Commit 2023-12-13 19:05 8a221878
View on Github →feat(Data/Polynomial/RingDivision): improvements to Polynomial.rootMultiplicity
(#8563)
Main changes:
- add
Monic.mem_nonZeroDivisors
andmem_nonZeroDivisors_of_leadingCoeff
which states that a monic polynomial (resp. a polynomial whose leading coefficient is not zero divisor) is not a zero divisor. - add
rootMultiplicity_mul_X_sub_C_pow
which states that* (X - a) ^ n
adds the root multiplicity ata
byn
. - change the conditions in
rootMultiplicity_X_sub_C_self
,rootMultiplicity_X_sub_C
androotMultiplicity_X_sub_C_pow
fromIsDomain
toNontrivial
. - add
rootMultiplicity_eq_natTrailingDegree
which relatesrootMultiplicity
andnatTrailingDegree
, andeval_divByMonic_eq_trailingCoeff_comp
. - add
le_rootMultiplicity_mul
which is similar tole_trailingDegree_mul
. - add
rootMultiplicity_mul'
which slightly generalizesrootMultiplicity_mul
InData/Polynomial/FieldDivision
: - add
rootMultiplicity_sub_one_le_derivative_rootMultiplicity_of_ne_zero
which slightly generalizesrootMultiplicity_sub_one_le_derivative_rootMultiplicity
. - add
derivative_rootMultiplicity_of_root_of_mem_nonZeroDivisors
which slightly generalizesderivative_rootMultiplicity_of_root
. - add several theorems relating roots of iterate derivative to
rootMultiplicity
In addition: - move
eq_of_monic_of_associated
from RingDivision to Monic and generalize. - add
dvd_cancel
lemmas to NonZeroDivisors. - add
algEquivOfCompEqX
: two polynomials that compose to X both ways induces an isomorphism of the polynomial algebra. - add divisibility lemmas to Polynomial/Derivative.