% Author: Alan Barnes <barnesa@aston.ac.uk>
psexplim 8;
% expand as far as 8th power (default is 6)
cos!-series:=ps(cos x,x,0);
sin!-series:=ps(sin x,x,0);
atan!-series:=ps(atan x,x,0);
tan!-series:=ps(tan x,x,0);
cos!-series*tan!-series; % should series for sin(x)
df(cos!-series,x); % series for sin(x) again
cos!-series/atan!-series; % should be expanded
tmp:=ps(1/(1+x^2),x,infinity);
df(tmp,x);
ps(df(1/(1+x^2),x),x,infinity);
tmp*x; % not expanded as a single power series
ps(tmp*x,x,infinity); % now expanded
ps(1/(a*x-b*x^2),x,a/b); % pole at expansion point
ps(cos!-series*x,x,2);
tmp:=ps(x/atan!-series,x,0);
tmp1:=ps(atan!-series/x,x,0);
tmp*tmp1; % should be 1, of course
cos!-sin!-series:=ps(cos sin!-series,x,0);
% cos(sin(x))
tmp:=cos!-sin!-series^2;
tmp1:=ps((sin(sin!-series))^2,x,0);
tmp+tmp1; % sin^2 + cos^2
psfunction tmp1;
% function represented by power series tmp1
tmp:=tan!-series^2;
psdepvar tmp;
% in case we have forgotten the dependent variable
psexpansionpt tmp; % .... or the expansion point
psterm(tmp,6); % select 6th term
psterm(tmp,10); % select 10th term (series extended automtically)
tmp1:=ps(1/(cos x)^2,x,0);
tmp1-tmp; % sec^2-tan^2
ps(int(e^(x^2),x),x,0); % integrator not called
tmp:=ps(1/(y+x),x,0);
ps(int(tmp,y),x,0); % integrator called on each coefficient
pscompose(cos!-series,sin!-series);
% power series composition cos(sin(x)) again
cos!-sin!-series;
% should be same as previous result
psfunction cos!-sin!-series;
tmp:=ps(log x,x,1);
tmp1:=pscompose(tmp, cos!-series);
% power series composition of log(cos(x))
df(tmp1,x); % series for -tan x
psreverse tan!-series;
% should be series for atan x
atan!-series;
tmp:=ps(e^x,x,0);
psreverse tmp;
% NB expansion of log x in powers of (x-1)
pschangevar(tan!-series,y);
end;