I have a representation of a linear equation in standard form (ax+by+c=0) which I am representing as a set of coefficients: a,b,c.
I want to normalize these so that any two equations that represent the same line can be compared programatically to see if they're equal just using the co-efficients. For this I need the co-efficients of any two equations representing the same line to be equivalent after normalizing.
I normalized the values by dividing all coefficients by which scales the coefficients to be the same but I don't know how to account for sign changes in this.
For example, if I have equations: 2x+-4y+2=0 (represented as 2, -4, 2) and -2x+4y+-2=0 (represented as -2, 4, -2), how can I transform the coefficients to make them equal?