# WeierstrassPreparation R¶

weier.spad line 1 [edit on github]

R: Field

This package implements the Weierstrass preparation theorem `f`

for multivariate power series. weierstrass(`v`

, `p`

) where `v`

is a variable, and `p`

is a TaylorSeries(`R`

) in which there is term of form c*v^s where `c`

is a constant. Let `s`

be minimal as above. The result is a list of TaylorSeries coefficients A[`i`

] of the equivalent polynomial A = A[0] + A[1]`*v`

+ A[2]`*v^2`

+ … + A[`s`

-1]`*v^`

(`s`

-1) + `v^s`

such that p=A*B , `B`

being a TaylorSeries of minimum degree 0

- weierstrass: (Symbol, TaylorSeries R) -> List TaylorSeries R
`weierstrass(v, ts)`

where`v`

is a variable and`ts`

is a TaylorSeries, implements the Weierstrass Preparation Theorem. The result is a list of TaylorSeries that are the coefficients of the equivalent series.