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+//page 133

+//Example 4.9

+clc;

+clear;

+close;

+disp('M is the ideal in F[x] generated by:');

+disp('(x-1)*(x+2)^2');

+disp('(x+2)^2*(x+3)');

+disp('(x-3)','and');

+x = poly(0,"x");

+p1 = (x-1)*(x+2)^2;

+p2 = (x+2)^2*(x-3);

+p3 = (x-3);

+disp('M = (x-1)*(x+2)^2 F[x] + (x+2)^2*(x-3) + (x-3)');

+disp('Then M contains:');

+t = 1/2*(x+2)^2*((x-1) - (x-3));

+disp(t);

+disp('i.e., M contains (x+2)^2');

+disp('and since, (x+2)^2 = (x-3)(x-7) - 17');

+disp('So M contains the scalar polynomial 1.');

+disp('So, M = F[x] and given polynomials are relatively prime.');

+//end