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

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

[Mattias Engdegård]

Thank you for reporting this. It seems that Calc first simplifies gcd(0,n) to n and then computes sum(n,n,-1,-1) = -1.
We could either make gcd(0,x)=gcd(x,0)=|x|, or try preventing sum from simplifying its operand first, or both.
For the smallest possible change, what about the hack below?

--- a/lisp/calc/calc-comb.el
+++ b/lisp/calc/calc-comb.el
@@ -241,8 +241,8 @@ calcFunc-gcd
         (calcFunc-gcd (math-neg a) b))
        ((Math-looks-negp b)
         (calcFunc-gcd a (math-neg b)))
-       ((Math-zerop a) b)
-       ((Math-zerop b) a)
+       ((Math-zerop a) (math-abs b))
+       ((Math-zerop b) (math-abs a))
        ((and (Math-ratp a)
              (Math-ratp b))
         (math-make-frac (math-gcd (if (eq (car-safe a) 'frac) (nth 1 a) a)

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

[David Ongaro]

On 15.05.20, 03:19, "Mattias Engdegård" <mattiase@acm.org> wrote:

> Thank you for reporting this. It seems that Calc first simplifies gcd(0,n) to n and then computes sum(n,n,-1,-1) = -1.
> We could either make gcd(0,x)=gcd(x,0)=|x|, or try preventing sum from simplifying its operand first, or both.
> For the smallest possible change, what about the hack below?

I see, so the simplest reproduction of the bug doesn't involve the sum, but just the evaluation of gcd(0, x) or gcd(x, 0). Your fix seems sensible to me, I don't see why you consider it a 'hack'. The simplification gcd(0, x)=gcd(x, 0)=abs(x) seems legit and matches the gcd definition "The largest positive integer that divides each of the integers".

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

[Mattias Engdegård]

15 maj 2020 kl. 19.44 skrev David Ongaro <david.ongaro@hamburg.de>:

> I see, so the simplest reproduction of the bug doesn't involve the sum, but just the evaluation of gcd(0, x) or gcd(x, 0). Your fix seems sensible to me, I don't see why you consider it a 'hack'. The simplification gcd(0, x)=gcd(x, 0)=abs(x) seems legit and matches the gcd definition "The largest positive integer that divides each of the integers".

Quite, but there is a small possibility that further simplification relies on the gcd(0,x)=x behaviour. You never know with Calc: it is complex and everything seems interconnected. After all, abs is often an obstacle in algebraic transforms; you often end up splitting cases.

That said, it's probably the right thing to do. Now pushed to master, which means that you need to build a development snapshot from source, or apply the change (60cd6cce55) to your Emacs.