connectionForm -- computes the connection matrix

Usage:

connectionForm I

connectionForm A
Inputs:
- I, an ideal, of the Weyl algebra
- A, a list, a system of connection matrices
Outputs:
- a net, the connection matrix

Description

This method encodes the system of connection matrices in a single matrix. Its entries are differential one-forms in the variables of the underlying Weyl algebra.

i1 : D = makeWeylAlgebra(QQ[x,y]);

i2 : I = ideal(x*dx^2-y*dy^2+2*dx-2*dy, x*dx+y*dy+1);

o2 : Ideal of D

i3 : connectionForm I

o3 = | -1/xdx -y/xdx+dy |
     | 0      -2/ydy    |

The following example computes the connection matrix of the $D$-ideal annihilating $sin(xy)$ and $cos(xy)$

i4 : D = makeWeylAlgebra(QQ[x,y]);

i5 : I = ideal (dx^2-y^2, dy^2-x^2);

o5 : Ideal of D

i6 : A = pfaffianSystem(I,{1_D,dx});

i7 : connectionForm A

o7 = | 0         dx+x/ydy |
     | y2dx+xydy 1/ydy    |

Caveat

The output is purely for visualizing purposes.

Ways to use connectionForm:

connectionForm(Ideal)
connectionForm(List)

For the programmer

The object connectionForm is a method function.

The source of this document is in ConnectionMatrices/docs.m2:310:0.

connectionForm -- computes the connection matrix

Description

Caveat

See also

Ways to use connectionForm:

For the programmer