Maxima Function
revert (expr, x)
revert2(expr,x,n)
These functions return the reversion of expr, a Taylor series about zero in the variable x.
revert
returns a polynomial of degree equal to the highest power in expr.
revert2
returns a polynomial of degree n,
which may be greater than, equal to, or less than the degree of expr.
load ("revert")
loads these functions.
Examples:
(%i1) load ("revert")$ (%i2) t: taylor (exp(x) - 1, x, 0, 6); 2 3 4 5 6 x x x x x (%o2)/T/ x + -- + -- + -- + --- + --- + . . . 2 6 24 120 720 (%i3) revert (t, x); 6 5 4 3 2 10 x - 12 x + 15 x - 20 x + 30 x - 60 x (%o3)/R/ - -------------------------------------------- 60 (%i4) ratexpand (%); 6 5 4 3 2 x x x x x (%o4) - -- + -- - -- + -- - -- + x 6 5 4 3 2 (%i5) taylor (log(x+1), x, 0, 6); 2 3 4 5 6 x x x x x (%o5)/T/ x - -- + -- - -- + -- - -- + . . . 2 3 4 5 6 (%i6) ratsimp (revert (t, x) - taylor (log(x+1), x, 0, 6)); (%o6) 0 (%i7) revert2 (t, x, 4); 4 3 2 x x x (%o7) - -- + -- - -- + x 4 3 2