382 | | Rational Field, |
383 | | Ideal (a - 1, b^4 + b^3 + b^2 + b + 1, c - b^2, d - b^3, e |
384 | | + b^3 + b^2 + b + 1) of Multivariate Polynomial Ring in e, |
385 | | d, c, b, a over Rational Field, |
386 | | Ideal (a - 1, b^2 + 3*b + 1, c + b + 3, d - 1, e - 1) of |
| 384 | Rational Field, Ideal (a - 1, b^2 + 3*b + 1, c + b + 3, d |
| 385 | - 1, e - 1) of Multivariate Polynomial Ring in e, d, c, b, |
| 386 | a over Rational Field, Ideal (a^4 + a^3 + a^2 + a + 1, b - |
| 387 | 1, c + a^3 + a^2 + a + 1, d - a^3, e - a^2) of |
388 | | Rational Field, |
389 | | Ideal (a^4 + a^3 + a^2 + a + 1, b - 1, c + a^3 + a^2 + a + |
390 | | 1, d - a^3, e - a^2) of Multivariate Polynomial Ring in e, |
391 | | d, c, b, a over Rational Field, Ideal (a^4 + a^3 + a^2 + a |
392 | | + 1, b - a, c - a, d^2 + 3*d*a + a^2, e + d + 3*a) of |
393 | | Multivariate Polynomial Ring in e, d, c, b, a over |
394 | | Rational Field, |
| 389 | Rational Field, Ideal (a^4 + a^3 + a^2 + a + 1, b - a, c - |
| 390 | a, d^2 + 3*d*a + a^2, e + d + 3*a) of Multivariate |
| 391 | Polynomial Ring in e, d, c, b, a over Rational Field, |
397 | | d, c, b, a over Rational Field, |
398 | | Ideal (a^4 + a^3 + a^2 + a + 1, b^3 + b^2*a + b^2 + b*a^2 |
399 | | + b*a + b + a^3 + a^2 + a + 1, c + b^2*a^3 + b^2*a^2 + |
400 | | b^2*a + b^2, d - b^2*a^2 - b^2*a - b^2 - b*a^2 - b*a - |
401 | | a^2, e - b^2*a^3 + b*a^2 + b*a + b + a^2 + a) of |
| 394 | d, c, b, a over Rational Field, Ideal (a^4 + a^3 + a^2 + a |
| 395 | + 1, b^3 + b^2*a + b^2 + b*a^2 + b*a + b + a^3 + a^2 + a + |
| 396 | 1, c + b^2*a^3 + b^2*a^2 + b^2*a + b^2, d - b^2*a^2 - |
| 397 | b^2*a - b^2 - b*a^2 - b*a - a^2, e - b^2*a^3 + b*a^2 + b*a |
| 398 | + b + a^2 + a) of Multivariate Polynomial Ring in e, d, c, |
| 399 | b, a over Rational Field, Ideal (a^4 + a^3 + a^2 + a + 1, |
| 400 | b^2 + 3*b*a + a^2, c + b + 3*a, d - a, e - a) of |
403 | | Rational Field, |
404 | | Ideal (a^4 + a^3 + a^2 + a + 1, b^2 + 3*b*a + a^2, c + b + |
405 | | 3*a, d - a, e - a) of Multivariate Polynomial Ring in e, |
406 | | d, c, b, a over Rational Field, |
407 | | Ideal (a^4 + a^3 + 6*a^2 - 4*a + 1, 11*b^2 - 6*b*a^3 - |
408 | | 10*b*a^2 - 39*b*a - 2*b - 16*a^3 - 23*a^2 - 104*a + 24, |
409 | | 11*c + 3*a^3 + 5*a^2 + 25*a + 1, 11*d + 3*a^3 + 5*a^2 + |
410 | | 25*a + 1, 11*e + 11*b - 6*a^3 - 10*a^2 - 39*a - 2) of |
411 | | Multivariate Polynomial Ring in e, d, c, b, a over |
412 | | Rational Field, |
413 | | Ideal (a^4 - 4*a^3 + 6*a^2 + a + 1, 11*b^2 - 6*b*a^3 + |
414 | | 26*b*a^2 - 41*b*a + 4*b + 8*a^3 - 31*a^2 + 40*a + 24, 11*c |
415 | | + 3*a^3 - 13*a^2 + 26*a - 2, 11*d + 3*a^3 - 13*a^2 + 26*a |
416 | | - 2, 11*e + 11*b - 6*a^3 + 26*a^2 - 41*a + 4) of |
417 | | Multivariate Polynomial Ring in e, d, c, b, a over |
418 | | Rational Field, |
419 | | Ideal (a^2 + 3*a + 1, b - 1, c - 1, d - 1, e + a + 3) of |
420 | | Multivariate Polynomial Ring in e, d, c, b, a over |
421 | | Rational Field, Ideal (a^2 + 3*a + 1, b + a + 3, c - 1, d |
422 | | - 1, e - 1) of Multivariate Polynomial Ring in e, d, c, b, |
423 | | a over Rational Field] |
| 402 | Rational Field, Ideal (a^4 - 4*a^3 + 6*a^2 + a + 1, 11*b^2 |
| 403 | - 6*b*a^3 + 26*b*a^2 - 41*b*a + 4*b + 8*a^3 - 31*a^2 + |
| 404 | 40*a + 24, 11*c + 3*a^3 - 13*a^2 + 26*a - 2, 11*d + 3*a^3 |
| 405 | - 13*a^2 + 26*a - 2, 11*e + 11*b - 6*a^3 + 26*a^2 - 41*a + |
| 406 | 4) of Multivariate Polynomial Ring in e, d, c, b, a over |
| 407 | Rational Field, Ideal (a^4 + a^3 + 6*a^2 - 4*a + 1, 11*b^2 |
| 408 | - 6*b*a^3 - 10*b*a^2 - 39*b*a - 2*b - 16*a^3 - 23*a^2 - |
| 409 | 104*a + 24, 11*c + 3*a^3 + 5*a^2 + 25*a + 1, 11*d + 3*a^3 |
| 410 | + 5*a^2 + 25*a + 1, 11*e + 11*b - 6*a^3 - 10*a^2 - 39*a - |
| 411 | 2) of Multivariate Polynomial Ring in e, d, c, b, a over |
| 412 | Rational Field, Ideal (a^2 + 3*a + 1, b - 1, c - 1, d - 1, |
| 413 | e + a + 3) of Multivariate Polynomial Ring in e, d, c, b, |
| 414 | a over Rational Field, Ideal (a^2 + 3*a + 1, b + a + 3, c |
| 415 | - 1, d - 1, e - 1) of Multivariate Polynomial Ring in e, |
| 416 | d, c, b, a over Rational Field] |