bug#41279: 26.3; Calc: sum(gcd(0,n),n,-1,-1) evaluates to -1

[David Ongaro]

By accident I noticed that this algebraic expression yields 6 instead of
8 which would be correct:

    sum(sum(gcd(n, k), k, -1, 1), n, -1, 1) => 6

I could narrow it down to this, which yields -1 instead of 1

    sum(gcd(0, n), n , -1, -1) => -1

Notably gcd(0, -1) evaluates to 1 as it should be. Also we have

    sum(gcd(n, 0), n, -1, -1) => -1

but

    sum(sum(gcd(n, k), k, 0, 0), n, -1, -1) => -1

    sum(sum(gcd(n, k), k, -1, -1), n, 0, 0) => 1

which violates gcd(n, k) = gcd(k, n). We also have

    sum(sum(gcd(n, k) = 1, k, -1, 1), n, -1, 1) => 7

    sum(sum(abs(gcd(n, k)), k, -1, 1), n, -1, 1) => 8

which seems to confirm that it's not just the sum function but the
combination of sum and gcd which might introduce the problem.

To reproduce you can simply enter Calc embedded mode with C-x 8 e in a
buffer with this email content, put the point on a corresponding
formular and reevaluate with SPACE.

I'd appreciate if this could be fixed.

David



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