http://www.mapleprimes.com/questions/41577-Laurent-Series en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Thu, 11 Jun 2026 03:38:18 GMT Thu, 11 Jun 2026 03:38:18 GMT The latest answers and comments added to the Question, Laurent series http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/questions/41577-Laurent-Series http://www.mapleprimes.com/questions/41577-Laurent-Series?ref=Feed:MaplePrimes:Laurent series:Comments#answer77541 Primarily it is not a Maple problem and IIRC it goes like this: f smooth in 0 implies there is a w in the ring s.th. k[x,y] = k[w,f] is a local isomorphism and it induces ring/(f) = k[w] in 0 (this is what you call the embedding, but it is achieved that way). Essentially this follows from the implicite function theorem. Geometrically it means: if the curve is smooth you have a (local) tangent, a complementary vector spans the space. Which are your new coordinates. One has to be a bit carefully since you are in characteristic p > 0. For the final step - Laurent series - be careful, not sure whether Maple needs 1/n! which is not given in your case. What you mean is the completed local ring (a limit construction) to which the stuff always embeds. Then the Laurent series are the quotient field (as your local ring is integer). I am not aware of a directly applicable package, may be you dig for 'abstract algebra' and Maple, may be http://mihailovs.com/Alec/ . Or other CAS software dedicated to commutative algebra / algebraic geometry. But if you write down the Math then it should translatable to Maple later, i think it allows finite fields (do not know whether abstract or only for explicit cases). Primarily it is not a Maple problem and IIRC it goes like this: f smooth in 0 implies there is a w in the ring s.th. k[x,y] = k[w,f] is a local isomorphism and it induces ring/(f) = k[w] in 0 (this is what you call the embedding, but it is achieved that way). Essentially this follows from the implicite function theorem. Geometrically it means: if the curve is smooth you have a (local) tangent, a complementary vector spans the space. Which are your new coordinates. One has to be a bit carefully since you are in characteristic p > 0. For the final step - Laurent series - be careful, not sure whether Maple needs 1/n! which is not given in your case. What you mean is the completed local ring (a limit construction) to which the stuff always embeds. Then the Laurent series are the quotient field (as your local ring is integer). I am not aware of a directly applicable package, may be you dig for 'abstract algebra' and Maple, may be http://mihailovs.com/Alec/ . Or other CAS software dedicated to commutative algebra / algebraic geometry. But if you write down the Math then it should translatable to Maple later, i think it allows finite fields (do not know whether abstract or only for explicit cases). 77541 Sat, 07 Apr 2007 17:36:50 Z Axel Vogt Axel Vogt http://www.mapleprimes.com/questions/41577-Laurent-Series?ref=Feed:MaplePrimes:Laurent series:Comments#answer77538 People have asked for this feature before, but not that many. The computer algebra system <a href="http://magma.maths.usyd.edu.au/">Magma</a> can do that. People have asked for this feature before, but not that many. The computer algebra system <a href="http://magma.maths.usyd.edu.au/">Magma</a> can do that. 77538 Sat, 07 Apr 2007 18:04:12 Z JacquesC JacquesC http://www.mapleprimes.com/questions/41577-Laurent-Series?ref=Feed:MaplePrimes:Laurent series:Comments#answer77536 No series expansion needed I think, it should be all in the context of finite series, the rest are formal embeddings. No series expansion needed I think, it should be all in the context of finite series, the rest are formal embeddings. 77536 Sun, 08 Apr 2007 00:41:16 Z Axel Vogt Axel Vogt http://www.mapleprimes.com/questions/41577-Laurent-Series?ref=Feed:MaplePrimes:Laurent series:Comments#comment85698 Maple is very well equipped with lots of functions to deal with polynomials over finite fields. See ?modp as one entry point. Maple is very well equipped with lots of functions to deal with polynomials over finite fields. See ?modp as one entry point. 85698 Sun, 08 Apr 2007 02:13:37 Z JacquesC JacquesC