[Maxima-discuss] Internal representation of "Taylor sums"

[Eduardo O. <edu...@gm...>]

Hi list,

a few hours ago I tried to use my luatree thing -
http://anggtwu.net/eev-maxima.html#luatree - to understand the
low-level representation of Taylor series, and I discovered that

  1) it doesn't recognize the difference between "Taylor sums" - this
     is an informal term; the correct term is canonical rational
     expressions, a.k.a. CREs - and normal sums,

  2) op and args also don't recognize the difference,

  3) the internal representation of "Taylor sums" and "normal sums" is
     very different, and ratp distinguishes them.

We can see all that in this example:

  a : taylor(sin(x),x,0,5);
  b : x - x^3/6 + x^5/120;
  op(a);
  op(b);
  args(a);
  args(b);
  :lisp #$a$
  :lisp #$b$
  ratp(a);
  ratp(b);

it yields:

  (%i1) a : taylor(sin(x),x,0,5);
                                    3    5
                                   x    x
  (%o1)/T/                     x - -- + --- + . . .
                                   6    120
  (%i2) b : x - x^3/6 + x^5/120;
                                    5     3
                                   x     x
  (%o2)                            --- - -- + x
                                   120   6
  (%i3) op(a);
  (%o3)                                  +
  (%i4) op(b);
  (%o4)                                  +
  (%i5) args(a);
                                         3   5
                                        x   x
  (%o5)                           [x, - --, ---]
                                        6   120
  (%i6) args(b);
                                    5      3
                                   x      x
  (%o6)                           [---, - --, x]
                                   120    6
  (%i7) :lisp #$a$

  ((MRAT SIMP (((%SIN SIMP) $X) $X) (sin(x)490 X491)
    (($X ((5 . 1)) 0 NIL X491 . 2)) TRUNC)
   PS (X491 . 2) ((5 . 1)) ((1 . 1) 1 . 1) ((3 . 1) -1 . 6) ((5 . 1) 1 .
120))
  (%i7) :lisp #$b$

  ((MPLUS SIMP) $X ((MTIMES SIMP) ((RAT SIMP) -1 6) ((MEXPT SIMP) $X 3))
   ((MTIMES SIMP) ((RAT SIMP) 1 120) ((MEXPT SIMP) $X 5)))
  (%i7) ratp(a);
  (%o7)                                true
  (%i8) ratp(b);
  (%o8)                                false
  (%i9)

In the example above a is a MRAT and b is a MPLUS. Is there a standard
way to access the components of an MRAT from Maxima? What do people
use when they need to inspect the innards of MRATs from Maxima?

Thanks in advance!
  Eduardo Ochs
  http://anggtwu.net/eev-maxima.html