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    hacklex
    @hacklex
    just read on primitive polys in the book... that wording tho.
    a poly [t1*x] t2
    in t2, with lc==t1*x
    followed so far, although skipped the splitting part since it is not relevant to the case
    so basically, integrate_primitive_polynomial(x*t1*t2, [D[x]=1, D[t1]=-2x*t1, D[t2]=t1])?
    Aaron Meurer
    @asmeurer
    something like that
    hacklex
    @hacklex
    ok trying to trace what happens to that input...
    I mean, in my mind
    what p.expr.has(DE.t) is?
    Aaron Meurer
    @asmeurer
    DE.t will be t1
    unless it's in the decrement level block, then it will be t0
    hacklex
    @hacklex
    t is t2 here?
    so DE.t is t1, makes sense
    Aaron Meurer
    @asmeurer
    oh yeah, I started from 0
    hacklex
    @hacklex
    what does p.expr.has() mean?
    Aaron Meurer
    @asmeurer
    In that while loop, p and q gain a degree with each iteration
    expr.has(x) checks if x appears in expr
    hacklex
    @hacklex
    as coefficient?
    or as summand?
    Aaron Meurer
    @asmeurer

    In that while loop, p and q gain a degree with each iteration

    normally they should not do that

    hacklex
    @hacklex
    p is a poly in [supposedly?] t2?
    Aaron Meurer
    @asmeurer
    anywhere in the expression
    not p.has(DE.t) checks if p is a constant polynomial wrt t
    hacklex
    @hacklex
    oh
    so it checks the poly variable, not poly coefficient
    this naming somehow confuses me, sorry
    p is a poly in t, and we ask if p has t anywhere? well yes, without t it would be a const
    a const poly in t, ofc
    so it considers such a poly already-reduced to a poly in lower tower
    and returns said poly as a "t-free remainder"
    to be dealt later when you get to deal with the lower-level tower
    wait, do I at least have the order right in my mind?
    Aaron Meurer
    @asmeurer
    I think you have it right
    hacklex
    @hacklex
    so that first we deal with polys in t2, compute and get back to towers in t1, and finally x
    so we go from the deepest level back to x
    I see, the recursion, that chops away t-free pieces
    so basically, it endlessly chops pieces off x*t1*t2?
    from what you said so far, I'm afraid I can't deduce whether it was the deepest level of recursion or not
    but if we continue tracing as if it was the case,
    what is frac_in?
    Aaron Meurer
    @asmeurer
    I think it is stuck at the top level
    it converts something into a fraction
    it's a helper function from what I mentioned above where sympy doesn't support rational functions directly
    hacklex
    @hacklex
    can we extract the parameters it got stuck with?
    I mean, what did p look like
    at the top level
    hacklex
    @hacklex
    Anyway I perceive that is a rather late hour now (3AM for me) -- thank you for your time!
    I'm only curious, so there is no rush, I'm just slowly studying math as a hobby.
    hope you'll find another few minutes for me later, as comments from a living person who actually implemented this stuff helps me more than anything else
    Thanks and have a good day, night or whatever it is now in your timezone :)
    Aaron Meurer
    @asmeurer
    I would suggest running the code yourself, and either add print statements or step through it in a debugger