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[Merged by Bors] - feat: add ofScientific lemmas for Complex/RCLike/Quaternion #39628

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[Merged by Bors] - feat: add ofScientific lemmas for Complex/RCLike/Quaternion #39628

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1fddd16
feat: add `ofScientific` lemmas for `Complex`
eric-wieser May 20, 2026
376d5c8
and for rclike
eric-wieser May 20, 2026
f865d15
and for quaternion
eric-wieser May 20, 2026
9f533b4
forgot to commit
eric-wieser May 20, 2026
c39b047
golf and fix names
eric-wieser May 20, 2026
a8fe9f2
Merge branch 'master' into ofScientific
eric-wieser May 25, 2026
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12 changes: 12 additions & 0 deletions Mathlib/Algebra/Quaternion.lean
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Expand Up @@ -1173,6 +1173,18 @@ instance instRatCast : RatCast ℍ[R] where ratCast q := (q : R)

@[norm_cast] lemma coe_ratCast (q : ℚ) : ↑(q : R) = (q : ℍ[R]) := rfl

section ofScientific
open OfScientific (ofScientific)
variable (m : ℕ) (s : Bool) (e : ℕ)

@[norm_cast] lemma coe_ofScientific : ((ofScientific m s e : R) : ℍ[R]) = ofScientific m s e := rfl
@[simp] lemma re_ofScientific : (ofScientific m s e : ℍ[R]).re = ofScientific m s e := rfl
@[simp] lemma imI_ofScientific : (ofScientific m s e : ℍ[R]).imI = 0 := rfl
@[simp] lemma imJ_ofScientific : (ofScientific m s e : ℍ[R]).imJ = 0 := rfl
@[simp] lemma imK_ofScientific : (ofScientific m s e : ℍ[R]).imK = 0 := rfl

end ofScientific
Comment on lines +1176 to +1186

@ocfnash ocfnash May 25, 2026

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It's quite hard to think of how we'd ever use these but I guess they're very cheap to add / maintain.


variable [LinearOrder R] [IsStrictOrderedRing R] (a b : ℍ[R])

@[simps -isSimp]
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14 changes: 14 additions & 0 deletions Mathlib/Analysis/RCLike/Basic.lean
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Expand Up @@ -631,6 +631,20 @@ theorem ratCast_re (q : ℚ) : re (q : K) = q := by rw [← ofReal_ratCast, ofRe
@[simp, rclike_simps, norm_cast]
theorem ratCast_im (q : ℚ) : im (q : K) = 0 := by rw [← ofReal_ratCast, ofReal_im]

open OfScientific (ofScientific)

@[rclike_simps, norm_cast]
theorem ofReal_ofScientific (m : ℕ) (s : Bool) (e : ℕ) :
((ofScientific m s e : ℝ) : K) = ofScientific m s e := ofReal_nnratCast _

@[simp, rclike_simps]
theorem ofScientific_re (m : ℕ) (s : Bool) (e : ℕ) :
re (ofScientific m s e : K) = ofScientific m s e := by rw [← ofReal_ofScientific, ofReal_re]

@[simp, rclike_simps, norm_cast]
theorem ofScientific_im (m : ℕ) (s : Bool) (e : ℕ) :
im (ofScientific m s e : K) = 0 := by rw [← ofReal_ofScientific, ofReal_im]
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ocfnash marked this conversation as resolved.

/-! ### Norm -/

theorem norm_of_nonneg {r : ℝ} (h : 0 ≤ r) : ‖(r : K)‖ = r :=
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6 changes: 6 additions & 0 deletions Mathlib/Data/Complex/Basic.lean
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Expand Up @@ -347,6 +347,8 @@ instance instRatCast : RatCast ℂ where ratCast q := ofReal q
@[simp, norm_cast] lemma ofReal_intCast (n : ℤ) : ofReal n = n := rfl
@[simp, norm_cast] lemma ofReal_nnratCast (q : ℚ≥0) : ofReal q = q := rfl
@[simp, norm_cast] lemma ofReal_ratCast (q : ℚ) : ofReal q = q := rfl
@[simp, norm_cast] lemma ofReal_ofScientific (m : ℕ) (s : Bool) (e : ℕ) :
ofReal (OfScientific.ofScientific m s e : ℝ) = OfScientific.ofScientific m s e := rfl

@[simp] lemma re_ofNat (n : ℕ) [n.AtLeastTwo] : (ofNat(n) : ℂ).re = ofNat(n) := rfl
@[simp] lemma im_ofNat (n : ℕ) [n.AtLeastTwo] : (ofNat(n) : ℂ).im = 0 := rfl
Expand All @@ -358,6 +360,10 @@ instance instRatCast : RatCast ℂ where ratCast q := ofReal q
@[simp, norm_cast] lemma im_nnratCast (q : ℚ≥0) : (q : ℂ).im = 0 := rfl
@[simp, norm_cast] lemma ratCast_re (q : ℚ) : (q : ℂ).re = q := rfl
@[simp, norm_cast] lemma ratCast_im (q : ℚ) : (q : ℂ).im = 0 := rfl
@[simp] lemma re_ofScientific (m : ℕ) (s : Bool) (e : ℕ) :
(OfScientific.ofScientific m s e : ℂ).re = OfScientific.ofScientific m s e := rfl
@[simp] lemma im_ofScientific (m : ℕ) (s : Bool) (e : ℕ) :
(OfScientific.ofScientific m s e : ℂ).im = 0 := rfl


/-! ### Ring structure -/
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