feature request: imagpart (bessel_y)

Maxima knows that imagpart ( bessel_j(1,x))  is
identically zero (since x is by default real).

This allows much faster use of quad_qag
via nint, as shown below, as compared with
the analogous calculation for bessel_y.

In the following, details=true, so information
about method  appears.

----------------------------------
(%i1) load(nint);
(%o1) "c:/work2/nint.mac"

/* case  bessel_j  */

(%i2) imagpart(bessel_j(1,x));
(%o2) 0

(%i3) imagpart(bessel_j(2,sqrt(2)*x));
(%o3) 0

(%i4) nint(bessel_j(1,x)*bessel_j(2,sqrt(2)*x),x,1,1000,strong_osc);
  quad_qag  
(%o4) 0.47382488780922

(%i5) time(%);
(%o5) [6.42]

(%i6) goutL;
(%o6) [[qag,0.47382488780922,3.0088677226459195E-9,7843,0]]

(%i7) gargL;
(%o7) [[qag,bessel_j(1,x)*bessel_j(2,sqrt(2)*x),x,1,1000,3,epsrel = 1.0E-8,
        limit = 700]]

/*  case  bessel_y   */

(%i8) imagpart(bessel_y(1,x));
(%o8) 'imagpart(bessel_y(1,x))

(%i9) imagpart(bessel_y(2,sqrt(2)*x));
(%o9) 'imagpart(bessel_y(2,sqrt(2)*x))

(%i10) nint(bessel_y(1,x)*bessel_y(2,sqrt(2)*x),x,1,1000,strong_osc);
  quad_qag  
(%o10) 0.44737052335548

(%i11) time(%);
(%o11) [19.78]

(%i12) goutL;
(%o12) [[[qag,0.44737052335548,3.0438548004320586E-9,7905,0],
         [qag,0.0,0.0,31,0]]]

(%i13) gargL;
(%o13) [[[qag,
          'realpart(bessel_y(1,x))*'realpart(bessel_y(2,sqrt(2)*x))
           -'imagpart(bessel_y(1,x))*'imagpart(bessel_y(2,sqrt(2)*x)),x,1,
          1000,3,epsrel = 1.0E-8,limit = 700],
         [qag,
          'imagpart(bessel_y(1,x))*'realpart(bessel_y(2,sqrt(2)*x))
           +'realpart(bessel_y(1,x))*'imagpart(bessel_y(2,sqrt(2)*x)),x,1,
          1000,3,epsrel = 1.0E-8,limit = 700]]]
-----------------------------------------------------------

Hence the feature request: 

Add imagpart knowledge to  bessel_y code
and simplification.

Ted Woollett