[SCIP] Why SCIP reformulates bilinear constraints while writing problem in CIP format?

[Vladimir V. Voloshinov]

Dear SCIP developers,
we use the following console command to convert NL-file to CIP format (as
an input of ParaSCIP). E,g, for PROBLEm.nl it looks like
$ echo "write problem PROBLEM.cip quit" | scipampl PROBLEM.nl -i
It works correctly, but recently I noticed some strange reformulation of
constraints in resulting CIP-file.
It seems, that it concerns homogeneous expressions only. At least I did not
found that  "reformulation" for "non-homogeneous" constraints.

E.g. if original problem has constraints on norm of vector of variables
x[1]^2 + x[2]^2 = 1,
then it will appear into the following form (no questions!)
[quadratic] <cons_norm>: <x[1]>[C]^2 +<x[2]>[C]^2 == 1;

But if original problem has constraint on vectors product
x[1]*y[2] - x[2]*y[1] <= 0,
then it will appear in CIP file in the following (equivalent)  form:
[quadratic] <cons_vp>:  +0.5<x[1]>[C]<y[2]>[C] -0.5<x[2]>[C]<y[1]>[C]
-0.5<x[2]>[C]<y[1]>[C] +0.5<x[1]>[C]<y[2]>[C] <= 0;
But why?! What is the reason for this transformation?

Best regards,
Vladimir V. Voloshinov,
head of lab. C-3 "Distributed computing algorithms",
http://www.iitp.ru/ru/researchlabs/1040.htm,
Center for Distributed Computing, http://distcomp.ru, Institute for
Information Transmission Problems RAS
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