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2020-08-13 13:45:18 -0500 | asked a question | In Sage Notebook, does sage compile all programs in a cell ? Sometimes, in Sagenotebook, when I put many programs in the same cell, for example, the definition of a class, methods within this class and functions , it seems that Sage compiles the class defintions and methods, but ignores the functions. |

2020-08-13 08:13:18 -0500 | marked best answer | does sage allow computation of a groebner basis of an ideal J in the quotient ring Z/pZ[X_1,...X_r]/I? I define the following rings and ideals: I then compute: and examine the result of that computation: Is it really the Groebner basis of Did Sage really compute in A/I and not in A? |

2020-08-13 08:12:03 -0500 | marked best answer | how to delete all programs, inputs and output in the sage console ? I've tried all commands I know : reset(), !clear, %clear i, -ipython history clear, ipython history trim, --ipython locate profile default to clear history in my sage console but all of these do not work , , |

2020-08-13 08:11:00 -0500 | marked best answer | may an object in sage lose its type in a method within a class ? Many thanks to @slelievre for his response and to @tmonteil for his comments. Here is the original Sage code. It and a little bit long but perhaps all these are useful to see what goes wrong: In the fonction "CCODE", when constructing the objet "CORPS" by |

2020-08-13 08:10:15 -0500 | marked best answer | how to evaluate a polynomial in a quotient ring ? I define a polynomial ring and its quotient by an ideal: I define an element in this quotient ring: I want to evaluate this element at $(x, y, z) = (2, 3, 4)$. I tried this, and got this error message: How can I calculate |

2020-08-13 08:09:27 -0500 | marked best answer | how to get the coefficient of a multivariate polynomial with respect to a specific variable and degree, in a quotient ring ? Here is what I tried. |

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2020-08-13 08:06:32 -0500 | marked best answer | How to make Sage know that a set is an ideal I have constructed the following ideal in the ring $$ R = F[X,Y,Z]/(X^2-1,Y^2-1,Z^2-1) $$ where $F=GF(3)$ and $x$ (resp; $y$, $z$) is the residue class of $X$ (resp. $Y$, $Z$) modulo the ideal $(X^2-1, Y^2-1, Z^2-1)$. By its construction, the set $J$ is indeed an ideal, containing 2187 elements, so it is hard to write or copy all its elements. I want to find a Groebner basis of $J$, by writing but Sage returns This error seems to mean that Sage doesn' t remember that $J$ is the above set anymore and consider $J$ as an inappropriate new objet of a new ring $R$! I must first construct the ideal and then compute That works, but, as I previously said, it is not easy to construct the ideal $H$ because that needs copy and paste 2187 elements! Therefore I'd like to know whether there is another way to the task, without copying and pasting all of the elements of $J$, and declaring the ideal of these elements, is there a way to convert a set of elements in a ring (which is already an ideal) to the underlying ideal? |

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2020-08-13 03:55:15 -0500 | commented question | How to make Sage know that a set is an ideal Strangely, when I write the Sage programs in the text editor of Asksage, the line containing "def" (for example def vect2pol(c,Vars in the preceeding code) is outside of the box containing the remaining part of the program. Can you explain how to correct it ? |

2020-08-13 03:45:33 -0500 | commented answer | How to make Sage know that a set is an ideal Strangely, the method groebner_basis() works for an ideal in the quotient ring R (see the above example, in the comments in response to slelievre). Perhaps, as you have said, Sage use the lift() method to compute a GrÃ¶bner basis in $F3[X,Y,Z]$ and the returned to $R$. I was confused when I first used this for ideals in quotient ring, this is why I asked the question "Does sage allow computation of a groebner basis of an ideal J in the quotient ring Z/pZ[X_1,...X_r]/I? |

2020-08-13 03:35:49 -0500 | commented question | How to make Sage know that a set is an ideal The set $J$ is then those of the polynomials of $R$ which vanishes on ${(1,2,1)}$ (It may be not be equal to the initial $J$ in my question), but that doesn't matter, it also contains 2187 elements). Using the command nbruin gave below, I entered J1=ideal(*J);J1 B=J1.groebner_basis();B and Sage returned [x - 1, y + 1, z - 1]. The problem is solved : $J1$ is the ideal whose elements are the same as those of $J$ and no copy and paste were needeed! |

2020-08-13 02:55:22 -0500 | commented question | How to make Sage know that a set is an ideal For the construction of the POLS, I used the following program : def vect2pol(c,Vars): where : c is a tuple of an element from a finite field Vars a list of monomials with the same length as c for example list2pol((1, 2, 1, 2, 0, 0, 1, 1),[1, z, y, y produces x In my case, POLS is the list of elements of $R$. I first construct the cartesian product $F3^8$ : S=Set(list(cartesian_product([F3]*8))). Then I apply the function vect2pol to the elements of S, with Vars =[1, z, y, y POLS={vect2pol(c,Vars) for c in S ... (more) |

2020-08-13 02:30:05 -0500 | commented answer | How to make Sage know that a set is an ideal Thank you very much, the command you give works : using the ideal $J$ from above, I write H=ideal(*J) then B =H.groebner_basis() and Sage return the result! No copy and paste of the elements of $J$ are needed, wonderful ! |

2020-08-13 00:21:28 -0500 | commented question | How to make Sage know that a set is an ideal Thank for your remarks, the set $F$ is the finite field $GF(3)$ as you knew. The ideal $J$ is a "multicyclic code" of dimension $3$, and is equal the set of polynomials of $R$ which vanishes on a finite subset of $F^3$. Here is the code : def code(POLS,ZER): In my case, POLS is the set of polynomials of $R$ ( of degree $\leqslant (1,1)$, using the lexicographical order) and ZER a subset of $F^3$ consisting of a unique element. More time is needed to provide the codes for constructing POLS, I will provide these latter on. |

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