Theorems · Theorem · commutative algebra
PowerSeries.IsWeierstrassDivisionAt.eq_mul_add
∀ {A : Type u_1} [inst : CommRing A] {f g q : PowerSeries A} {r : Polynomial A} {I : Ideal A},
f.IsWeierstrassDivisionAt g q r I → f = g * q + ↑r- Cited by
- 11 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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
- Polynomialstatement and proof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- PowerSeriesstatement and proof · cited by 797
- Polynomial.toPowerSeriesstatement · cited by 96
- PowerSeries.IsWeierstrassDivisionAtstatement and proof · cited by 12
Cited by11
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassDivision.elimproof · cited by 3
- PowerSeries.IsWeierstrassDivisionAt.smulproof · cited by 2
- PowerSeries.IsWeierstrassDivisorAt.mod_smulproof · cited by 2
- PowerSeries.IsWeierstrassDivisorAt.div_smulproof · cited by 2
- PowerSeries.IsWeierstrassDivisionAt.addproof · cited by 2
- PowerSeries.IsWeierstrassDivisorAt.div_addproof · cited by 1
- PowerSeries.IsWeierstrassDivision.isWeierstrassFactorizationproof · cited by 1
- PowerSeries.IsWeierstrassDivisionAt.coeff_f_sub_r_memproof · cited by 1
- PowerSeries.IsWeierstrassDivisorAt.mod_addproof · cited by 1
- PowerSeries.eq_mul_weierstrassDiv_add_weierstrassModproof · cited by 0
- PowerSeries.IsWeierstrassDivisorAt.mk_mod'_eq_selfproof · cited by 0