On Saturday, April 7, 2018 at 5:21:39 AM UTC-4, Peter Luschny wrote:
I do understand that simplifying is hard and that Maple made
some progress over the years. Still it is worth to see some
examples where it fails (failed?) at least in the hope that
such cases will be included by Maple in their test examples.
A := proc(len) local egf, ser, coef:
egf := (log(sqrt((1-2*x)^2+1)+1)-log(1-2*x))/sqrt(2):
ser := series(egf,x,len+2):
coef := n -> simplify(n!*coeff(ser,x,n)):
seq(lprint(coef(n)), n=1..len): end:
A(20);
1
3
13
75
561
5355
63405
894915
14511105
263544435
5284255725
116065424475
2778006733425
72093290744475 (2017526711525325/2)*(275807*2^(1/2)+390050)*2^(1/2)/(2^(1/2)+1)^15 (60547198550713875/2)*(665857*2^(1/2)+941664)*2^(1/2)/(2^(1/2)+1)^16 (1938662110170410625/2)*(1607521*2^(1/2)+2273378)*2^(1/2)/(2^(1/2)+1)^17 (65941564342927147875/2)*(3880899*2^(1/2)+5488420)*2^(1/2)/(2^(1/2)+1)^18 (2374177441960545346125/2)*(9369319*2^(1/2)+13250218)*2^(1/2)/(2^(1/2)+1)^19 (90211614359319635056875/2)*(22619537*2^(1/2)+31988856)*2^(1/2)/(2^(1/2)+1)^20
On the other hand, for example,
(1/2)*(275807*sqrt(2)+390050)*sqrt(2)/(sqrt(2)+1)^15: simplify(%);
returns 1.
I agree that it would be better if `simplify` would produce the integer forms for those.
I notice that replacing the command `simplify` with either `radnormal` or `evala` produces those integers, pretty quickly.
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