This doesn't work:
fricas
(1) -> L := [ A = 2*P1+P2, B = 2*P2+P1, C = 2*Q1+Q2, D = 2*Q2+Q1]
\label{eq1}\begin{array}{@{}l} \displaystyle \left[{A ={P 2 +{2 \ P 1}}}, \:{B ={{2 \ P 2}+ P 1}}, \:{C ={Q 2 +{2 \ Q 1}}}, \: \right. \ \ \displaystyle \left.{D ={{2 \ Q 2}+ Q 1}}\right]
(1) Type: List(Equation(Polynomial(Integer)))
fricas
solve(L, [P1,P2])
\label{eq2}\left[ \right]
(2) Type: List(List(Equation(Fraction(Polynomial(Integer)))))
But it should, observe this:
fricas
SA:=solve([L.1,L.2],[P1,P2])
\label{eq3}\left[{\left[{P 1 ={\frac{- B +{2 \ A}}{3}}}, \:{P 2 ={\frac{{2 \ B}- A}{3}}}\right]}\right]
(3) Type: List(List(Equation(Fraction(Polynomial(Integer)))))
fricas
SB:=solve([L.3,L.4],[Q1,Q2])
\label{eq4}\left[{\left[{Q 1 ={\frac{- D +{2 \ C}}{3}}}, \:{Q 2 ={\frac{{2 \ D}- C}{3}}}\right]}\right]
(4) Type: List(List(Equation(Fraction(Polynomial(Integer)))))
First two equationa do not depend on Q_i, the later two don't depend on P_i.
Now check it again the initial set:
fricas
S:=[SA.1.1,SA.1.2,SB.1.1,SB.1.2]
\label{eq5}\begin{array}{@{}l} \displaystyle \left[{P 1 ={\frac{- B +{2 \ A}}{3}}}, \:{P 2 ={\frac{{2 \ B}- A}{3}}}, \: \right. \ \ \displaystyle \left.{Q 1 ={\frac{- D +{2 \ C}}{3}}}, \:{Q 2 ={\frac{{2 \ D}- C}{3}}}\right]
(5) Type: List(Equation(Fraction(Polynomial(Integer))))
fricas
map(x+->eval(x,S),L)
\label{eq6}\left[{A = A}, \:{B = B}, \:{C = C}, \:{D = D}\right]
(6) Type: List(Equation(Expression(Integer)))
Status: open => duplicate