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Macaulay2Doc :: minimalPresentation(Matrix)

minimalPresentation(Matrix) -- minimally present source and target of a matrix

Synopsis

Description

If the source and target of f are graded, then minimal presentations of the source and target modules for f are computed using minimalPresentation(Module) and g is the matrix corresponding to f with source and target the minimally presented source and target. If either the source or target of f is not graded then an attempt is made to improve their presentations and gis the matrix with resulting source and target. An example follows.
i1 : R = ZZ/32003[a..d];
i2 : f = inducedMap(coker matrix {{a,1,b},{c,3,b+d}},R^2)

o2 = | 1 -10668 |
     | 0 0      |

o2 : Matrix
i3 : g = prune f

o3 = | -3 1 |

o3 : Matrix
i4 : source g

      2
o4 = R

o4 : R-module, free
i5 : target g

o5 = cokernel | b+16001d a-10668c |

                            1
o5 : R-module, quotient of R

This function does not remove elements from the base field from the matrix, but rather minimally presents the source and target and gives the corresponding new map. For example:

i6 : m = matrix{{a,1,b},{c,3,b+d}}

o6 = | a 1 b   |
     | c 3 b+d |

             2       3
o6 : Matrix R  <--- R
i7 : prune m

o7 = | a 1 b   |
     | c 3 b+d |

             2       3
o7 : Matrix R  <--- R
Unlike above, nothing changes.

Caveat

Check out the example just above.

See also