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2019-06-29 19:01:11 +0100 | asked a question | Calculating Cauchy Integrals in Sage Hi! I am relatively new to complex analysis and I am trying to write down the following integral in Sage Math: $$ I(k) = \frac{1}{2i\pi}\oint\frac{(1-t^2)}{(1-t)^n}\frac{dt}{t^{k+1}} $$ from a paper that can be found at: http://magali.bardet.free.fr/Publis/l... The contour is a unit circle around the origin with a radius less than 1. whereby $$S(n) = \frac{(1-t^2)}{(1-t)^n} $$ is a formal power series. The Cauchy Integral will produce the k-th coefficient of $S(n)$. I tried doing the following: I realize this is probably Thank you! |

2018-11-30 17:10:57 +0100 | commented answer | Reduction In Quotient Rings (x^2 - x = 0) Perfect! Thank you, you've saved me a considerable amount of time by not having to lift all my polynomials to a quotient ring |

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2018-11-30 09:38:24 +0100 | commented question | Reduction In Quotient Rings (x^2 - x = 0) Ok, I believe that by doing it works. But this can make the code quite ugly if I need to work exclusively with this Q...is there a better way of doing this, please? |

2018-11-30 09:38:24 +0100 | asked a question | Reduction In Quotient Rings (x^2 - x = 0) Hi, Thank you for taking the time to read this, it is very much appreciated. My question concerns how to ensure that a polynomial within a quotient ring has the following property: whereby x is any variable in the quotient ring and k is a positive integer. This is the way I tried to go about the situation: I created a polynomial ring Since I am not working within a quotient ring, x^2 (or any of the other three variables) does not 'become' 0. Since I would like the property of x^2 = 0, I decided to create a quotient ring with some field equations: whereby However, when I print f1, it, w^2 is still w^2 and has not reduced down to 0. I was wondering if I am missing something, please? This gets annoying because I am going to be working with Macaulay Matrices and hence, it is essential that I work within a quotient ring. Maybe I am missing some mathematics since this is all very new to me... This is my sage input: How would go about to ensure that w^2 = 0? I've already tried adding the original polynomial to the field equations when creating the quotient ring and changing its ring afterwards, like so: But as you can see, nothing happened... Thank you! |

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