[Merged by Bors] - feat: recognize scientific notation in norm_num
#1707
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* `Rat` * `DivisionRing`s
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* `Rat.ofScientific` was made irreducible
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We implement #1706. In addition to a `norm_num` extension for `OfScientific.ofScientific`, we implement extensions for * `Int.ofNat` * `mkRat` * `Rat.cast`/`RatCast.ratCast` which made implementation more convenient. We also patch up the other two `*.cast` evaluators consistently while we're at it. We create an instance of `OfScientific K` for any division ring `K`. See [Zulip discussion here](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/OfScientific) for the original discussion, and [this Zulip discussion](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/finishing.20up.20ofScientific.20in.20norm_num) for the more recent one.
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We implement #1706. In addition to a `norm_num` extension for `OfScientific.ofScientific`, we implement extensions for * `Int.ofNat` * `mkRat` * `Rat.cast`/`RatCast.ratCast` which made implementation more convenient. We also patch up the other two `*.cast` evaluators consistently while we're at it. We create an instance of `OfScientific K` for any division ring `K`. See [Zulip discussion here](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/OfScientific) for the original discussion, and [this Zulip discussion](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/finishing.20up.20ofScientific.20in.20norm_num) for the more recent one.
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We implement #1706. In addition to a `norm_num` extension for `OfScientific.ofScientific`, we implement extensions for * `Int.ofNat` * `mkRat` * `Rat.cast`/`RatCast.ratCast` which made implementation more convenient. We also patch up the other two `*.cast` evaluators consistently while we're at it. We create an instance of `OfScientific K` for any division ring `K`. See [Zulip discussion here](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/OfScientific) for the original discussion, and [this Zulip discussion](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/finishing.20up.20ofScientific.20in.20norm_num) for the more recent one.
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We implement #1706. In addition to a `norm_num` extension for `OfScientific.ofScientific`, we implement extensions for * `Int.ofNat` * `mkRat` * `Rat.cast`/`RatCast.ratCast` which made implementation more convenient. We also patch up the other two `*.cast` evaluators consistently while we're at it. We create an instance of `OfScientific K` for any division ring `K`. See [Zulip discussion here](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/OfScientific) for the original discussion, and [this Zulip discussion](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/finishing.20up.20ofScientific.20in.20norm_num) for the more recent one.
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We implement #1706. In addition to a `norm_num` extension for `OfScientific.ofScientific`, we implement extensions for * `Int.ofNat` * `mkRat` * `Rat.cast`/`RatCast.ratCast` which made implementation more convenient. We also patch up the other two `*.cast` evaluators consistently while we're at it. We create an instance of `OfScientific K` for any division ring `K`. See [Zulip discussion here](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/OfScientific) for the original discussion, and [this Zulip discussion](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/finishing.20up.20ofScientific.20in.20norm_num) for the more recent one.
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We implement #1706. In addition to a `norm_num` extension for `OfScientific.ofScientific`, we implement extensions for * `Int.ofNat` * `mkRat` * `Rat.cast`/`RatCast.ratCast` which made implementation more convenient. We also patch up the other two `*.cast` evaluators consistently while we're at it. We create an instance of `OfScientific K` for any division ring `K`. See [Zulip discussion here](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/OfScientific) for the original discussion, and [this Zulip discussion](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/finishing.20up.20ofScientific.20in.20norm_num) for the more recent one.
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We implement #1706.
In addition to a
norm_numextension forOfScientific.ofScientific, we implement extensions forInt.ofNatmkRatRat.cast/RatCast.ratCastwhich made implementation more convenient. We also patch up the other two
*.castevaluators consistently while we're at it.We create an instance of
OfScientific Kfor any division ringK.See Zulip discussion here for the original discussion, and this Zulip discussion for the more recent one.
=,≠,<, and≤functionality fornorm_num#1568Ratfunctionality forring#1711RatCastinto std4 batteries#101Rat.ofScientific@[irreducible]batteries#109-->