- Usage:
`coefAndMonomials = degHomPolMap(r, l, v, d)`

- Inputs:
`r`, a matrix, single row matrix with polynomials*f*_{1},...,f_{n}`l`, a list, list {d1,...,dn} of degrees corresponding to the degrees of*f*_{1},...,f_{n}`v`, a list, list of variables of the polynomial ring R with respect to which the polynomials fi's are homogeneous of degree 'di' (to take into account for elimination)`d`, an integer, the degree in 'var' of the homogeneous strand of the map f (i.e.: R_d)

- Outputs:
`List`, a list, a list {monomials, coefficients} of the coefficients and monomials of the morphism f

Let R be a polynomial ring in two groups of variables *R=S[X _{1},...,X_{r}]* and

This function returns a sequence with two elements: first the list of monomials of degree d in 'var'; Second, the matrix f_d with entries in S in the base of monomials.

For computing the base of monomials, it needs as a second argument the list *d _{1},...,d_{n}* of the degrees of the fi's in

i1 : R=QQ[a,b,c,x,y] o1 = R o1 : PolynomialRing |

i2 : f1 = a*x^2+b*x*y+c*y^2 2 2 o2 = a*x + b*x*y + c*y o2 : R |

i3 : f2 = 2*a*x+b*y o3 = 2a*x + b*y o3 : R |

i4 : M = matrix{{f1,f2}} o4 = | ax2+bxy+cy2 2ax+by | 1 2 o4 : Matrix R <--- R |

i5 : l = {x,y} o5 = {x, y} o5 : List |

i6 : dHPM = degHomPolMap (M,l,2) o6 = (| x2 xy y2 |, {2} | a 2a 0 |) {2} | b b 2a | {2} | c 0 b | o6 : Sequence |

i7 : dHPM = degHomPolMap (M,{2,1},l,2) o7 = (| x2 xy y2 |, {2} | a 2a 0 |) {2} | b b 2a | {2} | c 0 b | o7 : Sequence |

i8 : R=QQ[a,b,c,d,e,f,g,h,i,x,y,z] o8 = R o8 : PolynomialRing |

i9 : f1 = a*x+b*y+c*z o9 = a*x + b*y + c*z o9 : R |

i10 : f2 = d*x+e*y+f*z o10 = d*x + e*y + f*z o10 : R |

i11 : f3 = g*x+h*y+i*z o11 = g*x + h*y + i*z o11 : R |

i12 : M = matrix{{f1,f2,f3}} o12 = | ax+by+cz dx+ey+fz gx+hy+iz | 1 3 o12 : Matrix R <--- R |

i13 : l = {x,y,z} o13 = {x, y, z} o13 : List |

i14 : dHPM = degHomPolMap (M,l,1) o14 = (| x y z |, {1} | a d g |) {1} | b e h | {1} | c f i | o14 : Sequence |

i15 : dHPM = degHomPolMap (M,{1,1,1},l,1) o15 = (| x y z |, {1} | a d g |) {1} | b e h | {1} | c f i | o15 : Sequence |

- 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.
- coefficients -- monomials and their coefficients

- degHomPolMap(Matrix,List,List,ZZ)
- degHomPolMap(Matrix,List,ZZ)