Question

Discrete math

1) Using MatLab (any language is fine just say what language is used).

function d=lemma_gcd(a,b)
%This program will return the greatest common divisor for input variables a
%and b where a and b are integers such that they are not both 0. It uses
%Lemma 4.8.3 on page 225.

%Note: gcd(a,b)=gcd(-a,b)=gcd(a,-b)=gcd(-a,-b), so
a=abs(a);
b=abs(b);

%This following section sets up the arrays we will use to store the
%changing values of our variables as a sequence. "c" will be the count
%variabe, stored in "C", "a" and "b" will also bechanging and stored in "A"
%and "B" arrays through the iterations of the loops.

c=0;
C(1)=c; %Stores c=0 in the array, C
%Next find the initial a and b to kick the program into gear

if a==0 & b==0
fprintf('You cannot input these variables\n')
d=inf;
else
if floor(a)~=a
fprintf('You cannot input these variables\n')
d=inf;
if floor(b)~=b
fprintf('You cannot input these variables\n')
d=inf;
  
  
  
  
  
  
  
  
end
end
end

Answer 1

MATLAB CODE:-

function d=lemma_gcd(a,b)

%This program will return the greatest common divisor for input variables a

%and b where a and b are integers such that they are not both 0. It uses

%Lemma 4.8.3 on page 225.

%Note: gcd(a,b)=gcd(-a,b)=gcd(a,-b)=gcd(-a,-b), so

a=abs(a);

b=abs(b);

%This following section sets up the arrays we will use to store the

%changing values of our variables as a sequence. "c" will be the count

%variabe, stored in "C", "a" and "b" will also be changing and stored in "A"

%and "B" arrays through the iterations of the loops.

c=0;

C(1)=c; %Stores c=0 in the array, C

%Next find the initial a and b to kick the program into gear

if a==0 & b==0

fprintf('You cannot input these variables\n')

d=inf;

return

else

if floor(a)~=a

fprintf('You cannot input these variables\n')

d=inf;

return

end

if floor(b)~=b

fprintf('You cannot input these variables\n')

d=inf;

return

end

end

% Swap m and n if m less than n

% to allow the algorithm to function properly

if a==0

d=b;

return

end

if b==0

d=a;

return

end

if a < b

tmp = a;

a = b;

b = tmp;

end

% Result of modulus is zero so we have found the gcd

if mod(a,b) == 0

d = b;

else

d = lemma_gcd(b,mod(a,b)); % Euclid's algorithm

end

end