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isIntegrable -- checks whether a list of matrices fulfills the integrability conditions

Description

Checks whether a list of $n$ matrices $A_i$ in $\operatorname{Mat}_{m\times m}(k(x_1..x_n))$ satisfy $[A_i,A_j] = \partial_i(A_j) - \partial_j(A_i)$ for all $i,j$. This is the case, in particular, when they come from a $D_n$-module, respectively from a $D_n$-ideal.

i1 : D = makeWeylAlgebra(QQ[x,y], {1, 2});
i2 : I = ideal(x*dx^2 - y*dy^2 + dx-dy, x*dx+y*dy+1);

o2 : Ideal of D
i3 : A = connectionMatrices I;
i4 : assert isIntegrable(D, A)
i5 : assert isIntegrable A

Caveat

The matrices need to be defined over the base fraction field of $D_n$.

See also

Ways to use isIntegrable:

  • isIntegrable(List)
  • isIntegrable(PolynomialRing,List)

For the programmer

The object isIntegrable is a method function.


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/ConnectionMatrices/docs.m2:363:0.