Re: [Maxima-discuss] kronecker delta

[Barton W. <wi...@un...>]

There is no option variable or alternative integrate function that uses kron_delta in the way that you suggested.  Other than the effort required to extend Maxima to do this (and the added cost of maintaining more complex code), there is no particular reason why Maxima lacks this ability.


Although I do not recommend it for general work, there is an optional package abs_integrate, that has some ability to do what you suggest: examples:

  (%i5) load(abs_integrate)$

  (%i6) conditional_integrate(sin(m*x),x);
  (%o6) %if(m#0,-cos(m*x)/m,0)

The Maxima subst doesn't know anything about the meaning of %if:

  (%i7) subst(m=0,%);
    expt: undefined: 0 to a negative exponent.

Possibly this is correct, but it's such a mess that it removes my will to check it:

  (%i8) conditional_integrate(sin(m*x)*sin(n*x),x);

  (%o8) %if((n-m#0) %and (n+m#0),-((n-m)*sin((n+m)*x)+(n+m)*sin((m-    n)*x))/(2*n^2-2*m^2),%if((n-m#0) %and (n+m=0),%if(n#0,(sin(2*n*x)-2*n*x)/(4*n),0),%if((n-m=0) %and (n+m#0),%if(n#0,-(sin(2*n*x)-2*n*x)/(4*n),0),0)))




________________________________
From: José A. Vallejo Rodríguez <jos...@gm...>
Sent: Tuesday, March 28, 2017 11:32:28 PM
To: <max...@li...>
Subject: [Maxima-discuss] kronecker delta

Maxima has an implementation of the Kronecker delta ('kron_delta'), however, it is not used at all by the integration routines:

(%i1) declare(m,integer);
(%o1) done
(%i2) declare(n,integer);
(%o2) done
(%i3) integrate(sin(m*x)*sin(n*x),x,0,2*%pi)/%pi;
(%o3) 0
(%i4) integrate((sin(m*x))^2,x,0,2*%pi)/%pi;
(%o4) 1

Is there a way to make 'integrate' aware of 'kron_delta'?
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José Antonio Vallejo
Faculty of Sciences
State University of San Luis Potosi (Mexico)
http://galia.fc.uaslp.mx/~jvallejo<https://urldefense.proofpoint.com/v2/url?u=http-3A__galia.fc.uaslp.mx_-257Ejvallejo&d=DwMFaQ&c=9ZQuuHhOefNvAzlN-3viIA&r=Y-7rxY5GkJ0PrHulpV2qSA&m=JqLRZfwg-nhQX3ueeJ6DOq5AkyF7VGK1EmDET__uu60&s=0eSpu8v1XFyzt8lOPLl8kvo7oEV81hihM47peNHHMaY&e=>
_____________________________________