Edit detail for #339 interpreter gives up in loop revision 2 of 2

The following is a very surprising for a novice, and a bit surprising for me:

(1) -> c 0==1; c 1==1; c n==c(n-1)+s*(reduce(+,[q^k*c(k)*c(n-1-k) for k in 1..n-1]));

c 5

   Internal Error
   The function * with signature (%, Integer) -> % is missing from 
      domain Fraction(Polynomial (Integer))

Note that the type of c 5 is FRAC POLY INT. This is, because Axiom is not smart enough to realize inside the loop that is a polynomial if is nonnegative. The following is more surprising, though:

coefficient(univariate(c(5),s),3)

   >> System error:
   The function BOOT::|*1;c;1;initial| is undefined.

Axiom manages - after a lot of trying- to coerce univariate(c(5),s) to a SUP FRAC POLY INT. Wow.

[coefficient(univariate(c(n),s),1) for n in 0..4]

   >> System error:
   The function BOOT::|*1;c;1;initial| is undefined.

But why does it give up here?

Martin

univariate applied to rational function produces rational function. Given actual value Axiom/FriCAS can see that rational function is a polynomial and retract it. But in a loop FriCAS has only expression producing rational functions and can not predict that the result will be a polynomial.

Zq:=SUP(INT)

(1)

q:Zq := monomial(1,1)

   Compiled code for c has been cleared.

(2)

Zqs:=SUP(Zq)

(3)

s:Zqs := monomial(1$Zq,1)

(4)

macro mac(n) == c(n-1) + s*(reduce(+,[q^k*c(k)*c(n-1-k) for k in 1..n-1]))

c(n: Integer): Zqs == (n=0 or n=1 => 1; mac n)

   Function declaration c : Integer -> SparseUnivariatePolynomial(
      SparseUnivariatePolynomial(Integer)) has been added to workspace.
   1 old definition(s) deleted for function or rule c

c 0

Compiling function c with type Integer -> SparseUnivariatePolynomial
      (SparseUnivariatePolynomial(Integer))

(5)

c 1

(6)

c 2

(7)

mac 2

(8)

I don't know but the output of c(2) is wrong. I would have expected "? ? + 1" in accordance to mac(2). So the typed form of you example doesn't work. And the output looks ugly anyway. :-(

Ralf

Here I even don't define the type of the function:

)clear all

   All user variables and function definitions have been cleared.
c 0==1; c 1==1; c n==c(n-1)+s*(reduce(+,[q^k*c(k)*c(n-1-k) for k in 1..(n-1)::NNI]));

[coefficient(univariate(c(n),s),1) for n in 0..4]

Compiling function c with type Integer -> Polynomial(Integer)

Compiling function G36 with type Integer -> Boolean

(9)

I don't know why it gives up in your exemple though.

Greg