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intmat2mons -- monomials from a matrix

Synopsis

Usage:
intmat2mons(m,R)
Inputs:
- a matrix, a matrix, whose rows represent the exponent vectors
- a ring, the ring, whose elements the monomials shall be
Outputs:
- an ideal, an ideal in R generated by the monomials in R whose exponent vectors are given by m.

Description

This functions interprets the rows of the matrix m as exponent vectors of monomials in R. It returns the ideal generated by these monomials.

i1 : R=ZZ/37[x,y,t];

i2 : m=matrix({{3,0,0},{2,1,0},{0,3,0},{1,2,7}})

o2 = | 3 0 0 |
     | 2 1 0 |
     | 0 3 0 |
     | 1 2 7 |

              4        3
o2 : Matrix ZZ  <--- ZZ

i3 : I=intmat2mons(m,R)

             3   2    3     2 7
o3 = ideal (x , x y, y , x*y t )

o3 : Ideal of R

i4 : n=mons2intmat(I)

o4 = | 3 0 0 |
     | 2 1 0 |
     | 0 3 0 |
     | 1 2 7 |

              4        3
o4 : Matrix ZZ  <--- ZZ

i5 : m==n

o5 = true

See also

mons2intmat -- matrix of leading exponents

Ways to use `intmat2mons` :

intmat2mons(Matrix,Ring)
intmat2mons(Matrix,Ring,ZZ) -- monomials from a matrix