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Topic: symbolic integration problem by change from maple->mupad kernel
Replies: 4   Last Post: May 23, 2014 7:42 AM

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Christopher Creutzig

Posts: 278
Registered: 2/24/09
Re: symbolic integration problem by change from maple->mupad kernel
Posted: May 23, 2014 7:42 AM
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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(s-1.255)*heaviside(1.818-s))+90*(heaviside(s-1.818)*heaviside(3.131-s)))*(s-0.938^2);
>> 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) two-argument 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




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