# 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
-------------------------------

```