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gaugeTransform -- computes the gauge transform of a system of connection matrices

Description

This method computes the gauge transform of a system of connection matrices for a given invertible matrix that encodes a change of basis.

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 : A = connectionMatrices I;
i4 : M = matrix {{x,0}, {0,y}};

             2      2
o4 : Matrix D  <-- D
i5 : gaugeTransform(M, A, D)

o5 = {| 0 -1 |, | 0 x/y    |}
      | 0 0  |  | 0 (-1)/y |

o5 : List

It is also possible to compute the gauge transform of a system of connection matrices containing parameters.

See also

Ways to use gaugeTransform:

  • gaugeTransform(Matrix,List)
  • gaugeTransform(Matrix,List,PolynomialRing)

For the programmer

The object gaugeTransform is a method function.


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/ConnectionMatrices/docs.m2:228:0.