# Difference between revisions of "ApCoCoA-1:Weyl.InIw"

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Weyl.InIw(I4,[0,0,0,0,1,1,1,1]); --This function is implemented only for positive weights! | Weyl.InIw(I4,[0,0,0,0,1,1,1,1]); --This function is implemented only for positive weights! | ||

ERROR: All weights shoud be strictly positive | ERROR: All weights shoud be strictly positive | ||

− | CONTEXT: Error( | + | CONTEXT: Error("All weights shoud be strictly positive") |

------------------------------- | ------------------------------- | ||

Weyl.InIw(I4,[1,1,1,1,2,2,1,1]); | Weyl.InIw(I4,[1,1,1,1,2,2,1,1]); |

## Latest revision as of 13:50, 29 October 2020

This article is about a function from ApCoCoA-1. |

## Weyl.InIw

Computes the initial ideal of a D-ideal `I` in Weyl algebra `A_n` with respect to the weight vector `W=(u_i,v_i)`.

### Syntax

Weyl.InIw(I:IDEAL,W:LIST):IDEAL

### 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 ideal of a D-ideal `I` 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 `InIw(P,W)` is an ideal of graded ring of D with respect to weight vector `W`. Due to limitations in CoCoA4, all `u_i` and `v_i` should be positive integers. Computation of initial ideal if `u+v= 0` is not implemented yet.

@param

*I*An ideal in the Weyl algebra.@param

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

`I`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 A4::=QQ[x[1..4],d[1..4]]; I4:=Ideal(d[2]d[3]-d[1]d[4],x[1]d[1]-x[4]d[4]-1,x[2]d[2]+x[4]d[4]+1,x[3]d[3]+x[4]d[4]+2); Weyl.InIw(I4,[0,0,0,0,1,1,1,1]); --This function is implemented only for positive weights! ERROR: All weights shoud be strictly positive CONTEXT: Error("All weights shoud be strictly positive") ------------------------------- Weyl.InIw(I4,[1,1,1,1,2,2,1,1]); -- CoCoAServer: computing Cpu Time = 0.016 ------------------------------- Ideal(x[2]x[3]x[4]d[4]^2 - x[1]x[4]^2d[4]^2, x[1]x[4]d[3]d[4] + x[2]x[4]d[4]^2, x[1]x[4]d[2]d[4], x[2]d[1]d[4], x[3]d[1]d[4] + x[4]d[2]d[4], x[1]d[1], x[2]d[2], x[3]d[3] + x[4]d[4], d[2]d[3] - d[1]d[4]) ------------------------------- Weyl.InIw(I4,[1,2,1,1,2,2,1,1]); -- CoCoAServer: computing Cpu Time = 0.032 ------------------------------- Ideal(x[2]x[4]d[4]^2, x[1]x[4]d[2]d[4], x[2]d[1]d[4], x[3]d[1]d[4] + x[4]d[2]d[4], x[1]d[1], x[2]d[2], x[3]d[3] + x[4]d[4], d[2]d[3] - d[1]d[4]) ------------------------------- Weyl.InIw(I4,[2,2,2,2,1,1,1,1]); -- CoCoAServer: computing Cpu Time = 0.031 ------------------------------- Ideal(x[2]x[3]x[4]d[4]^2 - x[1]x[4]^2d[4]^2, x[1]x[4]d[3]d[4] + x[2]x[4]d[4]^2, x[1]x[4]d[2]d[4] + x[3]x[4]d[4]^2, x[2]d[1]d[4] + x[4]d[3]d[4], x[3]d[1]d[4] + x[4]d[2]d[4], x[1]d[1] - x[4]d[4], x[2]d[2] + x[4]d[4], x[3]d[3] + x[4]d[4], d[2]d[3] - d[1]d[4]) -------------------------------

### See also