next | previous | forward | backward | up | top | index | toc | Macaulay2 website
Macaulay2Doc :: leadTerm(Matrix)

leadTerm(Matrix) -- get the greatest term of each column

Synopsis

Description

In Macaulay2, each free module over a polynomial ring comes equipped with a monomial order and this routine returns the matrix whose i-th column is the lead term of the i th column of f.
i1 : R = QQ[a..d];
i2 : f = matrix{{0,a^2-b*c},{c,d}}

o2 = | 0 a2-bc |
     | c d     |

             2       2
o2 : Matrix R  <--- R
i3 : leadTerm f

o3 = | 0 a2 |
     | c 0  |

             2       2
o3 : Matrix R  <--- R
Coefficients are included in the result:
i4 : R = ZZ[a..d][x,y,z];
i5 : f = matrix{{0,(a+b)*x^2},{c*x, (b+c)*y}}

o5 = | 0  (a+b)x2 |
     | cx (b+c)y  |

             2       2
o5 : Matrix R  <--- R
i6 : leadTerm f

o6 = | 0  ax2 |
     | cx 0   |

             2       2
o6 : Matrix R  <--- R
The argument f can also be a Gröbner basis, in which case the lead term matrix of the generating matrix of f is returned.

See also