Coercion into series

*To*: mathgroup at smc.vnet.net*Subject*: [mg71449] Coercion into series*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Sun, 19 Nov 2006 01:10:05 -0500 (EST)

Any time that an object like O[x] appears in a sum of terms, Mathematica will convert the whole sum into a power series. E.g. a x + Exp[x] + O[x]^3 SeriesData[x, 0, {1, 1 + a, 1/2}, 0, 3, 1] Cos[z] + O[z, Pi/2]^4 SeriesData[z, Pi/2, {-1, 0, 1/6}, 1, 4, 1] and so on... Consider the following equation eq=(y + b)*(y + c) == a^4 + y^2 + 3; Obviously Solve[eq, {b, c}] Solve::svars: Equations may not give solutions for all "solve" variables. {{b -> (3 + a^4 - c*y)/(c + y)}} However how the appearance of O[y]^3 below "makes" Solve give solution for {b,c} Solve[(y + b)*(y + c) == (a^4 + y^2 + 3) + O[y]^3, {b, c}] {{b -> -Sqrt[-3 - a^4], c -> Sqrt[-3 - a^4]}, {b -> Sqrt[-3 - a^4], c -> -Sqrt[-3 - a^4]}} Thanks a lot. Dimitris

**Follow-Ups**:**Re: Coercion into series***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>