I’m using maple 11. In my problem, I’ve five axioms: 

solve({x11*x11+x12*y11+x13*z11=x11*x11+x12*x21+x13*x31,

x11*x12+x12*y12+x13*z12=x11*x12+x12*x22+x13*x32,

x11*x13+x12*y13+x13*z13=x11*x13+x12*x23+x13*x33,

 

x11*x21+x12*y21+x13*z21=x21*x11+x22*x21+x23*x31,

x11*x22+x12*y22+x13*z22=x21*x12+x22*x22+x23*x32,

x11*x23+x12*y23+x13*z23=x21*x13+x22*x23+x23*x33,

 

x11*x31+x12*y31+x13*z31=x31*x11+x32*x21+x33*x31,

Warning, computation interrupted

 

> solve({x11*x11+x12*y11+x13*z11=x11*x11+x12*x21+x13*x31,

x11*x12+x12*y12+x13*z12=x11*x12+x12*x22+x13*x32,

x11*x13+x12*y13+x13*z13=x11*x13+x12*x23+x13*x33,

 

x11*x21+x12*y21+x13*z21=x21*x11+x22*x21+x23*x31,

x11*x22+x12*y22+x13*z22=x21*x12+x22*x22+x23*x32,

x11*x23+x12*y23+x13*z23=x21*x13+x22*x23+x23*x33,

I'm having a problem to run this Maple. Thank you for your help. > solve({e1⊢e1=e1,e2⊢e2=e2, e1⊣e1=alpha1*e1+alpha2*e2,e1⊣e2=alpha3*e1+alpha4*e2,e2⊣e1=alpha5*e1+alpha6*e2,e2⊣e2=alpha7*e1+alpha8*e2, (e1⊣e1)⊣e1=e1⊣(e1⊣e1),(e1⊣e1)⊣e1=e1⊣(e1⊢e1),(e1⊢e1)⊣e1=e1⊢(e1⊣e1),(e1⊣e1)⊢e1=e1⊢(e1⊢e1),(e1⊢e1)⊢e1=e1⊢(e1⊢e1), (e1⊣e1)⊣e2=e1⊣(e1⊣e2),(e1⊣e1)⊣e2=e1⊣(e1⊢e2),(e1⊢e1)⊣e2=e1⊢(e1⊣e2),(e1⊣e1)⊢e2=e1⊢(e1⊢e2),(e1⊢e1)⊢e2=e1⊢(e1⊢e2), (e1⊣e2)⊣e1=e1⊣(e2⊣e1),(e1⊣e2)⊣e1=e1⊣(e2⊢e1),(e1⊢e2)⊣e1=e1⊢(e2⊣e1),(e1⊣e2)⊢e1=e1⊢(e2⊢e1),(e1⊢e2)⊢e1=e1⊢(e2⊢e1), (e1⊣e2)⊣e2=e1⊣(e2⊣e2),(e1⊣e2)⊣e2=e1⊣(e2⊢e2),(e1⊢e2)⊣e2=e1⊢(e2⊣e2),(e1⊣e2)⊢e2=e1⊢(e2⊢e2),(e1⊢e2)⊢e2=e1⊢(e2⊢e2), (e2⊣e1)⊣e1=e2⊣(e1⊣e1),(e2⊣e1)⊣e1=e2⊣(e1⊢e1),(e2⊢e1)⊣e1=e2⊢(e1⊣e1),(e2⊣e1)⊢e1=e2⊢(e1⊢e1),(e2⊢e1)⊢e1=e2⊢(e1⊢e1), (e2⊣e1)⊣e2=e2⊣(e1⊣e2),(e2⊣e1)⊣e2=e2⊣(e1⊢e2),(e2⊢e1)⊣e2=e2⊢(e1⊣e2),(e2⊣e1)⊢e2=e2⊢(e1⊢e2),(e2⊢e1)⊢e2=e2⊢(e1⊢e2), (e2⊣e2)⊣e1=e2⊣(e2⊣e1),(e2⊣e2)⊣e1=e2⊣(e2⊢e1),(e2⊢e2)⊣e1=e2⊢(e2⊣e1),(e2⊣e2)⊢e1=e2⊢(e2⊢e1),(e2⊢e2)⊢e1=e2⊢(e2⊢e1), (e2⊣e2)⊣e2=e2⊣(e2⊣e2),(e2⊣e2)⊣e2=e2⊣(e2⊢e2),(e2⊢e2)⊣e2=e2⊢(e2⊣e2),(e2⊣e2)⊢e2=e2⊢(e2⊢e2),(e2⊢e2)⊢e2=e2⊢(e2⊢e2)},{alpha1,alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8});

I'm having a problem to convert my answer to radical term. I've use 'convert' command' but Maple doesn't work. Thank you for your help. >solve({a1^2*alpha+a2^2*beta=a1, 2*a1*a2*alpha+a2^2*gamma=a2, a1*b1*alpha+a2*b2*beta=b1, a1*b2*alpha+a2*b1*alpha+a2*b2*gamma=b2, b1^2*alpha+b2^2*beta=a1+b1, 2*b1*b2*alpha+b2^2*gamma=a2+b2, a1*b2<>b1*a2},{a1,a2,b1,b2}); >convert(%,radical);