# ApCoCoA-1:Weyl.Inw

## Weyl.Inw

Computes the initial form of a polynomial in Weyl algebra `A_n` with respect to the weight vector `W=(u_i,v_i)`.

### Syntax

Weyl.Inw(P:POLY,W:LIST):POLY

### Description

*Please note:* The function(s) explained on this page is/are using the *ApCoCoAServer*. You will have to start the ApCoCoAServer in order to use it/them.

Computes the initial form of a normally ordered Weyl polynomial P in the Weyl algebra D with respect to weight vector `W=(u,v)` such that `u+v >= 0`. Here `u=(u1,...,un)` and `v=(v1,...,vn)` are weights of indeterminates `[x1,...,xn]` and `[y1,...,yn]` respectively. Note that `Inw(P,W)` is a polynomial in the graded ring of D with respect to weight vector `W`.

@param

*P*A polynomial in the Weyl algebra.@param

*W*A list of n positive integers, where n = number of indeterminates.@return A polynomial, which is the initial form of

`P`with respect to`W`.

*Beta Warning:* This method, package or class is a beta version. It may not work as intended or its interface may change in the next version! So please be careful when you're intending to use it.

#### Example

Use A2::=QQ[x[1..2],d[1..2]]; W:=[0,0,1,1]; Weyl.Inw(x[1]d[1]+x[1],W); x[1]d[1] ------------------------------- Weyl.Inw(x[1]d[1]+d[1],W); x[1]d[1] + d[1] ------------------------------- Weyl.Inw(x[1]d[1]+x[2]d[2]+d[2]^2,W); d[2]^2 ------------------------------- Weyl.Inw(3x[1]d[1]^2+4x[2]d[1]+d[2]^2,W); 3x[1]d[1]^2 + d[2]^2 ------------------------------- W2:=[-1,-1,1,1]; Weyl.Inw(3x[1]d[1]+4x[2]d[1]+6x[2]d[2],W2); 3x[1]d[1] + 4x[2]d[1] + 6x[2]d[2] ------------------------------- Weyl.Inw(0,W); 0 -------------------------------

### See also