In an equation, is that possible to give two uknowns'ratio expression by using "solve" function or other accessible way ?

The equation is , is that possible to get "a/c" directly by "solve" function or other symbolic functions?

syms p p0 a r k alpha Y G 
syms A B c d
sigma_re=-p0-B*r^(-(1+k));
sigma_thetae=-p0+B/k*r^(-(1+k));
sigma_rp=Y/(alpha-1)+A*r^(k*(alpha-1));
sigma_thetap=Y/(alpha-1)+A*alpha*r^(k*(alpha-1));
eqn1=subs(sigma_thetae,r,c)==subs(sigma_thetap,r,c);
eqn2=subs(sigma_re,r,c)==subs(sigma_rp,r,c);
[A1 B1]=solve([eqn1 eqn2],[A B]);
sigma_re=simplify(subs(sigma_re,B,B1),"IgnoreAnalyticConstraints",true)

sigma_re = 

sigma_thetae=simplify(subs(sigma_thetae,B,B1),"IgnoreAnalyticConstraints",true)

sigma_thetae = 

sigma_rp=simplify(subs(sigma_rp,A,A1),"IgnoreAnalyticConstraints",true)

sigma_rp = 

sigma_thetap=simplify(subs(sigma_thetap,A,A1),"IgnoreAnalyticConstraints",true)

sigma_thetap = 

sigma_rp_a=simplify(subs(sigma_rp,r,a),"IgnoreAnalyticConstraints",true)

sigma_rp_a = 

eqn3=sigma_rp_a==-p

eqn3 = 

[Star Strider]

‘is that possible to get "a/c" directly by "solve" function or other symbolic functions?’

Please expand on this.

What result do you want?

.

[Guoyao.Li]

I mean the expression of "c/a" derived by .

And I have tried by the following way. However, I wonder is there easy way to get the result.

syms A B c d p p0 a r k alpha Y G
sigma_re=-p0-B*r^(-(1+k));
sigma_thetae=-p0+B/k*r^(-(1+k));
sigma_rp=Y/(alpha-1)+A*r^(k*(alpha-1));
sigma_thetap=Y/(alpha-1)+A*alpha*r^(k*(alpha-1));
eqn1=subs(sigma_thetae,r,c)==subs(sigma_thetap,r,c);
eqn2=subs(sigma_re,r,c)==subs(sigma_rp,r,c);
[A1 B1]=solve([eqn1 eqn2],[A B]);
sigma_re=simplify(subs(sigma_re,B,B1),"IgnoreAnalyticConstraints",true);
sigma_thetae=simplify(subs(sigma_thetae,B,B1),"IgnoreAnalyticConstraints",true);
sigma_rp=simplify(subs(sigma_rp,A,A1),"IgnoreAnalyticConstraints",true);
sigma_thetap=simplify(subs(sigma_thetap,A,A1),"IgnoreAnalyticConstraints",true);
sigma_rp_a=simplify(subs(sigma_rp,r,a),"IgnoreAnalyticConstraints",true)

sigma_rp_a = 

c1=solve(subs(sigma_rp_a,a,1)==-p,c,"IgnoreAnalyticConstraints",true)

c1 = 

a1=solve(subs(sigma_rp_a,c,1)==-p,a,"IgnoreAnalyticConstraints",true)

a1 = 

c_a=c1/a1 %% c/a

c_a = 

Answer 1

[Walter Roberson]

syms A B c d p p0 a r k alpha Y G
sigma_re=-p0-B*r^(-(1+k));
sigma_thetae=-p0+B/k*r^(-(1+k));
sigma_rp=Y/(alpha-1)+A*r^(k*(alpha-1));
sigma_thetap=Y/(alpha-1)+A*alpha*r^(k*(alpha-1));
eqn1=subs(sigma_thetae,r,c)==subs(sigma_thetap,r,c);
eqn2=subs(sigma_re,r,c)==subs(sigma_rp,r,c);
[A1 B1]=solve([eqn1 eqn2],[A B]);
sigma_re=simplify(subs(sigma_re,B,B1),"IgnoreAnalyticConstraints",true);
sigma_thetae=simplify(subs(sigma_thetae,B,B1),"IgnoreAnalyticConstraints",true);
sigma_rp=simplify(subs(sigma_rp,A,A1),"IgnoreAnalyticConstraints",true);
sigma_thetap=simplify(subs(sigma_thetap,A,A1),"IgnoreAnalyticConstraints",true);

sigma_rp_a=simplify(subs(sigma_rp,r,a),"IgnoreAnalyticConstraints",true)

sigma_rp_a = 

syms c_a
temp = simplify(subs(sigma_rp_a, c, c_a*a))

temp = 

output = simplify(solve(temp==-p,c_a,"IgnoreAnalyticConstraints",true))

output = 

[Guoyao.Li]

Thank you !!!