| [12] |
|
| [13] |
|
| [4] |
| [5] | [-1*y + x*z^2, y^2*z - x, -1*z + x^2*y, y^3 - x^2*z, -1*z^3 + x*y^2, -1*y*z^2 + x^3, z^4 - x^2] [-1*y + x*z^2, y^2*z - x, -1*z + x^2*y, y^3 - x^2*z, -1*z^3 + x*y^2, -1*y*z^2 + x^3, z^4 - x^2] |
| [6] |
| [7] | Groebner fan of the ideal: Ideal (-1*y + x*z^2, y^2*z - x, -1*z + x^2*y) of Polynomial Ring in x, y, z over Rational Field Groebner fan of the ideal: Ideal (-1*y + x*z^2, y^2*z - x, -1*z + x^2*y) of Polynomial Ring in x, y, z over Rational Field |
| [8] | Ideal (-1*y + x*z^2, y^2*z - x, -1*z + x^2*y) of Polynomial Ring in x, y, z over Rational Field Ideal (-1*y + x*z^2, y^2*z - x, -1*z + x^2*y) of Polynomial Ring in x, y, z over Rational Field |
| [9] | 33 33 |
| [10] | [[-1*z + z^15, -1*z^11 + y, -1*z^9 + x], [z^11 - y, -1*z + y*z^4, -1*z^8 + y^2, -1*z^9 + x], [z^8 - y^2, -1*z + y*z^4, -1*y + y^2*z^3, -1*z^5 + y^3, -1*y^2*z + x], [z^5 - y^3, -1*z + y*z^4, -1*y + y^2*z^3, -1*z^2 + y^4, -1*y^2*z + x], [z^2 - y^4, -1*y + y^6*z, -1*z + y^9, -1*y^2*z + x], [z - y^9, -1*y + y^15, -1*y^11 + x], [z - y^9, y^11 - x, -1*y + x*y^4, -1*y^8 + x^2], [z^2 - y^4, y^2*z - x, -1*z + y^9, -1*y^6 + x*z, -1*y + x*y^4, -1*y^8 + x^2], [z^2 - y^4, y^2*z - x, y^8 - x^2, -1*y^6 + x*z, -1*y + x*y^4, -1*z + x^2*y, -1*y^5 + x^3], [z^2 - y^4, y^2*z - x, y^6 - x*z, -1*y + x*y^4, -1*y^3 + x^2*z, -1*z + x^2*y, -1*y^5 + x^3], [z^2 - y^4, y^2*z - x, y^5 - x^3, -1*y + x*y^4, -1*y^3 + x^2*z, -1*z + x^2*y, -1*y^2 + x^4], [z - x^2*y, y^8 - x^2, -1*y + x*y^4, -1*x + x^2*y^3, -1*y^5 + x^3], [z - x^2*y, y^5 - x^3, -1*y + x*y^4, -1*x + x^2*y^3, -1*y^2 + x^4], [z - x^2*y, y^2 - x^4, -1*x + x^6*y, -1*y + x^9], [z^5 - y^3, -1*z + y*z^4, y^2*z - x, -1*z^2 + y^4, -1*y + x*z^2, -1*z^3 + x*y^2, -1*z^4 + x^2], [z^4 - x^2, y^2*z - x, -1*z^2 + y^4, -1*y + x*z^2, -1*z^3 + x*y^2, -1*y^3 + x^2*z, -1*z + x^2*y, -1*y*z^2 + x^3], [z^3 - x*y^2, y^2*z - x, -1*z^2 + y^4, -1*y + x*z^2, -1*y^3 + x^2*z, -1*z + x^2*y, -1*y*z^2 + x^3], [z^3 - x*y^2, y*z^2 - x^3, y^2*z - x, -1*z^2 + y^4, -1*y + x*z^2, -1*y^3 + x^2*z, -1*z + x^2*y, -1*y^2 + x^4], [z^3 - x*y^2, y*z^2 - x^3, y^2*z - x, y^3 - x^2*z, -1*y + x*z^2, -1*z + x^2*y, -1*y^2 + x^4], [z^8 - y^2, -1*z + y*z^4, y^2*z - x, -1*z^5 + y^3, -1*y + x*z^2, -1*z^6 + x*y, -1*z^4 + x^2], [z^6 - x*y, -1*z + y*z^4, y^2*z - x, -1*z^5 + y^3, -1*y + x*z^2, -1*z^3 + x*y^2, -1*z^4 + x^2], [z^4 - x^2, y^2*z - x, y^3 - x^2*z, -1*y + x*z^2, -1*z^3 + x*y^2, -1*z + x^2*y, -1*y*z^2 + x^3], [z^4 - x^2, y*z^2 - x^3, y^2*z - x, y^3 - x^2*z, -1*y + x*z^2, -1*z^3 + x*y^2, -1*z + x^2*y, -1*y^2 + x^4], [z^4 - x^2, y*z^2 - x^3, y^2 - x^4, -1*y + x*z^2, -1*z + x^2*y, -1*x + x^4*z, -1*z^3 + x^5], [z^3 - x^5, y*z^2 - x^3, y^2 - x^4, -1*y + x*z^2, -1*z + x^2*y, -1*x + x^4*z, -1*y*z + x^6], [z^3 - x^5, y*z - x^6, y^2 - x^4, -1*y + x*z^2, -1*z + x^2*y, -1*x + x^4*z, -1*z^2 + x^8], [z^2 - x^8, y*z - x^6, y^2 - x^4, -1*z + x^2*y, -1*x + x^4*z, -1*y + x^9], [z^2 - x^8, y - x^9, -1*x + x^4*z, -1*z + x^11], [z - x^11, y - x^9, -1*x + x^15], [z^9 - x, -1*z + y*z^4, -1*z^8 + y^2, -1*y + x*z^2, -1*z^6 + x*y, -1*z^4 + x^2], [z^9 - x, y - x*z^2, -1*z + x*z^6, -1*z^4 + x^2], [z^4 - x^2, y - x*z^2, -1*z + x^3*z^2, -1*x + x^4*z, -1*z^3 + x^5], [z^3 - x^5, y - x*z^2, -1*z + x^3*z^2, -1*x + x^4*z, -1*z^2 + x^8]] [[-1*z + z^15, -1*z^11 + y, -1*z^9 + x], [z^11 - y, -1*z + y*z^4, -1*z^8 + y^2, -1*z^9 + x], [z^8 - y^2, -1*z + y*z^4, -1*y + y^2*z^3, -1*z^5 + y^3, -1*y^2*z + x], [z^5 - y^3, -1*z + y*z^4, -1*y + y^2*z^3, -1*z^2 + y^4, -1*y^2*z + x], [z^2 - y^4, -1*y + y^6*z, -1*z + y^9, -1*y^2*z + x], [z - y^9, -1*y + y^15, -1*y^11 + x], [z - y^9, y^11 - x, -1*y + x*y^4, -1*y^8 + x^2], [z^2 - y^4, y^2*z - x, -1*z + y^9, -1*y^6 + x*z, -1*y + x*y^4, -1*y^8 + x^2], [z^2 - y^4, y^2*z - x, y^8 - x^2, -1*y^6 + x*z, -1*y + x*y^4, -1*z + x^2*y, -1*y^5 + x^3], [z^2 - y^4, y^2*z - x, y^6 - x*z, -1*y + x*y^4, -1*y^3 + x^2*z, -1*z + x^2*y, -1*y^5 + x^3], [z^2 - y^4, y^2*z - x, y^5 - x^3, -1*y + x*y^4, -1*y^3 + x^2*z, -1*z + x^2*y, -1*y^2 + x^4], [z - x^2*y, y^8 - x^2, -1*y + x*y^4, -1*x + x^2*y^3, -1*y^5 + x^3], [z - x^2*y, y^5 - x^3, -1*y + x*y^4, -1*x + x^2*y^3, -1*y^2 + x^4], [z - x^2*y, y^2 - x^4, -1*x + x^6*y, -1*y + x^9], [z^5 - y^3, -1*z + y*z^4, y^2*z - x, -1*z^2 + y^4, -1*y + x*z^2, -1*z^3 + x*y^2, -1*z^4 + x^2], [z^4 - x^2, y^2*z - x, -1*z^2 + y^4, -1*y + x*z^2, -1*z^3 + x*y^2, -1*y^3 + x^2*z, -1*z + x^2*y, -1*y*z^2 + x^3], [z^3 - x*y^2, y^2*z - x, -1*z^2 + y^4, -1*y + x*z^2, -1*y^3 + x^2*z, -1*z + x^2*y, -1*y*z^2 + x^3], [z^3 - x*y^2, y*z^2 - x^3, y^2*z - x, -1*z^2 + y^4, -1*y + x*z^2, -1*y^3 + x^2*z, -1*z + x^2*y, -1*y^2 + x^4], [z^3 - x*y^2, y*z^2 - x^3, y^2*z - x, y^3 - x^2*z, -1*y + x*z^2, -1*z + x^2*y, -1*y^2 + x^4], [z^8 - y^2, -1*z + y*z^4, y^2*z - x, -1*z^5 + y^3, -1*y + x*z^2, -1*z^6 + x*y, -1*z^4 + x^2], [z^6 - x*y, -1*z + y*z^4, y^2*z - x, -1*z^5 + y^3, -1*y + x*z^2, -1*z^3 + x*y^2, -1*z^4 + x^2], [z^4 - x^2, y^2*z - x, y^3 - x^2*z, -1*y + x*z^2, -1*z^3 + x*y^2, -1*z + x^2*y, -1*y*z^2 + x^3], [z^4 - x^2, y*z^2 - x^3, y^2*z - x, y^3 - x^2*z, -1*y + x*z^2, -1*z^3 + x*y^2, -1*z + x^2*y, -1*y^2 + x^4], [z^4 - x^2, y*z^2 - x^3, y^2 - x^4, -1*y + x*z^2, -1*z + x^2*y, -1*x + x^4*z, -1*z^3 + x^5], [z^3 - x^5, y*z^2 - x^3, y^2 - x^4, -1*y + x*z^2, -1*z + x^2*y, -1*x + x^4*z, -1*y*z + x^6], [z^3 - x^5, y*z - x^6, y^2 - x^4, -1*y + x*z^2, -1*z + x^2*y, -1*x + x^4*z, -1*z^2 + x^8], [z^2 - x^8, y*z - x^6, y^2 - x^4, -1*z + x^2*y, -1*x + x^4*z, -1*y + x^9], [z^2 - x^8, y - x^9, -1*x + x^4*z, -1*z + x^11], [z - x^11, y - x^9, -1*x + x^15], [z^9 - x, -1*z + y*z^4, -1*z^8 + y^2, -1*y + x*z^2, -1*z^6 + x*y, -1*z^4 + x^2], [z^9 - x, y - x*z^2, -1*z + x*z^6, -1*z^4 + x^2], [z^4 - x^2, y - x*z^2, -1*z + x^3*z^2, -1*x + x^4*z, -1*z^3 + x^5], [z^3 - x^5, y - x*z^2, -1*z + x^3*z^2, -1*x + x^4*z, -1*z^2 + x^8]] |
| [11] |
|
| [14] |
|
Name:
Password: X
X
Saved Objects
Variables
G (sage.rings.groebner_fan.GroebnerFan) I (sage.rings.multi_polynomial_ideal.MPolynomialIdeal) R (list) x (sage.rings.multi_polynomial_element.MPolynomial_polydict) y (sage.rings.multi_polynomial_element.MPolynomial_polydict) z (sage.rings.multi_polynomial_element.MPolynomial_polydict) Attached Files
|