Dprune -- prunes a D-module

Synopsis

Usage:

Dprune M
Inputs:
- M, a matrix or a module
Optional inputs:
- MinimalGenerators => a Boolean value, default value true, indicates whether a Gröbner basis should be computed
Outputs:
- a matrix or a module of the same type as M

Description

Finds another (possibly smaller) representation of a D-module. If given a matrix, prunes its cokernel; the result is a matrix whose cokernel is isomorphic.

i1 : W = makeWA(QQ[x,y])

o1 = W

o1 : PolynomialRing, 2 differential variable(s)

i2 : M = matrix{{x,dx},{1,1}}

o2 = | x dx |
     | 1 1  |

             2      2
o2 : Matrix W  <-- W

i3 : Dprune M

o3 = | x-dx |

             1      1
o3 : Matrix W  <-- W

i4 : Dprune coker M

o4 = cokernel | x-dx |

                            1
o4 : W-module, quotient of W

i5 : M = matrix{{x,dx},{x,y}}

o5 = | x dx |
     | x y  |

             2      2
o5 : Matrix W  <-- W

i6 : Dprune M

o6 = | dx x xy-xdx |
     | y  x 0      |

             2      3
o6 : Matrix W  <-- W

Ways to use Dprune :

Dprune(Matrix)
Dprune(Module)

For the programmer

The object Dprune is a method function with options.