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2016-10-03 23:01:20 +0200 | commented answer | number fields and irreducible polynomials Okay, I see. Thank you very much. :-) |

2016-10-03 16:14:14 +0200 | commented answer | number fields and irreducible polynomials Hmm.. That's good information but when I have some more polynomials, it looks hard to control variables. When I want to get the splitting field of |

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2016-10-02 07:26:00 +0200 | asked a question | number fields and irreducible polynomials Hello gentle people. Let's see an example. The extension field of Can I check irreducibility of a polynomial in a number field? Is there any method which makes a number field by given polynomial? Thanks in advance. |

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2015-04-17 16:11:47 +0200 | commented answer | How can I get the coefficient of a Dirichlet series? okay. Thank you very much for your kind answers. :) |

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2015-04-17 06:47:11 +0200 | commented answer | How can I get the coefficient of a Dirichlet series? I found "dirichlet_series.py". It contains "Copyright (C) 2015 Ralf Stephan". Maybe that's the development version you said. But I have some problem. Hmm.. It doesn't work. How to solve that problem? |

2015-04-16 15:28:56 +0200 | commented answer | How can I get the coefficient of a Dirichlet series? That's awesome. Very useful information. Thanks. But I'm not sure how to use the commands in the "Dirichlet_series.sage" in order to (1-3(-s))*zeta__series(n)^2. How to control "s"?? |

2015-04-16 15:11:17 +0200 | commented question | How can I get the coefficient of a Dirichlet series? I see. I edited the title. Thanks. |

2015-04-15 18:10:04 +0200 | asked a question | How can I get the coefficient of a Dirichlet series? Hello. Let's see this example. where f(x) is the Riemann zeta function and x is complex variable. If Re(s) is sufficiently large then g(x) is converges. We only view this g(x) as a formal Dirichlet series. What I want is coefficients. The Riemann zeta function is rewritten by We can also rewrite the g(x) by the sum of For given Is there any helpful sage command ?? Thanks. |

2015-03-27 04:10:08 +0200 | marked best answer | save and load in SAGE Hello. In my case, I am using SAGE in my macbook. For example... At first, I make In terminal, I go to the folder which has And then I load file by using the below command. After some calculations, I make My question is how can I save
It is almost same as ordinary text file. But if I use the command In that case, if I want to change value of before variables then... it is uncomfortable. Is there any good way to save some datas? |

2015-03-27 04:10:07 +0200 | marked best answer | breaking out of while, for loops. Hello. Actually, my problem is to get all new representatives. But I think it is only an algorithmic problem to me. My consideration is following: Let `A` be a group and`Rep=[A]` . And`i=0` Make `i=i+1` and the list`L` of all subgroups with index`2^i` .Make empty list `New` .For `B` in`L` ,**if**`B` is not conjugate to any group in`Rep` then add to`Rep` and add to`New` **else**do nothing.**If**`New` is empty then**return**`Rep` **else**make`New` empty list and go to STEP 2.
How can I do this in SAGE.... I cannot give a simple example. :( In my problem, A=[1,x,x^2], Rep=[A], i=0 (A is a generator of the rank 3 Z-module in Z[x]) i=i+1, L : the list of all submodule of A with index 2^i. New=[] For B in L, [ For C in Rep, t=False, if B~C then t=true. ] If t=False then Rep=Rep+[B] and New=New+[B] If len(New)==0 then return Rep else New=[] and go to STEP 2.
If you have some question I WILL answer as soon as possible. :) Thanks. |

2015-03-27 04:10:07 +0200 | marked best answer | Can I get coefficients of a vector with respect to given basis for a vector space. Hello. I have a question. For example, - make vector space
`V` by a basis`B=[1+x,3*x,x^2]` over the field of rationals`Q` `v=3*x^2+17*x+5` in V`v=a*B[0]+b*B[1]+c*B[2]` for some`a,b,c` in`Q` `[a,b,c]` =?
We easily know the solution of previous example. In general, for given basis And is it possible to the case of matrix space ( Thanks. :) |

2015-03-27 04:09:54 +0200 | marked best answer | How can I get an invertible matrix X with integral entries and AX=XB, where A and B are matrices with integral entries. Let M be the set of all n by n matrices with integral entries. For A and B in M, how can I get an invertible matrix X in M with AX=XB in Sage. I can partially solve that problem in GAP following method. - V={ X in Mn(QQ) | AX=XB }
(V is a vector space over QQ) - Basis(V)={B_1,B_2, ..., B_k}
(I wonder which number k it is according to the changes of A and B.) Make X=a_1 * B_1 + ... +a_k * B_k , a_i in some interval in ZZ. Check two things which are X in Mn(ZZ) and the existence of the inverse of X in Mn(ZZ).
I can find such X for some easy matrices A,B. How can I solve this problem in Sage? Thanks. |

2015-03-27 04:08:59 +0200 | marked best answer | How to get a vector space generated by a list of matrices? Sage is very nice. I want to get a matrix space. For example, - F=GF(p)
- V= " vector space over F generated by [M1, M2, ... ,Mn] ,which Mi are n by n matrices with its coefficients in F "
V consist of matrices. In general, how can I get such V? Many thanks~ |

2015-03-27 04:07:43 +0200 | marked best answer | Can I draw a graph whose vertices have two kind of labels? Hello. I want to draw a graph. Each vertex connects to another information. For example, Then 1,2 --> Dog and 3,4 --> Cat.
Is that possible? Thanks. |

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