- Usage:
`macaulayFormula(v,m)`

- Outputs:
- a list, a list of two matrices such that the ratio of their determinants is the Macaulay resultant of f_1,...,f_n with respect to the variables
`v`

- a list, a list of two matrices such that the ratio of their determinants is the Macaulay resultant of f_1,...,f_n with respect to the variables

Let *f _{1},...,f_{n}* be a polynomials two groups of variables

Remark: if D2 is the empty matrix, its determinant has to be understood as 1 (and not zero, which is the case in Macaulay2 since the empty matrix is identified to the zero.

i1 : R=QQ[a..i,x,y,z] o1 = R o1 : PolynomialRing |

i2 : f1 = a*x+b*y+c*z o2 = a*x + b*y + c*z o2 : R |

i3 : f2 = d*x+e*y+f*z o3 = d*x + e*y + f*z o3 : R |

i4 : f3 = g*x+h*y+i*z o4 = g*x + h*y + i*z o4 : R |

i5 : M = matrix{{f1,f2,f3}} o5 = | ax+by+cz dx+ey+fz gx+hy+iz | 1 3 o5 : Matrix R <--- R |

i6 : l = {x,y,z} o6 = {x, y, z} o6 : List |

i7 : MR = macaulayFormula (l,M) o7 = ({1} | a d g |, 0) {1} | b e h | {1} | c f i | o7 : Sequence |

- eliminationMatrix -- returns a matrix that represents the image of the map
- detComplex -- This function calculates the determinant of a graded ChainComplex with respect to a subset of the variables of the polynomial ring in a fixed degree.
- listDetComplex -- This function calculates the list with the determinants of some minors of the maps of a graded ChainComplex with respect to a subset of the variables of the polynomial ring in a fixed degree.
- minorsComplex -- This function calculates some minors of the maps of a graded ChainComplex with respect to a subset of the variables of the polynomial ring in a fixed degree. The choice of the minors is according to the construction of the determinant of a complex
- mapsComplex -- This function calculates the maps of a graded ChainComplex with respect to a subset of the variables of the polynomial ring in a fixed degree.

- macaulayFormula(List,Matrix)