Behavior of implicit sets containing linear combinations of vectors

[Vladyslav Shtabovenko]

Hi,

as I understand, FORM actually only supports implicit vectors sets where each element is a single vector.
Nevertheless, the following code "works" with a somewhat unexpected result:

off statistics;

CF prop, F;
S mq, s;
Auto V k,p, v;

L amp = prop(k1,mq)*prop(-k1+k2,mq)*prop(k3,mq)*prop(k1-p1+k2,0);
id prop(v?{k1,-k1, k2,-k2,k1+k2,k1-k2,-k1-k2,-k1+k2,k3,-k3},mq) = prop(v,mq)*F(v);

print;
.end

yields

amp =
      prop(k1,mq)*prop(k3,mq)*prop( - k1 + k2,mq)*prop(k1 + k2 - p1,0)*F(k1)*
      F(k3);

It seems that in this case the compiler interprets {k1,-k1, k2,-k2,k1+k2,k1-k2,-k1-k2,-k1+k2,k3,-k3} as
{k1,-k1, k2,-k2,k1,k2,k1,-k2,-k1,-k2,-k1,+k2,k3,-k3} which can be confirmed by trying to write an id statement
that uses the position of the element in a set

id prop(v?{k1,-k1, k2,-k2,k1+k2,k1-k2,-k1-k2,-k1+k2,k3,-k3}[n],mq) = prop(v,mq)*F({1,2,3,4,5,6,7,8,9,10}[n]);

leads to

Array bound check during set substitution
    value is 13

Is this behavior mentioned somewhere in a manual, or would one rather classify it as a bug?

Cheers,
Vlad

[Takahiro Ueda]

In a discussion of Issue #78, Jos said

Vector sets can only consist of vectors like p, not -p.

So, I guess there was an implicit assumption that the definition of a set in the reference manual,

A set is a (non-empty) collection of variables that should all be of the same type.

was also applied to implicitly declared sets; sums of variables are not expected. Then, it was extended to allow "minus vectors" like -p in v4.2.0.

Indeed, usual Set statements and implicitly declared sets seem to share the parser (which sounds reasonable); the same happens also for usual set declarations.

On names;
V p1,p2;
Set pp: p1,p2,p1+p2;
.end

and

On names;
V p1,p2;
CF f;
id f(p1?{p1,p2,p1+p2}) = 1;
.end

are accepted by FORM but print the set as p1 p2 p1 -p2. Interestingly, the last element of the set (-p2) has a minus sign. If I change Vectors to Symbols,

S p1,p2;
Set pp: p1,p2,p1+p2;
.end

then this gives an error:

test.frm Line 2 --> Illegal use of - sign in set. Can use only with vector or n
umber

which sounds like the routine is very "optimized" to parse minus vectors.

Having said that, FORM should give appropriate errors if they are not allowed (as Ben said in #78), so I would call it a kind of "bug".