forming an ideal from a matrix
After defining a matrix (see
inputting a matrix) ,
M, the ideal generated by the entries of the matrix is obtained using the command
ideal.
i1 : R = ZZ/101[a..e];

i2 : M = matrix{{a^2*bc^2, a*b^2d^3, c^5d},{a^2*b, b*c*d, c^5}}
o2 =  a2bc2 ab2d3 c5d 
 a2b bcd c5 
2 3
o2 : Matrix R < R

i3 : ideal M
2 2 2 2 3 5 5
o3 = ideal (a b  c , a b, a*b  d , b*c*d, c  d, c )
o3 : Ideal of R

forming a matrix from an ideal
In much the same way we can construct a 1 by n (where n is the number of generators of
I), matrix from the n generators of an ideal
I using the command,
generators.
i4 : I = ideal(a^2*bc^2+c*d, a*b^2b*d^3, c^5,d+e);
o4 : Ideal of R

i5 : generators I
o5 =  a2bc2+cd bd3+ab2 c5 d+e 
1 4
o5 : Matrix R < R

The abbreviation
gens can be used for
generators.