------------------------------ if the input is: RAct((1+x)*(1+2*x)/x,x,n,N,10); the output is [n+1+(-6*n-9)*N+(n+2)*N^2, -n/(n+1)+N, [1, 1, 1, 1], [3+2*2^(1/2), 5.828427125] , 1, [2*ln(3+2*2^(1/2))/(ln(3+2*2^(1/2))+1), 1.276082872], [2*ln(3+2*2^(1/2))/( ln(3+2*2^(1/2))-1), 4.622100831], .6931471805599453094172321214581765680755, ln (2), [0, 2], [1, 3]] ------------------------------ if the input is: RAct((1+15*x)*(1+17*x)/x,x,n,N,10); the output is [-4*n-4+(64*n+96)*N+(-n-2)*N^2, -4*n/(n+1)+N, [1, 1, 1, 1], [32+2*255^(1/2), 63\ .93743885], 4, [2*(ln(32+2*255^(1/2))-ln(2))/(ln(32+2*255^(1/2))+1), 1.34347486\ 0], [2*(ln(32+2*255^(1/2))-ln(2))/(ln(32+2*255^(1/2))-2*ln(2)-1), 3.911421232], .1251631429540060142535300477244131914151, ln(17/15), [0, 4], [1, 32]] ------------------------------ if the input is: RAct((1+1000*x)*(1+1001*x)*(1+1002*x)/x^2,x,n,N,10); the output is [-4*(3*n+8)*(n+2)*(n+1)-2*(n+2)*(18*n^2+75*n+73)*N+(3*n+7)*(27054015*n^2+ 117234065*n+120240066)*N^2-2*(3*n+5)*(2*n+5)*(n+3)*N^3, -4*(3*n+8)*(n+1)^2*n/(3 *n+2)/(2*n+5)/(3+2*n)/(n+3)-(3*n+8)*(3*n+4)*(n+1)*(27054015*n^2+63126035*n+ 30060016)/(3*n+5)/(3*n+2)/(2*n+5)/(3+2*n)/(n+3)*N-(n+2)*(18*n^2+75*n+73)/(3*n+5 )/(2*n+5)/(n+3)*N^2+N^3, [2, 1, 1, 5], [3/4*(27162369396197033999+160320160*I* 2505^(1/2))^(1/3)+27108138060003/4/(27162369396197033999+160320160*I*2505^(1/2) )^(1/3)+9018005/4, 6763503.750], abs(3/2*(1002001+20040020*I*2505^(1/2))^(1/3)+ 3006003/2/(1002001+20040020*I*2505^(1/2))^(1/3)+1), [(2*ln(3/4*( 27162369396197033999+160320160*I*2505^(1/2))^(1/3)+27108138060003/4/( 27162369396197033999+160320160*I*2505^(1/2))^(1/3)+9018005/4)-ln(abs(3/2*( 1002001+20040020*I*2505^(1/2))^(1/3)+3006003/2/(1002001+20040020*I*2505^(1/2))^ (1/3)+1)))/(ln(3/4*(27162369396197033999+160320160*I*2505^(1/2))^(1/3)+ 27108138060003/4/(27162369396197033999+160320160*I*2505^(1/2))^(1/3)+9018005/4) +2), 1.330734584], [(2*ln(3/4*(27162369396197033999+160320160*I*2505^(1/2))^(1/ 3)+27108138060003/4/(27162369396197033999+160320160*I*2505^(1/2))^(1/3)+9018005 /4)-ln(abs(3/2*(1002001+20040020*I*2505^(1/2))^(1/3)+3006003/2/(1002001+ 20040020*I*2505^(1/2))^(1/3)+1)))/(ln(3/4*(27162369396197033999+160320160*I* 2505^(1/2))^(1/3)+27108138060003/4/(27162369396197033999+160320160*I*2505^(1/2) )^(1/3)+9018005/4)-ln(abs(3/2*(1002001+20040020*I*2505^(1/2))^(1/3)+3006003/2/( 1002001+20040020*I*2505^(1/2))^(1/3)+1))-2), 4.023572521], .\ 6640071835015580815724024129761948454767e-13, .\ 6640071835015580815724024129761948454767e-13, [0, 0, 1], [1, 3006002, 15060078036004]] ------------------------------ if the input is: RAct((1+x)^2*(1+((1+x)/x)^2*7),x,n,N,10); the output is Error, (in ln) numeric exception: division by zero ------------------------------ if the input is: RAct((1+x)^2*(1+(1+x)/x*4),x,n,N,10); the output is [2*(2*n+1)*(44*n+73)*(n+1)+(-25696*n^3-94024*n^2-107900*n-37622)*N+10*(3+2*n)*( n+2)*(44*n+29)*N^2, -1/5*n*(44*n+29)*(2*n-1)/(44*n-15)/(2*n+1)/(n+1)+N, [2, 1, 5, 29], [73/5+22/5*11^(1/2), 29.19314908], 1/5, [(2*ln(73/5+22/5*11^(1/2))+ln(5 ))/(ln(73/5+22/5*11^(1/2))+2+ln(5)), 1.196743646], [(2*ln(73/5+22/5*11^(1/2))+ ln(5))/(ln(73/5+22/5*11^(1/2))-2), 6.082756269], .\ 7694605217731370888492934148614982874986e-1, .\ 7694605217731370888492934148614982874986e-1, [0, 1], [1, 13]] ------------------------------ if the input is: RAct((1+x)*(1+((1+x)/x)^2*8),x,n,N,10); the output is [-2*(3*n+8)*(n+2)*(n+1)+(n+2)*(18*n^2+75*n+73)*N-(3*n+7)*(114*n^2+494*n+507)*N^ 2+(3*n+5)*(2*n+5)*(n+3)*N^3, -4*(3*n+8)*(n+1)^2*n/(3*n+2)/(2*n+5)/(3+2*n)/(n+3) +2*(3*n+8)*(3*n+4)*(n+1)*(114*n^2+266*n+127)/(3*n+5)/(3*n+2)/(2*n+5)/(3+2*n)/(n +3)*N-(n+2)*(18*n^2+75*n+73)/(3*n+5)/(2*n+5)/(n+3)*N^2+N^3, [2, 1, 1, 5], [12*2 ^(2/3)+15*2^(1/3)+19, 56.94762837], -3*2^(2/3)+3*2^(1/3)+1, [(2*ln(12*2^(2/3)+ 15*2^(1/3)+19)-ln(-3*2^(2/3)+3*2^(1/3)+1))/(ln(12*2^(2/3)+15*2^(1/3)+19)+2), 1.\ 003486521], [(2*ln(12*2^(2/3)+15*2^(1/3)+19)-ln(-3*2^(2/3)+3*2^(1/3)+1))/(ln(12 *2^(2/3)+15*2^(1/3)+19)-ln(-3*2^(2/3)+3*2^(1/3)+1)-2), 287.8188661], .\ 9469823719442910405653452130285786158142e-3, .\ 9469823719442910405653452130285786158142e-3, [0, 0, 1], [1, 25, 1057]] ------------------------------ if the input is: RAct((1+101*x)*(1+102*x)*(1+104*x)/x^2,x,n,N,10); the output is [-36*(6427*n+17142)*(n+2)*(n+1)+2*(n+2)*(12943978*n^2+53939955*n+51777693)*N+( 1817035013*n^3+12114509150*n^2+26452656095*n+18849166602)*N^2-2*(2*n+5)*(6427*n +10715)*(n+3)*N^3, -324*(6427*n+17142)*(n+1)^2*n/(2*n+5)/(3+2*n)/(6427*n+4288)/ (n+3)-9*(6427*n+17142)*(n+1)*(1817035013*n^3+6663404111*n^2+7674742834*n+ 2693984644)/(2*n+5)/(3+2*n)/(6427*n+10715)/(6427*n+4288)/(n+3)*N+(n+2)*( 12943978*n^2+53939955*n+51777693)/(2*n+5)/(6427*n+10715)/(n+3)*N^2+N^3, [7, 1, 1, 10715], [1/12*(22597759486951559+288*I*5925684806877043^(1/2))^(1/3)+ 79930081297/12/(22597759486951559+288*I*5925684806877043^(1/2))^(1/3)+282719/12 , 70679.76425], abs(1/6*(-31229710669+324*I*5925684806877043^(1/2))^(1/3)+ 11689609/6/(-31229710669+324*I*5925684806877043^(1/2))^(1/3)-1007/3), [(2*ln(1/ 12*(22597759486951559+288*I*5925684806877043^(1/2))^(1/3)+79930081297/12/( 22597759486951559+288*I*5925684806877043^(1/2))^(1/3)+282719/12)-ln(abs(1/6*(-\ 31229710669+324*I*5925684806877043^(1/2))^(1/3)+11689609/6/(-31229710669+324*I* 5925684806877043^(1/2))^(1/3)-1007/3)))/(ln(1/12*(22597759486951559+288*I* 5925684806877043^(1/2))^(1/3)+79930081297/12/(22597759486951559+288*I* 5925684806877043^(1/2))^(1/3)+282719/12)+7), .8287382047], [(2*ln(1/12*( 22597759486951559+288*I*5925684806877043^(1/2))^(1/3)+79930081297/12/( 22597759486951559+288*I*5925684806877043^(1/2))^(1/3)+282719/12)-ln(abs(1/6*(-\ 31229710669+324*I*5925684806877043^(1/2))^(1/3)+11689609/6/(-31229710669+324*I* 5925684806877043^(1/2))^(1/3)-1007/3)))/(ln(1/12*(22597759486951559+288*I* 5925684806877043^(1/2))^(1/3)+79930081297/12/(22597759486951559+288*I* 5925684806877043^(1/2))^(1/3)+282719/12)-ln(abs(1/6*(-31229710669+324*I* 5925684806877043^(1/2))^(1/3)+11689609/6/(-31229710669+324*I*5925684806877043^( 1/2))^(1/3)-1007/3))-7), -4.839013881], .\ 6080194408576210324610525715153284049813e-9, .\ 6080194408576210324610525715153284049813e-9, [0, 0, 1], [1, 31414, 1644683908]] -------------------- the whole thing took, 10.731, seconds.