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2017-09-18 13:26:56 -0500 | commented answer | Remove a variable from a polynomial ring k(a,b)[x1,x2,x0] where a,b are parameters Thank you! That worked! How do we report the error? |

2017-09-01 14:09:49 -0500 | asked a question | Remove a variable from a polynomial ring k(a,b)[x1,x2,x0] where a,b are parameters I am trying to homogenize polynomials using variable After homogenization, I define the new polynomial ring with block order: Then in my program, I need to dehomogenize my polynomials by setting However, with the fraction field I didn't copy down the whole error message so it doesn't look so long. Is there a way to fix this? Thank you for your help! |

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2017-05-06 05:09:57 -0500 | commented question | Insert children of a specified node in a binary tree and retrieve all leaves of a binary tree. Yes, you are right. I didn't link the one with "insert" since it does not provide me the functionality I was looking for. So I found another one, which does not have "insert", and still cannot do anything since it does not provide a value for each node. Now I decide I should just make a "recursive list" to achieve my goal. It seems Sage does not have a good Binary Tree implementation, at least for my purpose. Thank you for your time! |

2017-05-04 14:22:32 -0500 | asked a question | Insert children of a specified node in a binary tree and retrieve all leaves of a binary tree. I am trying to use a binary tree to store data. When different cases happens at some step, I will need to create two children from the current node. I also need to collect all information on the leaves (nodes with no children). I use the following definition of binary trees: I can insert node the following way: But I couldn't find a way to visualize the tree. Also I don't know how to add two children of one certain node. For example, if I also looked at this page: (http://doc.sagemath.org/html/en/refer...). I couldn't see how to insert a node with values in it, or how to retrieve information of leaves. Do I have to define my own tree structure? Thank you for your help! |

2017-04-20 11:57:56 -0500 | commented question | How to compute syzygy module of an ideal in a quotient ring? That is a very smart solution. Thank you very much! |

2017-04-18 04:34:27 -0500 | asked a question | How to compute syzygy module of an ideal in a quotient ring? I am trying to compute the syzygy module of an ideal generated by two polynomials But this does not work with modulo Is there a way to do that? |

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2017-04-15 04:18:18 -0500 | commented answer | Division algorithm in a polynomial ring with variable coefficients Thank you for the detailed answer! It worked! |

2017-03-27 14:26:48 -0500 | asked a question | Division algorithm in a polynomial ring with variable coefficients I am working on an algorithm to divide a polynomial Here is an example of implementing the algorithm: Here is the result: and some other error messages. We can see that it worked well until the leading term is It gives the answer It gives error message. Is there a way to solve this? Thank you for your help! |

2017-03-13 05:19:06 -0500 | commented answer | The computation of Groebner basis not correct? I realized I forgot to put |

2017-03-12 16:44:16 -0500 | commented answer | The computation of Groebner basis not correct? Thanks for your answer! I never set parameters. So what is the default? I thought 'lex' means lexicographical order, with whichever order placed in the '< >'. I will check the instructions. |

2017-03-12 14:59:54 -0500 | asked a question | The computation of Groebner basis not correct? I was trying to compute a Groebner basis for the ideal I used the following code: The result is Since the computation is easy, I checked by hands but got different result. So I checked by Singular and got the same result as mine, which is So the result from Sage is wrong, since |

2017-02-28 16:53:33 -0500 | commented question | Computing square free part of a multivariate polynomial Do you mean an example? For example, if |

2017-02-28 14:49:14 -0500 | asked a question | Computing square free part of a multivariate polynomial In one of the algorithms I am working on, there is a part asking for the square-free part of a multivariate polynomial. I can find it using a complicated way, namely, But I think this must be a very inefficient way to do it. Is there a better way? Thank you! |

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2016-05-24 08:27:09 -0500 | edited question | Find the kernel of a matrix $A$ and make it a matrix. I am trying to write a function that computes the monic genrator of an ideal $I\in k[x_1,\dots,x_n]$, i.e., the generator of $I\cap k[x_i]$ for each $i$. For this I need to use linear algebra for the set $${1, x_i, x_i^2,\dots}$$ I write each one of them in terms of the basis for the quotient ring $k[x_1,\dots,x_n]/I$, and see if they are linearly dependent. Since I add in one more power a time, when I find a linearly dependent set, it should have nullity $1$. So if I can get the one element in basis of the kernel, I am done. But the $A.kernel()$ command in Sage gives me this: Is there a way to assign it as a vector using the kernel command? Or do I have to write my own function to implement it? Thank you for your help! |

2016-05-24 08:26:51 -0500 | commented answer | Find the kernel of a matrix $A$ and make it a matrix. Thank you. This works perfectly. And I am pretty sure I'll have one element in the basis. But I'll change the title. One more question, I also defined matrix A using "A=matrix(...)" and it worked. But after I tried import scipy, it does not work anymore. I have to do "A=Matrix(...)" instead. Since I don't want to use scipy anymore, is there a way to "export" this package? |

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