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% Author: Alan Barnes <barnesa@uhura.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; ps(cos!-series/atan!-series,x,0); % 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 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); psreverse tan!-series; % should be series for atan y atan!-series; tmp:=ps(e^x,x,0); psreverse tmp; % NB expansion of log y in powers of (y-1) end;