isHomogeneous Matrix -- test for homogeneity

isHomogeneous Matrix -- test for homogeneity

Synopsis:

Usage: t = isHomogeneous f

Function: isHomogeneous -- test for homogeneity

Input:

f, an instance of class Matrix: a map F <-- G

Output:

t, an instance of class Boolean: whether the matrix f is homogeneous

Associated with every matrix is an arbitary integer called its degree: it has nothing to do with the degrees of the entries of the matrix; see (degree,Matrix). The matrix f is called homogeneous if every entry f_(i,j) has degree equal to degree G_i - degree F_j + degree f. Another way to say it is that applying f to a homogeneous vector add degree f to its degree.

i1 : R = QQ[x];

i2 : f = map(F = R^{0}, G = R^{-1}, {{x^3}}, Degree => 2)



o2 = | x3 |



             1       1

o2 : Matrix R  <--- R

i3 : degree f



o3 = {2}



o3 : List

i4 : degree G_0



o4 = {1}



o4 : List

i5 : degree F_0



o5 = {0}



o5 : List

i6 : f * G_0



      3

o6 = x <0>



      1

o6 : R

i7 : degree (f * G_0)



o7 = {3}



o7 : List

i8 : isHomogeneous f



o8 = true