Dear Martin, I'm not proud about series but let me tell you what I use in series.
//1// I only use series in analysis, so series with severe variables are very rare for me. There are some sum(in x^i) sum(in y^j) ... x^i y^j = sum(in y^j) sum(in x^j) ... but this use of axiom isn't so fine because it's impossible to find the function from this serie in axiom. //2// Other CAS have a collect function : collect (x+x*y+y^2, x) = (y+1)*x + y^2 in (Ring without x) [x] collect (x+x*y+y^2, x) = y^2 + y*x + x in (Ring without y) [y] axiom does it by coerce. it's a good idea to have coerce (many coerce in fact) as you describe. //3// I hope that the serie 1/(1+a*x) in x around 0 remains easy to compute when a is fixed. It's not the same serie that 1/(1+x*y) in RN[[x,y]]. //4// Sometime I compute the recip of y=1+x+x^3 arround x=0. So I get a serie x=1-y+... Do you know if there is this revert function in axiom. It's not recip that is equal to 1/... //5// I use the coefficient function with polynom. By example M(a,0) and N(0,b) are points. Give a vector of (MN) line. The equation of the line is eqline := determinant matrix [[a,0,1],[0,b,1],[x,y,1]] (equal 0) A vector is vector [coefficient (eqline, y, 1), - coefficient (eqline, x, 1)]. I don't know if this method may be used for series. // 6 // An other exercice I do whith series is to find a naive way for the serie of the nth root of x=tan x when x -> %plusInfinity. So we write cos x * x = sin x and x = n*%pi + %pi/2 - a/n - b/n^2 ... You write the two series and find first a, then b, and so. ** I don't try this exercice with axiom ** Sometime I do it with maple. //7// Of corse some series I use aren't around 0 or have a not integer power... //8// I quickly try to test the silly series (x^a-a^x) and (x^x - a^a) for a fixed a when x is arround a but I can't with axiom. maple does it almost right by series (x^a-a^a, x=a, 6) //9// I feel difficult to use axiom because I don't have any clear idea about the syntax and the domain I must use. I have no short description which describes the domain and it's syntax. DMP aren't so equivalent to Polynomial, there is TS, UTS, Puiseux series, some coerce are right, other aren't. I'm happy to see that your change try to let only very view idea which can be universe and mathematically pretty ! I'm sorry if I'm out of your subject. Francois --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~----------~----~----~----~------~----~------~--~---
