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RandomRationalPoints :: findANonZeroMinor

findANonZeroMinor -- finds a non-vanishing minor at some randomly chosen point

Synopsis

Description

Given an ideal, a matrix, an integer and a user defined Strategy, this function uses the randomPoints function to find a point in $V(I)$. Then it plugs the point in the matrix and tries to find a non-zero minor of size equal to the given integer. It outputs the point and also one of the submatrices of interest along with the column and row indices that were used sequentially.

i1 : R = ZZ/5[x,y,z];
i2 : I = ideal(random(3,R)-2, random(2,R));

o2 : Ideal of R
i3 : M = jacobian(I);

             3       2
o3 : Matrix R  <--- R
i4 : findANonZeroMinor(2,M,I, Strategy => GenericProjection)

o4 = ({1, 2, 1}, {0, 1}, {0, 1}, {1} | xy-y2-2yz-2z2   2z  |)
                                 {1} | -x2-2y2+2xz+2z2 -2z |

o4 : Sequence

The option MinorPointAttempts is how many points to attempt before giving up.

See also

Ways to use findANonZeroMinor :

For the programmer

The object findANonZeroMinor is a method function with options.