
Re: symbolic integration problem by change from maple>mupad kernel
Posted:
May 23, 2014 7:42 AM


On 19.09.13 09:40, Manuel Höger wrote:
> But the mupad kernel is even not able to integrate a single Heaviside function with symbolic Boarders, which means it presents a "piecewise" function, and not the antiderivative.
Seems to work for me (14a):
>> syms x y >> int(heaviside(x), x, 1, y)
ans =
y*heaviside(y)
>> syms x s En mp eps >> smin=1.16; >> smax = mp^2+4*eps*En; >> sigma = (200*(heaviside(s1.255)*heaviside(1.818s))+90*(heaviside(s1.818)*heaviside(3.131s)))*(s0.938^2); >> f=int(sigma,s,smin,smax)
f =
piecewise([mp^2 + 4*En*eps <= 909/500, heaviside(mp^2 + 4...etc...
>> pretty(simplify(f)) %% manually cut off at column 71 for UseNet { / 2 \ { / 2 63001 \  49530813881802075 mp 4953081.. { #2  100 #5    + #4  #2   + .. { \ 400 / \ 281474976710656 70.. { { 1040605467887917.. { #4  #3 + .. { 140737488355328.. { { 738533945714947434578.. { .. { 28147497671065600000..
where
2 #1 == 500 mp + 2000 En eps
/ 2 251 \ #2 == heaviside mp + 4 En eps    \ 200 /
/ 2 ..  89155464987243735 mp 89155464987243735 En eps 162.. #3 == #6   +   .. \ 1125899906842624 281474976710656 11..
/ 2 7436529 \ #4 == #6  45 #5    \ 50000 /
2 #5 == mp + 4 En eps
/ 2 909 \ #6 == heaviside mp + 4 En eps    \ 500 /
The piecewise expression, I believe without having checked it manually, *is* the integral for your input. (Technically speaking, ?antiderivative? is the term for what an indefinite integral returns, i.e., a (one or) twoargument call to int.)
There certainly are ways of writing a piecewise expressions differently, but that does not actually change the expression, and the form returned by MuPAD makes it easier, in my eyes, to see the different cases.
HTH,
Christopher

