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So this is what I would have wanted to do.. prior to learning about it from here. :)

var('p, alpha, beta, q, A, B, J, K') h=solve([p==alpha+2betaq, A-Bp==Jq, pq-K-alphaq-beta*q^2==0],p,q,J) show(h.simplify_full()) show(h.simplify_full()) show(h.simplify_full()) show(h.rhs().diff(A).simplify_full()) show(h.rhs().diff(A).simplify_full()) show(h.rhs().diff(A).simplify_full())

So this is what I would have wanted to do.. prior to learning about it from here. :)

var('p, alpha, beta, q, A, B, J, K') h=solve([p==alpha+2betaq, q, A-Bp==Jq, q, pq-K-alphaq-beta*q^2==0],p,q,J) show(h.simplify_full()) show(h.simplify_full()) show(h.simplify_full()) show(h.rhs().diff(A).simplify_full()) show(h.rhs().diff(A).simplify_full()) show(h.rhs().diff(A).simplify_full())

So this is what I would have wanted to do.. prior to learning about it from here. :)

var('p, alpha, beta, q, A, B, J, K')
h=solve([p==alpha+2betaq,
A-Bp==Jq,
pq-K-alphaq-beta*q^2==0],p,q,J)
h=solve([p==alpha+2*beta*q, A-B*p==J*q, p*q-K-alpha*q-beta*q^2==0],p,q,J)
show(h.simplify_full())
show(h.simplify_full())
show(h.simplify_full())
show(h.rhs().diff(A).simplify_full())
show(h.rhs().diff(A).simplify_full())
show(h.rhs().diff(A).simplify_full())

show(h.rhs().diff(A).simplify_full())

So this is what I would have wanted to do.. prior to learning about it from here. :)

var('p, alpha, beta, q, A, B, J, K')
h=solve([p==alpha+2*beta*q, A-B*p==J*q, p*q-K-alpha*q-beta*q^2==0],p,q,J)
show(h.simplify_full())
show(h.simplify_full())
show(h.simplify_full())
show(h.rhs().diff(A).simplify_full())
show(h.rhs().diff(A).simplify_full())
show(h.rhs().diff(A).simplify_full())

and this..

h=solve([p==alpha+2*beta*q, A-B*p==J*q, p*q-K-alpha*q-beta*q^2==0],p,q,J,solution_dict=True)
show([[s.diff(A).simplify_full() for s in sol.values()] for sol in h])