ApCoCoA-1:Weyl.WLT

This article is about a function from ApCoCoA-1.

Weyl.WLT

Computes the leading term ideal of a D-ideal I in Weyl algebra A_n.

Syntax

Weyl.WLT(I:IDEAL):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.

This function computes the ideal of leading monomials of all the polynomials of a D-ideal I in the Weyl algebra D.

• @param I An ideal in the Weyl algebra.

• @return An ideal, which is leading term ideal of I.

Example

A1::=QQ[x,d];Use A1;
L:=x^2(x-1)(x-3)d^2-(6x^3-20x^2+12x)d+(12x^2-32x+12);
I:=Ideal(L,d^5);
Weyl.WLT(I);

-- CoCoAServer: computing Cpu Time = 0.016
-------------------------------
Ideal(xd^4, x^3d^2, x^2d^3, d^5)
-------------------------------
ChI:=Weyl.CharI(I);ChI;
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
The characteristic ideal lies in QQ[x,d]
--------------------------------------------------

-------------------------------
Ideal(d^5, x^4d^2 - 4x^3d^2 + 3x^2d^2, xd^3)
-------------------------------

Example

A2::=QQ[x[1..2],d[1..2]];
Use A2;

I:=Ideal(x[1]d[2],x[2]d[1]);
Weyl.WLT(I);
-- CoCoAServer: computing Cpu Time = 0.016
-------------------------------
Ideal(x[2]^2d[2], x[2]d[2]^2, x[1]d[1], x[2]d[1], x[1]d[2])
-------------------------------

See also

Weyl.InIw

Weyl.CharI