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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: 323 Registered: 2/24/09
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(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

Date Subject Author
9/18/13 Manuel Höger
9/18/13 jomethew@gmail.com
9/18/13 Steven Lord
9/19/13 Manuel Höger
5/23/14 Christopher Creutzig