Series expansions of denominators.

expand-den.frm

CF den;
S x;
S a,j,n,x1,x2;

S a,b,c;

L F1 = den(1-x);
L F2 = den(1-x)^2 / x;
L F3 = den(a+b*x      );
L F4 = den( +b*x+c*x^2);
L F5 = den(a+   +c*x^2);
L F6 = den(a+b*x+c*x^2);

* Expand denominators with respect to x up to O(x^5).

#define N "5"

label retry;
* The next two lines are for simplifying trivial den(x).
id den(x?!{0,}) = 1/x;
denominators den;
* Note that "splitarg ((x)),den" doesn't change den(x).
splitarg ((x)),den;
* For long arguments, workspace may overflow.
*repeat id den(a?,<x1?>,...,<x16?>,?xx) = den(a,<x1>+...+<x16>,?xx);
repeat id den(a?,x1?,x2?,?xx) = den(a,x1+x2,?xx);
id ifmatch->retry, den(0,x1?) = den(x1/x)/x;  * Factor out 1/x.
repeat;
* ONCE is needed. Otherwise x^-1 * den(1,-x)^2 matches x^-1 * den(1,-x) and x^0 * den(1,-x).
  id once, x^n? * den(a?,x1?) = x^n * sum_(j,0,`N'-n,sign_(j)*x1^j*(1/a)^(j+1));
  if (count(x,1) > `N') discard;
endrepeat;

B x;
P;
.end