%% Gives back beta-functions and anomalous dimensions,
%% given combinatorial factors S, a1, and a2.

function [betags,gamma_phi,gamma_phi2]=betas_gammas(d,gs,S,a1,a2)


%% Common factors
I2=0;
for X1=1:2
    for X2=1:2
        I2=I2+S(X1,X2)*gs(X1)*gs(X2);
    end
end

I4=0;
for X1=1:2
    for X2=1:2
        for X3=1:2
            for X4=1:2
                for X5=1:2
                    I4=I4+S(X1,X5)*a1(X5,X2,X3,X4)*gs(X1)*gs(X2)*gs(X3)*gs(X4);
                end
            end
        end
    end
end

I3=zeros(2,1);
for X=1:2
    for X1=1:2
        for X2=1:2
            for X3=1:2
                I3(X)=I3(X)+a1(X,X1,X2,X3)*gs(X1)*gs(X2)*gs(X3);
            end
        end
    end
end

I5A=zeros(2,1);
for X=1:2
    for X1=1:2
        for X2=1:2
            for X3=1:2
                for X4=1:2
                    for X5=1:2
                        I5A(X)=I5A(X)+a2(X,X1,X2,X3,X4,X5)*gs(X1)*gs(X2)*gs(X3)*gs(X4)*gs(X5);
                    end
                end
            end
        end
    end
end

I5B=zeros(2,1);
for X=1:2
    for X1=1:2
        for X2=1:2
            for X3=1:2
                I5B(X)=I5B(X)+a1(X,X1,X2,X3)*gs(X1)*gs(X2)*I3(X3);
            end
        end
    end
end

%% Anomalous dimensions and beta functions
% gamma_phi
gamma_phi=(1/6)*I2-(11/216)*(I2^2)+(1/9)*I4;

% gamma_phi2
gamma_phi2=I2-(1/24)*(I2^2)+I4;
    
% Beta functions
eta=gamma_phi;
betags=-I3+(7/24)*I2*I3-(1/2)*I5A-(3/4)*I5B;
betags=betags+((-6+d+3*eta)/2)*gs;

end