forcestd matrix M result standard basis [matrix C]

Create a matrix with an attached standard basis. This command forces the columns of M to be considered as a standard basis. If a change of basis matrix C is given, it will be placed in the attached standard basis as if it were the change of basis matrix. C should be a matrix having the same base ring and the same number of columns as M. Otherwise an error message is displayed. It is legal for the matrix M to not be graded. See the example below.

Warning: This command is useful if you happen to know that the columns of M form a standard basis, but the amount of computation to verify this is huge. This command makes each column monic, since Macaulay insists that every standard basis element be monic. If a change of basis matrix is given, it is changed accordingly.

The effect of the following example is to set the variables c to be the square root of -1, and d to be the square root of 3.

%  type j
; c2+1 d2-3 

%  forcestd j j 

%  poly f (ac+bd)^2

%  reduce j f f'

%  type f'
; 2abcd-a2+3b2