(d2) temp (c3) linenum:0\$ (c1) trial:a*cos(x+2*y)-a*sin(u-4*x); (d1) a cos(2 y + x) + a sin(4 x - u) (c2) intopois(trial^2); /a/guest/fateman/mac42/rat/pois2.o being loaded. [fasl /a/guest/fateman/mac42/rat/pois2.o] Maximum poisson coefficient is +-15 for each of the variables in [u, v, w, x, y, z] 2 a cos(4 y + 2 x) 2 2 (d2)/P/ ----------------- + a sin(2 y + 5 x - u) - a sin(2 y - 3 x + u) 2 2 a cos(8 x - 2 u) 2 - ----------------- + a 2 (c3) poisint(trial,y); a sin(2 y + x) (d3)/P/ -------------- 2 (c4) intopois(sin(x)^5)\$ (c5) printpois(sin(x)^5); 5/8 sin(x) - 5/16 sin(3 x) 1/16 sin(5 x) (d5) done (c6) /* poistrim is called with 6 arguments (the coefs of u ... z) and mapped over the terms as multiplication is done. This definition serves to discard terms when x's coef exceeds 3.*/ poistrim(uc,vc,wc,xc,yc,zc):= is(xc>3) \$ (c7) intopois(sin(x)^5); 5 sin(x) sin(3 x) (d7)/P/ -------- - -------- 8 4 (c8) /* This command substitutes u+e for v in the Poisson Series cos(v). The indeterminate e is not permitted in the argument of a trignometric form, so cos(u+e) is expanded as cos(e) cos(u) - sin(e) sin(u), and then the cos(e) and sin(e) terms are re-expressed as Taylor series, as shown below.*/ (powerdisp:true, /*display power series in right order*/ poissubst(u,v,cos(v),e,3)); 2 3 e e (d8)/P/ (1 - --) cos(u) + (- e + --) sin(u) 2 6 Batching done. (d9) pois.examp (c10) closefile();