group.init(ZR, 1) seems not to be the unit element of ZR

[BatchClayderman]

I just wonder why a ZR element multiplied by the unit element of ZR does not equal the ZR element itself. I also tested G1, G2, and GT, and they seemed correct. This only occurs in ZR. Thanks a lot.

Python 3.12.3 (main, Feb  4 2025, 14:48:35) [GCC 13.3.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> from charm.toolbox.pairinggroup import PairingGroup, G1, G2, GT, ZR, pair, pc_element as Element
>>> group = PairingGroup("MNT159")
>>> a = group.random(ZR)
>>> a
188815440526010565054965130509425098763942272676
>>> a * group.init(ZR, 1)
156580808495405483017373581644025127177670904615
>>> a * group.init(ZR, 1) == a
False

[BatchClayderman]

Moreover, I found it different between $a^2$ and $a \cdot a$. I am quite confused, as I am doing poly (get coeff) operations.

>>> a = group.init(ZR, 1)
>>> a
39550891532896283937502575885313771404912213068
>>> a * a
194235704597595070195113220508995291822197569133
>>> a ** 2
63826218164023919447182475197086168844097555376
>>> a ** group.init(ZR, 2)
49267280646517165064078019677736182628899789843

[Komorebi-Z]

I've pinpointed the issue to the longObjToMPZ() call within the Element_elem() initialization function in charm/core/math/pairing/pairingmodule.c, specifically during the conversion from mpz to PyLongObj types. Please see #328 for details. Could you please help test if this PR is effective in your environment? I'd be glad if it resolves your issue. By the way, a passive workaround is to downgrade your Python version below 3.12.

[BatchClayderman]

Thank you so much for fixing this issue. I have tested your PR, and it worked fine. Everything looks normal now.

Python 3.12.3 (main, Feb  4 2025, 14:48:35) [GCC 13.3.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> from charm.toolbox.pairinggroup import PairingGroup, G1, G2, GT, ZR, pair, pc_element as Element
>>> group = PairingGroup("MNT159")
>>> a = group.init(ZR, 1)
>>> a
1
>>> b = group.random(ZR)
>>> b
169851866263594407843832815149500595461809004778
>>> a * b
169851866263594407843832815149500595461809004778
>>> b * b
184426243201845971707370993815914046906457034898
>>> b ** 2
184426243201845971707370993815914046906457034898
>>> b ** group.init(ZR, 2)
184426243201845971707370993815914046906457034898
>>> c = group.random(G1)
>>> c
[238356461368512960310768958592326641699639523925, 420895074874704729138443633933109782619382057767]
>>> a * c
[238356461368512960310768958592326641699639523925, 420895074874704729138443633933109782619382057767]
>>>