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Macaulay2Doc :: matrix(Matrix)

matrix(Matrix) -- the matrix between generators

Synopsis

Description

Each homomorphism of modules $f : M \rightarrow N$ in Macaulay2 is induced from a matrix $f0 : \mathtt{cover} M \rightarrow \mathtt{cover} N$. This function returns this matrix.
i1 : R = QQ[a..d];
i2 : I = ideal(a^2,b^2,c*d)

             2   2
o2 = ideal (a , b , c*d)

o2 : Ideal of R
i3 : f = basis(3,I)

o3 = {2} | a b c d 0 0 0 0 0 0 0 0 |
     {2} | 0 0 0 0 a b c d 0 0 0 0 |
     {2} | 0 0 0 0 0 0 0 0 a b c d |

o3 : Matrix
i4 : source f

      12
o4 = R

o4 : R-module, free, degrees {12:3}
i5 : target f

o5 = image | a2 b2 cd |

                             1
o5 : R-module, submodule of R
The map f is induced by the following 3 by 12 matrix from R^12 to the 3 generators of I.
i6 : matrix f

o6 = {2} | a b c d 0 0 0 0 0 0 0 0 |
     {2} | 0 0 0 0 a b c d 0 0 0 0 |
     {2} | 0 0 0 0 0 0 0 0 a b c d |

             3       12
o6 : Matrix R  <--- R
To obtain the map that is the composite of this with the inclusion of I onto R, use super(Matrix).
i7 : super f

o7 = | a3 a2b a2c a2d ab2 b3 b2c b2d acd bcd c2d cd2 |

             1       12
o7 : Matrix R  <--- R

See also