Theorems · Theorem · commutative algebra
Algebra.discr_def
∀ (A : Type u) {B : Type v} {ι : Type w} [inst : DecidableEq ι] [inst_1 : CommRing A] [inst_2 : CommRing B]
[inst_3 : Algebra A B] [inst_4 : Fintype ι] (b : ι → B), Algebra.discr A b = (Algebra.traceMatrix A b).det- Defined in
- Mathlib.RingTheory.Discriminant
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fintypestatement and proof · cited by 7,736
- Matrix.detstatement · cited by 665
- Algebra.discrstatement · cited by 38
- Algebra.traceMatrixstatement · cited by 24
Cited by12
Results whose statement or proof uses this declaration.
- Algebra.discr_reindexproof · cited by 7
- Algebra.discr_eq_det_embeddingsMatrixReindex_pow_twoproof · cited by 4
- Algebra.discr_localizationLocalizationproof · cited by 3
- Algebra.discr_not_zero_of_basisproof · cited by 3
- Rat.numberField_discrproof · cited by 2
- Algebra.discr_of_matrix_vecMulproof · cited by 2
- Algebra.discr_eq_discr_of_algEquivproof · cited by 1
- Algebra.discr_mul_isIntegral_mem_adjoinproof · cited by 1
- Algebra.discr_isIntegralproof · cited by 0
- Algebra.discr_of_matrix_mulVecproof · cited by 0
- Algebra.discr_zero_of_not_linearIndependentproof · cited by 0
- isIntegral_discr_mul_of_mem_traceDualproof · cited by 0