Theorems · Theorem · number theory
UpperHalfPlane.coe_specialLinearGroup_apply
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : Algebra R ℝ] (g : Matrix.SpecialLinearGroup (Fin 2) R)
(z : UpperHalfPlane),
↑(g • z) =
(↑((algebraMap R ℝ) (↑g 0 0)) * ↑z + ↑((algebraMap R ℝ) (↑g 0 1))) /
(↑((algebraMap R ℝ) (↑g 1 0)) * ↑z + ↑((algebraMap R ℝ) (↑g 1 1)))- Cited by
- 10 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Complexstatement and proof · cited by 5,565
- Algebra.algebraMapstatement and proof · cited by 4,706
- Matrixstatement · cited by 4,303
- Units.valproof · cited by 1,966
- Complex.ofRealstatement and proof · cited by 1,654
- Matrix.detstatement · cited by 665
- UpperHalfPlanestatement and proof · cited by 626
Cited by10
Results whose statement or proof uses this declaration.
- UpperHalfPlane.modular_S_smulproof · cited by 9
- UpperHalfPlane.modular_T_zpow_smulproof · cited by 4
- UpperHalfPlane.specialLinearGroup_applystatement and proof · cited by 4
- ModularGroup.coe_T_zpow_smul_eqproof · cited by 3
- EisensteinSeries.D2_mulproof · cited by 2
- ModularGroup.smul_eq_lcRow0_addproof · cited by 1
- UpperHalfPlane.toSL2R_smul_Iproof · cited by 0
- UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_eq_zeroproof · cited by 0
- UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_ne_zeroproof · cited by 0
- ModularGroup.normSq_S_smul_lt_oneproof · cited by 0