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+--- Thread: The diff command counts faster than ∂/∂x (/thread-20955.html)
The diff command counts faster than ∂/∂x - hp-zl - 12-06-2023 06:55 AM
When I type "diff(Σ((-1)^(k+1)/k^x,k,1,20),x)" I get the result after about 4 seconds (appendix 1).
When I type "∂(Σ((-1)^(k+1)/k^x,k,1,20),x)" I get the result after about 3 minutes (sic!) (appendix 2).
CAS Mode. Firmware: 2.1.14730. HP-Prime G2.
CAS Settings. Simplify: Maximum ("Minimum" gives worse results).
The time() command probably does not take into account the formatting time of the result and its display, but the difference is apparent: 0.7 s vs. 29 s (Appendix 3).
Regards.
[attachment=12997] [attachment=12998] [attachment=12999]
RE: The diff command counts faster than ∂/∂x - Albert Chan - 12-06-2023 04:24 PM
Differentiation, unlike integration, is very mechanical, and should run very fast.
Problem is internal hard-coded simplify, that cannot be controlled by SIMPLIFY setting.
My guess is diff(f,x) is less "simplified" than ∂(f,x), thus run much faster.
OP problem, we want to stop sum from simplify f with common denominator, making a mess.
Instead of summing an expression, we sum a list, which bypass internal simpilfy code. (*)
Cas> lst := makelist(k -> (-1)^(k+1)/k^x, 1, 20)
Cas> f := sum(lst)
diff(f,x) or ∂(f,x) should now run very fast.
(*) sum(lst) = '+' operator applied to list, see https://www.hpmuseum.org/forum/thread-20389-post-176469.html#pid176469
Cas> (a+b)[1] (lst)
1 - 1/2^x + 1/3^x - 1/4^x + 1/5^x ... + 1/19^x - 1/20^x