Zulip Chat Archive
Stream: Is there code for X?
Topic: negation on module as linear map
Kevin Buzzard (Aug 26 2024 at 15:17):
I can't find this:
import Mathlib.Algebra.Module.LinearMap.Basic
def LinearMap.neg (R : Type*) [Ring R] (A : Type*) [AddCommGroup A] [Module R A] : A →ₗ[R] A where
toFun := (-·)
map_add' := neg_add
map_smul' r a := (smul_neg r a).symm
Do we not have it? Do we not want it for some reason? Have I named it correctly?
Ruben Van de Velde (Aug 26 2024 at 15:21):
import Mathlib.Algebra.Module.LinearMap.Basic
def LinearMap.neg (R : Type*) [Ring R] (A : Type*) [AddCommGroup A] [Module R A] : A →ₗ[R] A :=
-LinearMap.id
theorem LinearMap.neg_apply' (R : Type*) [Ring R] (A : Type*) [AddCommGroup A] [Module R A] (x : A) :
LinearMap.neg R A x = -x := rfl
Eric Wieser (Aug 26 2024 at 15:26):
Ruben Van de Velde (Aug 26 2024 at 15:46):
Or that!
Kevin Buzzard (Aug 26 2024 at 16:07):
Thanks both!
Last updated: May 02 2025 at 03:31 UTC