2019-12-06 15:51:39 -0600 | commented question | Solve set of equations with all unique values in sage Can you add the set of equations? Select your code and press the '101010' button to format it correctly. |

2019-12-05 13:45:39 -0600 | answered a question | How to use a string in a symbolic expression with SageMath? I would re-evaluate whether using strings is really what you want to do; probably whatever problem you have can be solved in a better way. Nevertheless, it is possible: |

2019-12-05 10:05:38 -0600 | received badge | ● Nice Answer (source) |

2019-12-05 05:38:56 -0600 | answered a question | How can I define a field of numbers by hitting to the field of rationals two roots of the same polynomial ? Note number fields in SageMath are abstract extensions of $\mathbb{Q}$; they come with several embeddings into $\mathbb{C}$; see below. Option 1 (number field from algebraic numbers): For other options, let's first find what polynomial we are talking about: Option 2 (splitting field): Option 3 (successive extensions): You can also make an absolute extension from the relative one: |

2019-11-27 02:13:32 -0600 | commented question | conditions among the variables @user789 if that's all, then just substitute e.g. $e=a+b-d$ into your polynomial. |

2019-11-23 05:45:07 -0600 | commented question | How to count rational points of a curve defined as an intersection of two zero sets? How can the first equation have any rational solutions? |

2019-11-22 04:37:07 -0600 | commented answer | Sagemath and TI-83 giving different answers Probably OP wants to know why taking the cube root in SageMath yields this particular root and not the real root. |

2019-11-20 07:28:10 -0600 | answered a question | Do newer versions change the way 'simplify' works? When you make a vague request (e.g. 'simplify'), there is a risk that the answer will change if you ask it again. Unfortunately I don't know what has changed or why. Maybe e.g. using I am guessing that you are interested in the expression as a polynomial in $x,y,Z$. A precise way to request the expression in that form is as follows (using polynomial rings): You could also factor each coefficient: |

2019-11-20 05:33:03 -0600 | commented answer | Why SageMath cannot inverte this matrix? You're welcome. That it takes a long time doesn't mean SageMath is not able to do it. Your original code works on my machine; it took 1 hour and 12 minutes. |

2019-11-19 10:31:51 -0600 | commented question | conditions among the variables This can be done (with some effort) in many cases, depending on the type of condition. Are the conditions linear equations, polynomial equations, trigonometric equations? An example would be great. |

2019-11-18 08:49:06 -0600 | commented question | simple script gives "ValueError: element is not in the prime field" The error depends on the information you've omitted, such as the definition of |

2019-11-17 17:05:04 -0600 | received badge | ● Nice Answer (source) |

2019-11-16 10:39:38 -0600 | commented answer | Why SageMath cannot inverte this matrix? It is working, but there seems to be some kind of bug in displaying the algebraic numbers. For example if you define |

2019-11-16 06:36:53 -0600 | answered a question | Why SageMath cannot inverte this matrix? Since $\bar{\mathbb{Q}}$ is a little big, try instead working in a number field $K$ that's big enough but as small as possible: Here $K$ is an abstract number field of degree $48$ with several (i.e. $48$) different embeddings into $\bar{\mathbb{Q}}$. For a given |

2019-11-15 04:17:53 -0600 | commented question | Sage 8.1 on Mint 19.2 doesn't start Those look like dependencies, yes. What is the issue with them? What is invalid? |

2019-11-15 03:01:35 -0600 | commented question | Sage 8.1 on Mint 19.2 doesn't start Please be more precise about the dependency issue (for the .deb file). |

2019-11-12 09:39:41 -0600 | answered a question | Vector multiplication For one, because you can't transpose $$e^{\left(-0.50 \delta_{0} + 0.19 \delta_{1} + 0.25 \delta_{2}\right)}$$ (Note that you specified 2 |

2019-11-09 02:21:35 -0600 | commented question | How to create a subgroup with MAGMA inside SAGE of a group created with MAGMA inside SAGE? Assuming that the rest of the code is correct, the issue is that you use the text |

2019-11-06 13:28:32 -0600 | answered a question | Bug report (z[0]+z[1]+z[2])^5 == z0^5 + z1^5 + z2^5 This is not a bug. Note the divisibility by 5 of all terms which are "missing" in your characteristic $p=5$ calculation. This is a consequence of the Freshman's dream: $(x+y)^p \equiv x^p + y^p \pmod p$; just apply it twice. It looks too good to be true, but it really is true in characteristic $p$ (the proof is in the linked article). |

2019-11-06 13:16:48 -0600 | commented question | maximizing sum over feasible set of vectors I didn't ask the question, but yes that's right. The binary ordering was just a (natural) suggestion. Of course the ordering is irrelevant, but probably some ordering is necessary for the implementation. |

2019-11-06 05:38:39 -0600 | commented question | maximizing sum over feasible set of vectors $|A|$ means the number of elements in $A$. To have $\underline{\alpha}$ be a vector one should choose an ordering of the (nonempty) subsets of $[5]$, e.g. by identifying them with binary strings of length 5 (not equal to $00000$). |

2019-10-31 04:50:03 -0600 | commented question | How to solve this algebraic equation by SageMath (rather than by hand) The relation $r^2u^4 - (a^2 + r^2 + t^2)u^2 + t^2 = 0$ holds. |

2019-10-30 14:31:49 -0600 | received badge | ● Nice Answer (source) |

2019-10-30 11:04:37 -0600 | answered a question | Plotting polynomials defined over a number field You have the right idea: do You might also like: |

2019-10-25 02:43:38 -0600 | answered a question | How can I map functions into polynomial coefficients Here is a way: Note the generators of the ring To get the coefficient of Or maybe more conveniently, something like: |

2019-10-22 07:06:00 -0600 | commented question | About algorithm for testing whether a point is in a V-polyhedron This may depend on the |

2019-10-22 04:01:22 -0600 | answered a question | Elliptic curves - morphism You can do this: |

2019-10-16 07:03:11 -0600 | commented answer | Finite field F_16=F_4[y]/(y**2+xy+1) (where F_4=F_2[x]/(x**2+x+1)) To avoid constructing the list you could use |

2019-10-15 16:12:33 -0600 | received badge | ● Nice Answer (source) |

2019-10-15 03:17:54 -0600 | commented question | how do I find kernel of a ring homomorphism? Please add a code sample including a definition of |

2019-10-15 02:47:06 -0600 | answered a question | Verma modules and accessing constants of proportionality Not sure if it's the best way, but you can do the following: |

2019-10-11 09:04:06 -0600 | answered a question | Adapt the nauty_directg function Entering In this case it simply calls an external program You can download and edit that program's source code, compile your new version, and call that one instead. To edit the source code you should start by looking at the file |

2019-10-05 03:49:37 -0600 | commented answer | uniform way to iterate over terms of uni-/multi-variate polynomials It's not very nice to change your question when it has received a correct answer, even if you suffered from the XY problem. Anyway, I updated the answer. In the future, please ask the new question separately (and link to the previous question). |

2019-10-04 02:00:03 -0600 | answered a question | uniform way to iterate over terms of uni-/multi-variate polynomials Define This ring (and its elements) will have different methods than the ordinary univariate ring (elements). Alternatively: keep your original ring, define An answer to the new question: Then you can do: |

2019-10-04 01:45:45 -0600 | commented answer | Request: Have the len function output a Sage Integer instead of a Python int Ah, there is a subtlety with |

2019-10-03 00:02:21 -0600 | commented answer | Request: Have the len function output a Sage Integer instead of a Python int It is not a bug. One should be aware of the difference between |

2019-10-02 09:20:41 -0600 | answered a question | Request: Have the len function output a Sage Integer instead of a Python int In the second part you are using Python Use |

2019-09-22 04:02:01 -0600 | answered a question | Defining q-binomial coefficients $\binom{n}{k}_q$ symbolic in $n, k$ If you want to make a symbolic sum then all the terms should be symbolic. Your example does not work because What you can do is to make $$\sum_{k=0}^{n} {n \choose k}_{q}$$ To check the identities that you are interested in, you will probably have to do some substitutions by hand, and/or pass an |

2019-09-22 03:42:51 -0600 | answered a question | Change of programmation of implicit It seems that you want the following: Output: |

2019-09-20 02:35:00 -0600 | answered a question | Wrong hessian The matrix you constructed by hand doesn't look like a Hessian to me. Here is the Hessian: $$\left(\begin{array}{rrr} A {\left(\alpha - 1\right)} \alpha x^{\alpha - 2} y^{\beta} & A \alpha \beta x^{\alpha - 1} y^{\beta - 1} & -p_{x} \\ A \alpha \beta x^{\alpha - 1} y^{\beta - 1} & A {\left(\beta - 1\right)} \beta x^{\alpha} y^{\beta - 2} & -p_{y} \\ -p_{x} & -p_{y} & 0 \end{array}\right)$$ |

2019-09-18 04:02:51 -0600 | commented question | How sage checks the irreducibility of a polynomial? Polynomial in one variable? Over which ring? |

2019-09-16 11:21:06 -0600 | answered a question | Check whether point is on a projective variety Sure, you can take a point from the ambient projective space and do a membership test: Internally this does a |

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