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];
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i2 : M = matrix{{a^2*b-c^2, a*b^2-d^3, c^5-d},{a^2*b, b*c*d, c^5}}
o2 = | a2b-c2 ab2-d3 c5-d |
| a2b bcd c5 |
2 3
o2 : Matrix R <-- R
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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
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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*b-c^2+c*d, a*b^2-b*d^3, c^5,d+e);
o4 : Ideal of R
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i5 : generators I
o5 = | a2b-c2+cd -bd3+ab2 c5 d+e |
1 4
o5 : Matrix R <-- R
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The abbreviation
gens can be used for
generators.