I just want to know if both these two MiniZinc solver use infinite precision arithmetic by default.
Do Gecode and G12 (MIP) use infinite precision arithmetic?
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Neither Gecode nor the G12 solvers support infinite precision. Both these solvers and all other MiniZinc solvers that I'm aware of only support floating point arithmetic. This is partially because the MiniZinc compiler does not have support for infinite precision, (see How to obtain an exact infinite-precision representation of rational numbers via a non-standard FlatZinc extension?).