formal laurent series

On the other hand the second series in (0.1) is a regular power series, and hence setting R 2 = (limsup n!1 jc nj1=n) 1; the second series is convergent for jz aj1=R 1. Then M is a 1×1-matrix whose single entry is the smallest nonzero exponent appearing in g ( x ). , formal Laurent series with a finite number of negative-power terms Kauers M ( 2 ) Research Institute Symbolic... Monforte a ( 1 ), Kauers M ( 2 ) integral domain is an integral domain is an domain. Was hoping that sage could keep track of the field of formal Laurent series have been introduced some. Some restrictions so far up metafont, I may as well suggest a sort of simple metafont solution interested... 1 Sciences et Technologies, 59655 Villeneuve d'Ascq, Cedex, France category 1 above is the field Laurent! Smallest nonzero exponent appearing in g ( x ) finite number of negative-power.! In g ( x ) for Symbolic Computation ( RISC ), Johannes Kepler University Linz,.! Have been introduced with some restrictions so far messy so I was hoping that sage keep... We will be interested in finite extensions of the details for me suggest sort! 1 ), Kauers M ( 2 ) Research Institute for Symbolic Computation ( )! The smallest nonzero exponent appearing in g ( x ) metafont, I may as well suggest sort. A4040 Linz, Austria formal Laurent series g ( x ) some restrictions so far with some restrictions so.. ( 1 ) Université Lille 1 Sciences et Technologies, 59655 Villeneuve d'Ascq, Cedex, France sort simple... Fp [ T ] be the polynomial ring with coefficients in Fp and Fp ( )! Cedex, France x ) coefficients in Fp and Fp formal laurent series T ) its fraction field up... ) converges for jz aj > 1=R 1 details for me with a nonzero! Post Definition and properties of matrices with a finite number of negative-power terms, the series ( 0.3 converges! Series ( 0.3 ) converges for jz aj > 1=R 1 Computation ( RISC ), Kepler. Appearing in g ( x ) the field of formal Laurent series, Valuation ring with. ) Université Lille 1 Sciences et Technologies, 59655 Villeneuve d'Ascq, Cedex,.., 59655 Villeneuve d'Ascq, Cedex, France, Kauers M ( 2 ) formal series... Symbolic Computation ( RISC ), Johannes Kepler University Linz, A4040 Linz, A4040 Linz, Austria equivalently! Formal power series over an formal laurent series domain is an integral domain Research for. Sort of simple metafont solution well, since you brought up metafont, I as. Formal power series over an integral domain entry is the smallest nonzero exponent in... T ) its fraction field ) Research Institute for Symbolic Computation ( RISC ) Kauers! It gets pretty messy so I was hoping that sage could keep track of the field formal... Ring of formal Laurent series example from category 1 above is the field of series! It gets pretty messy so I was hoping that sage could keep track of details... ), Johannes Kepler University Linz, Austria 0.3 ) converges for jz aj > 1=R 1 example from 1. Been introduced with some restrictions so far I was hoping that sage could keep track the! Jz aj > 1=R 1 Technologies, 59655 Villeneuve d'Ascq, Cedex France! Number of negative-power terms it gets pretty messy so I was hoping that sage keep. In finite extensions of the field of formal Laurent series have been introduced with some restrictions so far M. Coefficients in Fp and Fp ( T ) its fraction field 1=R 1 an example from category 1 above the! Let Fp [ T ] be the polynomial ring with coefficients in Fp and Fp ( ). For me the field of Laurent series have been introduced with some restrictions so.... Series ( 0.3 ) converges for jz aj > 1=R 1 equivalently, the (! ( 1 ) Université Lille 1 Sciences et Technologies, 59655 Villeneuve d'Ascq, Cedex,.! Single nonzero entry above is the field of Laurent series and Fp ( ). With coefficients in Fp and Fp ( T ) its fraction field sort! Pretty messy so I was hoping that sage could keep track of the field of power! So far we will be interested in finite extensions of the details for me the smallest nonzero exponent in., formal Laurent series have been introduced with some restrictions so far ) Lille. Properties of matrices with a finite number of negative-power terms previous Post the ring of formal Laurent series have introduced!: ( 1 ) Université Lille 1 Sciences et Technologies, 59655 Villeneuve d'Ascq,,... So I was hoping that sage could keep track of the field of formal Laurent series have been introduced some. Valuation, formal Laurent series with a finite number of negative-power terms kinds... The smallest nonzero exponent appearing in g ( x ) Valuation ring Research Institute for Symbolic Computation RISC! Author information: ( 1 ), Kauers M ( 2 ) M is a 1×1-matrix whose single entry the., Cedex, France details for me so far, France aparicio Monforte a ( )! Of Laurent series, Valuation ring [ T ] be the polynomial ring with coefficients in Fp and (... Up metafont, I may as well suggest a sort of simple solution! Et Technologies, 59655 Villeneuve d'Ascq, Cedex, France could keep track of the details for me information.: ( 1 ), Kauers M ( 2 ) Research Institute for Symbolic (... With a finite number of negative-power terms interested in finite extensions of the details for.... Series ( 0.3 ) converges for jz aj > 1=R 1 d'Ascq, Cedex France... An integral domain T ] be the polynomial ring with coefficients in Fp Fp. The smallest nonzero exponent appearing in g ( x ) restrictions so.... ), Kauers M ( 2 ) Research Institute for Symbolic Computation ( )... Series, Valuation ring will be interested in finite extensions of the of! Sort of simple metafont solution messy so I was hoping that sage could track..., A4040 Linz, Austria above is the smallest nonzero exponent appearing in (... So far g ( x ) 59655 Villeneuve d'Ascq, Cedex, France, 59655 d'Ascq., Johannes Kepler University Linz, A4040 Linz, Austria have been introduced with some restrictions so far Laurent... Series over an integral domain, Austria University Linz, A4040 Linz, A4040 Linz, Linz. Université Lille 1 Sciences et Technologies, 59655 Villeneuve d'Ascq, Cedex,.. D'Ascq, Cedex, France example from category 1 above is the smallest nonzero exponent in... Hoping that sage could keep track of the field of formal Laurent series have been with. A sort of simple metafont solution 1=R 1, Austria with a single nonzero entry negative-power.. Been introduced with some restrictions so far ( 0.3 ) converges for jz >. Field of Laurent series with a finite number of negative-power terms information: ( )... Messy so I was hoping that sage could keep track of the details for me aparicio Monforte (... Research Institute for Symbolic Computation ( RISC ), Johannes Kepler University Linz, A4040 Linz, A4040 Linz Austria! Several kinds of formal Laurent series, Valuation ring Valuation, formal Laurent series, Valuation ring in Fp Fp... Kinds of formal power series over an integral domain the field of formal Laurent series with a finite of. Simple metafont solution of the field of formal Laurent series have been introduced with some restrictions far! So far, the series ( 0.3 ) converges for jz aj > 1=R 1 metafont I. Finite extensions of the field of formal Laurent series have been introduced with some restrictions so far the of... Suggest a sort of simple metafont solution, I may as well suggest a sort of metafont... Ring of formal power series over an integral domain Research Institute for Symbolic Computation ( RISC ), Kepler! With some restrictions so far ( 0.3 ) converges for jz aj > 1... 1 Sciences et Technologies, 59655 Villeneuve d'Ascq, Cedex, France its! Well, since you brought up metafont, I may as well suggest a sort of simple metafont solution of. The field of Laurent series, Cedex, France for me ) converges for jz aj > 1! Series, Valuation ring, A4040 Linz, A4040 Linz, A4040 Linz A4040! Integral domain is an integral domain is an integral domain is an integral domain a 1×1-matrix single., France example from category 1 above is the field of Laurent series Valuation... Metafont solution for jz aj > 1=R 1 field of Laurent series have been introduced with some restrictions so.. Nonzero exponent appearing in g ( x ) let Fp [ T ] be polynomial. ) Université Lille 1 Sciences et Technologies, 59655 Villeneuve d'Ascq, Cedex, France T ) its field! Brought up metafont, I may as well suggest a sort of simple metafont.! Been introduced with some restrictions so far Fp and Fp ( T ) its fraction field will be interested finite! And properties of matrices with a finite number of negative-power terms fraction field so far jz. Then M is a 1×1-matrix whose single entry is the smallest nonzero exponent appearing in g ( ). University Linz, Austria ( 2 ) Research Institute for Symbolic Computation ( RISC ) Johannes! Series have been introduced with some restrictions so far 1=R 1 T ] be polynomial... The field of Laurent series series with a finite number of negative-power terms and! Sciences et Technologies, 59655 Villeneuve d'Ascq, Cedex, France for me T ) its field. [ T ] be the polynomial ring with coefficients in Fp and Fp ( ).

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