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sage: var('x y');
sage: (x^2-y^3).subs_expr(x^2==y^3)    
0    
sage: (x-conjugate(y)).subs_expr(x==conjugate(y))    
0

sage: var('x y');
sage: (x^2-y^3).subs_expr(x^2==y^3)    
0    
sage: (x-conjugate(y)).subs_expr(x==conjugate(y))    
0
sage: maxima('x-conjugate(y),x=conjugate(y)')     
0

sage: var('x y');
sage: (x^2-y^3).subs_expr(x^2==y^3)    
0    
sage: (x-conjugate(y)).subs_expr(x==conjugate(y))    
0   
sage: maxima('x^2-y^3,x^2=y^3')              
0
sage: maxima('x-conjugate(y),x=conjugate(y)')     
0

sage: var('x y');
sage: (x^2-y^3).subs_expr(x^2==y^3)    
0    
sage: (x-conjugate(y)).subs_expr(x==conjugate(y))    
0   
sage: maxima('x^2-y^3,x^2=y^3')              
0
sage: maxima('x-conjugate(y),x=conjugate(y)')     
0
#replace x^2 by y^3 in x^4-y^6
sage: maxima('ratsubst(y^3,x^2,x^4-y^6)')
0

sage: var('x y');
sage: (x^2-y^3).subs_expr(x^2==y^3)    
0    
sage: (x-conjugate(y)).subs_expr(x==conjugate(y))    
0   
sage: maxima('x^2-y^3,x^2=y^3')              
0
sage: maxima('x-conjugate(y),x=conjugate(y)')     
0
#replace x^2 by y^3 in x^4-y^6
sage: maxima('ratsubst(y^3,x^2,x^4-y^6)')
0
sage: maxima('scsimp(x^4-y^6,x^2=y^3)')
0

sage: var('x y');
sage: (x^2-y^3).subs_expr(x^2==y^3)    
0    
sage: (x-conjugate(y)).subs_expr(x==conjugate(y))    
0   
sage: maxima('x^2-y^3,x^2=y^3')              
0
sage: maxima('x-conjugate(y),x=conjugate(y)')     
0
#replace x^2 by y^3 in x^4-y^6
sage: maxima('ratsubst(y^3,x^2,x^4-y^6)')
0
#simplify according to the rules
sage: maxima('scsimp(x^4-y^6,x^2=y^3)')
0