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2021-06-10 16:56:16 +0100 | marked best answer | Pass a list of variable names as parameter to a polynomial ring I am trying to write a function that compute a vector space basis $B$ for the quotient ring $k[x_1,\dots,x_n]/I$. I want to make the list of variables as the input parameter. I tried this: It gave me error message. I also tried or None of them works. I know that works. So I can just type this before I run my function. But is there a way that I can make this as input of the function? |
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2021-02-02 22:28:26 +0100 | marked best answer | Solving polynomial equations with Groebner basis in $\mathbb{R}$ I am trying to solve the following system of polynomial equations: $$x^2+y^2+z^2=4\ x^2+2y^2=5\ xz=1$$ I used the following command to get a Groebner basis Now I want to use B.subs() to plug the solutions for $z$ to solve for $x,y$. It worked well for $z=\pm 1$. but not for the $1/\sqrt{2}$ since this is in polynomial ring $\mathbb{Q}[x,y,z]$. If I change the original QQ to RR, the numbers become all decimals. How can I still get exact solutions when using RR? I know I can compute this example by hands, but I'd like to know how to use Sage to solve this kind of problems. Thank you for any help! |
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2017-09-18 20:26:56 +0100 | 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 21:09:49 +0100 | 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 12:09:57 +0100 | 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 21:22:32 +0100 | 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 18:57:56 +0100 | 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 11:34:27 +0100 | 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? |
2017-04-15 11:18:18 +0100 | commented answer | Division algorithm in a polynomial ring with variable coefficients Thank you for the detailed answer! It worked! |
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2017-03-27 21:26:48 +0100 | 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! |
2017-03-27 21:13:38 +0100 | marked best answer | 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! |
2017-03-13 11:19:06 +0100 | commented answer | The computation of Groebner basis not correct? I realized I forgot to put |
2017-03-12 22:44:16 +0100 | 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 20:59:54 +0100 | 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 |