Axiom provides functionality to evaluate operators using a given evaluation function. Unfortunately, it is broken.

g := operator 'g;

Type: BasicOperator

eval(g(1783), g, i+->i)

(1)

Type: Expression(Integer)

eval(g(n), g, i+->i)

(2)

Type: Expression(Integer)

eval(a*g(n), g, i+->i)

(3)

Type: Expression(Integer)

eval(a*g(1783), g, i+->i)

(4)

Type: Expression(Integer)

I guess that the problem is in 'smprep$FS':

      smprep(lop, lexp, lfunc, p) ==
      ..(v := mainVariable p) case "failed" => p::%
      ..symbolIfCan(k := v::K) case SY => p::%
      ..g := (op := operator k)
      .....(arg := [eval(a,lop,lexp,lfunc) for a in argument k]$List(%))
      ..q := map(eval(#1::%, lop, lexp, lfunc),
      ...........univariate(p, k))$SparseUnivariatePolynomialFunctions2(MP, %)
      ..(n := position(name op, lop)) < minIndex lop => q g
      ..a:%  := 0
      ..f    := eval((lfunc.n) arg, lop, lexp, lfunc)
      ..e    := lexp.n
      ..while q ^= 0 repeat
      ....m  := degree q
      ....qr := divide(m, e)
      ....t1 := f ** (qr.quotient)::N
      ....t2 := g ** (qr.remainder)::N
      ....a  := a + leadingCoefficient(q) * t1 * t2
      ....q  := reductum q
      ..a

It seems that Axiom picks the wrong mainVariable in the broken case, namely a instead of g(1783). I badly need this fixed...

Martin

no patch available