Missed division by zero when using dollar variables on RHS

[jodavies]

The following script should crash, but instead yields test = 0;.

Symbol x;

Local test = x;

$num = 0;
$den = 0;

Identify x = $num/$den;

Print;
.end

If $num is set to any non-zero value or expression, FORM gives Division by zero during normalization as expected.

Thanks, Josh.

[jodavies]

Further, while trying to define

$test = 0/0;

causes a crash,

Symbol x,y,z;
Local F = x;
Bracket x,y,z;
.sort
$test = F[y]/F[z];

does not ($test gets the value 0). The same is true for

$test = 0/(1-1);

[tueda]

Another example to circumvent the division by zero error and get the (wrong) 0:

FORM 4.1 (Jun 10 2017, v4.1-20131025-355-g0bf5c58) 64-bits  Run: Mon Jun 19 18:58:12 2017
    S x,y;
    L F = x/y * replace_(y,0,x,0);
    P;
    .end

   F = 0;

I guess they are related to the subexpression substitution.

[vermaseren]

In this one you are on slippery ground. If it first replaces the x and then sees that you get zero, it never gets to replace the y. It is the same as taking the limit x->0,y->0 or the other way around.

Jos

On 19 jun. 2017, at 19:00, Takahiro Ueda notifications@github.com wrote:

Another example to circumvent the division by zero error and get the (wrong) 0:

FORM 4.1 (Jun 10 2017, v4.1-20131025-355-g0bf5c58) 64-bits Run: Mon Jun 19 18:58:12 2017 S x,y; L F = x/y * replace_(y,0,x,0); P; .end

F = 0; I guess they are related to the subexpression substitution.

— You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub https://github.com/vermaseren/form/issues/202#issuecomment-309502499, or mute the thread https://github.com/notifications/unsubscribe-auth/AFLxEurXHpzi90v_3g8H7VLVnc4xfptPks5sFqkrgaJpZM4N-gAZ.

[vermaseren]

To be more precise about what happens: In all these cases both replacements (the dollars, the F[z], etc) are made simultaneously. But now comes the point: 0 is not a value in a sense: there is no term. Hence when you have $x/$y it becomes no term when it does the $x. If it does the $y first that is inside a denominator function which than happily has a zero argument (because inside a function it does become zero. If an expression has no terms it is seen as zero. Hence if the $y goes first you get $x/den(0) after which the $x gives no terms. The normalization is done only after there are no more subexpressions to be substituted. (of course $x’/$y’ would give a crash).

This behaviour is very fundamental in FORM. Hence you should guard yourself against this kind of order of ‘limits’.

Jos

On 19 jun. 2017, at 19:33, Jos Vermaseren t68@nikhef.nl wrote:

In this one you are on slippery ground. If it first replaces the x and then sees that you get zero, it never gets to replace the y. It is the same as taking the limit x->0,y->0 or the other way around.

Jos

On 19 jun. 2017, at 19:00, Takahiro Ueda <notifications@github.com mailto:notifications@github.com> wrote:

Another example to circumvent the division by zero error and get the (wrong) 0:

FORM 4.1 (Jun 10 2017, v4.1-20131025-355-g0bf5c58) 64-bits Run: Mon Jun 19 18:58:12 2017 S x,y; L F = x/y * replace_(y,0,x,0); P; .end

F = 0; I guess they are related to the subexpression substitution.

— You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub https://github.com/vermaseren/form/issues/202#issuecomment-309502499, or mute the thread https://github.com/notifications/unsubscribe-auth/AFLxEurXHpzi90v_3g8H7VLVnc4xfptPks5sFqkrgaJpZM4N-gAZ.