Singular

D.14.1.15 arrCoordNormalize

Usage:

arrCoordChange(A, v);

Return:

[arr]: Arrangement after a coordinate change that transforms the arrangement such that after a tranformation x -> Tx + c we have the arrangement has the matrix representation [AT^-1|b+AT^-1c] such that [AT^-1]_v = I and [b+AT^-1c]_v = 0;

Note:

algorithm performs a base change if H_k is homogenous (i.e. has no) constant term and an affine transformation otherwise
Ax+b = 0, Transformation x = Ty+c: AT^-1y + AT^-1c + b = 0 Now we want to have (AT^-1)_v = I and (AT^-1c +b)_v = AT^-1_v*c + b_v = 0

LIB "arr.lib";
ring r = 0,(x,y,z),lp;
arr A = ideal(x,y,z,x+z+4);
intvec v = 1,2,4;
arrCoordNormalize(A,v);
==> _[1]=x
==> _[2]=y
==> _[3]=-x+z-4
==> _[4]=z
==>