Macaulay2 » Documentation
Packages » ConnectionMatrices » connectionMatrices
next | previous | forward | backward | up | index | toc

connectionMatrices -- computes the connection matrices of a $D_n$-ideal $I$ for a chosen basis

Description

Let $I$ be an ideal in the Weyl algebra $D_n$ and $B$ a basis for $R_n/R_nI$ over the base fraction field of $D_n$. If no basis is provided by the user, the basis is chosen to be the set of standard monomials of a Gröbner basis on $R_nI$ with regards to the weighted Lex order $(\partial_1 > \cdots > \partial_n > x_1 > \cdots > x_n)$ on the Weyl algebra.

i1 : D = makeWeylAlgebra(QQ[x,y], {2, 1})

o1 = D

o1 : PolynomialRing, 2 differential variable(s)
i2 : I = ideal (x*dx^2-y*dy^2+2*dx-2*dy, x*dx+y*dy+1)

                2             2
o2 = ideal (x*dx  + 2dx - y*dy  - 2dy, x*dx + y*dy + 1)

o2 : Ideal of D
i3 : A = connectionMatrices I

o3 = {| (-1)/x (-y)/x |, | 0 1      |}
      | 0      0      |  | 0 (-2)/y |

o3 : List

References

For more details, see [SST, pp. 37-40].

Ways to use connectionMatrices:

  • connectionMatrices(Ideal)
  • connectionMatrices(Ideal,List)

For the programmer

The object connectionMatrices is a method function.


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/ConnectionMatrices/docs.m2:192:0.