + 1751ef^2 - 1001f^3 - 231e^2 + 462ef - 231f^2)y)/(x + e^5* f + e^4f^2 - e^2f^4 + 2e^4f + e^3f^2 - 3e^2f^3 + f^5 + 3e^3f - 3e^2f^ 2 - 3ef^3 + 3f^4 + e^3 + e^2f - 5ef^2 + 3f^3 + e^2 - 2ef + f^2), J);

Singular output:

15yef9-3yf10+23ye9-33ye7f2-93ye2f7+27yef8+15yf9-3x2e7+62ye8+6x2e6f-82ye7f-12x2e5f2-3xye5f2-147ye6f2-6x2e2f5+3xye2f5+15x2ef6-366ye2f6-3x2f7-120yef7+120yf8-6x2e6+2xye6+8ye7+21x2e5f-3xye5f-67ye6f-12x2e4f2-3xye4f2-121ye5f2-57x2e2f4+6xye2f4-6x2ef5-3xyef5-405ye2f5+21x2f6-513yef6+225yf7-18x2e5-xye5+97ye6+93x2e4f-4xye4f-233ye5f+3x3e2f2+9x2e3f2-12xye3f2-82ye4f2-93x2e2f3-45xye2f3-81x2ef4+12xyef4+138ye2f4+54x2f5+12xyf5-816yef5+57yf6-3x3e3-36x2e4+21xye4+44ye5+3x3e2f+120x2e3f+41xye3f-120ye4f-3x3ef2-36x2e2f2-49xye2f2-3y2e2f2-215ye3f2-90x2ef3-30xyef3+648ye2f3+39x2f4+33xyf4-277yef4-483yf5+6x3e2-43x2e3-6xye3+3y2e3-455ye4-6x3ef+78x2e2f-66xye2f-3y2e2f-485ye3f+15x3f2-10xyef2+3y2ef2+641ye2f2-27x2f3+33xyf3+1130yef3-1152yf4-18x3e-16x2e2-64xye2-6y2e2-832ye3+3x3f+83x2ef-66xyef+6y2ef-352ye2f-39x2f2+86xyf2-15y2f2+1830yef2-1140yf3+30x3-37x2e-27xye+18y2e-658ye2+26x2f+26xyf-3y2f+780yef-443yf2+2x2+9xy-29y2-11ye-221yf-318y

15yef9-3yf10+23ye9-33ye7f2-93ye2f7+27yef8+15yf9-3x2e7+62ye8+6x2e6f-82ye7f-12x2e5f2-3xye5f2-147ye6f2-6x2e2f5+3xye2f5+15x2ef6-366ye2f6-3x2f7-120yef7+120yf8-6x2e6+2xye6+8ye7+21x2e5f-3xye5f-67ye6f-12x2e4f2-3xye4f2-121ye5f2-57x2e2f4+6xye2f4-6x2ef5-3xyef5-405ye2f5+21x2f6-513yef6+225yf7-18x2e5-xye5+97ye6+93x2e4f-4xye4f-233ye5f+3x3e2f2+9x2e3f2-12xye3f2-82ye4f2-93x2e2f3-45xye2f3-81x2ef4+12xyef4+138ye2f4+54x2f5+12xyf5-816yef5+57yf6-3x3e3-36x2e4+21xye4+44ye5+3x3e2f+120x2e3f+41xye3f-120ye4f-3x3ef2-36x2e2f2-49xye2f2-3y2e2f2-215ye3f2-90x2ef3-30xyef3+648ye2f3+39x2f4+33xyf4-277yef4-483yf5+6x3e2-43x2e3-6xye3+3y2e3-455ye4-6x3ef+78x2e2f-66xye2f-3y2e2f-485ye3f+15x3f2-10xyef2+3y2ef2+641ye2f2-27x2f3+33xyf3+1130yef3-1152yf4-18x3e-16x2e2-64xye2-6y2e2-832ye3+3x3f+83x2ef-66xyef+6y2ef-352ye2f-39x2f2+86xyf2-15y2f2+1830yef2-1140yf3+30x3-37x2e-27xye+18y2e-658ye2+26x2f+26xyf-3y2f+780yef-443yf2+2x2+9xy-29y2-11ye-221yf-318y


Bug report: Kernel dies after 1 hour while dividing polynomials

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 second10 seconds.

SAGE 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);


Singular source code:

In Singular you cannot use the operator "/" to divide polynomials, since "non divisible terms" will be discarded and set to zero, see manual https://www.singular.uni-kl.de/Manual/4-0-3/sing_150.htm#SEC189.

So in Singular we have to use the "lift" command to calculate the quotient "poly 1 / poly2":

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);

reduce((x^4 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)/(x + e^5*
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^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), J);

+ f^2;

poly t1 = lift(p2,p1)[1,1];


Singular output:

15yef9-3yf10+23ye9-33ye7f2-93ye2f7+27yef8+15yf9-3x2e7+62ye8+6x2e6f-82ye7f-12x2e5f2-3xye5f2-147ye6f2-6x2e2f5+3xye2f5+15x2ef6-366ye2f6-3x2f7-120yef7+120yf8-6x2e6+2xye6+8ye7+21x2e5f-3xye5f-67ye6f-12x2e4f2-3xye4f2-121ye5f2-57x2e2f4+6xye2f4-6x2ef5-3xyef5-405ye2f5+21x2f6-513yef6+225yf7-18x2e5-xye5+97ye6+93x2e4f-4xye4f-233ye5f+3x3e2f2+9x2e3f2-12xye3f2-82ye4f2-93x2e2f3-45xye2f3-81x2ef4+12xyef4+138ye2f4+54x2f5+12xyf5-816yef5+57yf6-3x3e3-36x2e4+21xye4+44ye5+3x3e2f+120x2e3f+41xye3f-120ye4f-3x3ef2-36x2e2f2-49xye2f2-3y2e2f2-215ye3f2-90x2ef3-30xyef3+648ye2f3+39x2f4+33xyf4-277yef4-483yf5+6x3e2-43x2e3-6xye3+3y2e3-455ye4-6x3ef+78x2e2f-66xye2f-3y2e2f-485ye3f+15x3f2-10xyef2+3y2ef2+641ye2f2-27x2f3+33xyf3+1130yef3-1152yf4-18x3e-16x2e2-64xye2-6y2e2-832ye3+3x3f+83x2ef-66xyef+6y2ef-352ye2f-39x2f2+86xyf2-15y2f2+1830yef2-1140yf3+30x3-37x2e-27xye+18y2e-658ye2+26x2f+26xyf-3y2f+780yef-443yf2+2x2+9xy-29y2-11ye-221yf-318y
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


Bug report: Kernel dies after 1 hour while dividing polynomials

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 10 seconds.

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);


Singular source code:

In Singular you cannot use the operator "/" to divide polynomials, since "non divisible terms" will be discarded and set to zero, see manual https://www.singular.uni-kl.de/Manual/4-0-3/sing_150.htm#SEC189.

So in Singular we have to use the "lift" command to calculate the quotient "poly 1 / poly2":

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];
lift(poly2,poly1)[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

 5 retagged FrédéricC 2539 ●3 ●28 ●53

Bug report: Kernel dies after 1 hour while dividing polynomials

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 10 seconds.

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);


Singular source code:

In Singular you cannot use the operator "/" to divide polynomials, since "non divisible terms" will be discarded and set to zero, see manual https://www.singular.uni-kl.de/Manual/4-0-3/sing_150.htm#SEC189.

So in Singular we have to use the "lift" command to calculate the quotient "poly 1 / poly2":

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(poly2,poly1)[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