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2019-02-21 14:16:28 +0200 | commented answer | Given a value and conditions, find a matrix with that value as its determinant Amazing, thank you! I'm very much a novice in Sage and Python, and have yet to dedicate time to trying to learn it properly, instead opting to just piece things together as and when. Think it might be time for me to go to basics.. |

2019-02-21 13:01:41 +0200 | asked a question | Given a value and conditions, find a matrix with that value as its determinant I'm not sure if the title is named too obscurely, so I'll give an example of what I'm talking. Say we have an integer matrix: M= 0 a b 0 (sorry for weird formatting; cannot seem to write matrices properly on here - any help with that as well? :P ) I want to find all values $(a,b) \in (-2,-1,0,1,2)$ such that $det(M)=2$. I've tried the following but I'm not sure how to finish it off / if this is the right way to go: As I say, I feel like the start would be a good way to go, but I'm stuck when reaching Any help would be great! |

2019-02-08 14:19:20 +0200 | commented answer | Minimal determinant of a matrix with varied entries Amazing; that makes sense and works perfectly for what I'm after. Thank you again! |

2019-02-08 12:02:35 +0200 | commented answer | Minimal determinant of a matrix with varied entries Yes, that's very much what I'm after - thank you! Couple of questions so I can check I understand the code: Why do we set Say I wanted to see the minimal value which was larger than a set number (say 1); presumably I would change the zero in this part of the code to a 1: (I know the matrix I've used isn't the best example for checking that!) |

2019-02-08 11:05:15 +0200 | asked a question | Minimal determinant of a matrix with varied entries I would like Sage to tell me to minimal value of the determinant of a matrix when a vary some entries over a set range. For example, say with the 4x4 matrix A (sorry for weird layout, I can't get the Latex code to work properly?): 0 1 i j 1 0 1 k 0 1 0 1 0 0 1 0 I'd like to know, for ${i,j,k} \in {0, \pm1}$, what the smallest non-trivial determinant is, and for which combination(s) of $i,j,k$ this is for. I'm still pretty new to Sage, so I'm a bit unsure of how to do this effectively, if it is at all possible to do this? Side note: I know I could of course write and this would give me the value of the determinant in terms of $i,j,k$. And in this example that would likely be much easier. The idea is that I'd like to do this with larger matrices (that aren't as nice as this), more variables, etc. It would obviously be nicer to have have Sage simply compute the smallest determinant and give the corresponding values for the variables than me have to plug it in. |

2019-02-01 12:33:43 +0200 | commented answer | Product of elements in a set Wow - the one thing I didn't try, and it was the simplest thing! Thank you. |

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2019-02-01 11:06:01 +0200 | asked a question | Product of elements in a set I have a set of numbers, and I would like to find the product of them. Generally speaking, the set of the numbers could be quite large, and will be complex, so I don't want to have to manually multiply them all. The example I have below only has 3 integer elements though.. My original thinking was something along the lines of: But I'm not sure how to: 1) define s[i] appropriately or 2) if this will work I assume at some point I need to define I'm working in a complex field, but again, I'm not sure where I would need to do that? |

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2019-01-18 10:11:45 +0200 | commented answer | Multiplying Roots of a Polynomial Thank you - this is perfect for what I'm after! |

2019-01-17 16:00:04 +0200 | asked a question | Multiplying Roots of a Polynomial Hello - I'm new to SAGE, so trying to get to grips with the basics! I have a polynomial $f = x^{2}((x+\frac{1}{x})^{2} - 1) $. I would like to be able to do to things: 1) See $f$ in the form $\beta(x - \alpha_1)(x-\alpha_2)(x-\alpha_3)(x-\alpha_4)$ 2) Know the value of $\beta (\prod_i \alpha_i)$ Using
Does not give me the linear factorisation, nor can I see a simple way of getting the product of the roots. In the long term I'm hoping to do this for polynomials of larger degree, so any advice would be great! |

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