# symbolic solution for a system of nonlinear equations in mathematica

Would appreciate any help on the following in mathematica I cant figure it out. I have a system of equations that I am trying to solve symbolically. I have 9 equations and 8 unknowns (I have also tried a version of this with 6 equations and 6 unknowns with same result :(
Note this is after I had quit all applications and had mathematica running alone for about 20hours.
No more memory available. Mathematica kernel has shut down. Try quitting other applications and then retry. Below I am showing the version with 6eqns and 6 unknowns

(*setting these to reduce equations to 6 equations and 6 unknowns*)
Subscript[b, 11] = 1;
Subscript[b, 21] = 0;

y11 = (Subscript[a, 11] *Subscript[b, 11]) - (Subscript[a, 21]*
Subscript[b, 21]) ;
y21 = (Subscript[a, 21] *Subscript[b, 11]) + (Subscript[a, 11]*
Subscript[b, 21]);

y13 = ((Subscript[K, 1 R]*Subscript[a, 11]) *
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$3$$]\)) + (Subscript[a, 11]
Subscript[b, 13]) - ((Subscript[K, 1 L]*Subscript[a, 21])*
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$2$$]\) *Subscript[b,
21]) + ((Subscript[K, 1 R]*Subscript[a, 11])* Subscript[b, 11]
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$2$$]\)) - ((Subscript[K,
1 L]*Subscript[a, 21])*
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$3$$]\)) - (Subscript[a, 21]
Subscript[b, 23]);
y23 = ((Subscript[K, 1 L]*Subscript[a, 21])*
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$3$$]\)) + (Subscript[a, 21]
Subscript[b, 13]) + ((Subscript[K, 1 R]*Subscript[a, 11])*
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$2$$]\) Subscript[b,
21]) + ((Subscript[K, 1 L]*Subscript[a, 21])* Subscript[b, 11]
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$2$$]\)) + ((Subscript[K,
1 R]*Subscript[a, 11]) *
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$3$$]\)) + (Subscript[a, 11]
Subscript[b, 23]);

y15 = ((Subscript[K, 2 R]*Subscript[a, 11])*
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$5$$]\)) + (3 *(Subscript[K,
1 R]*Subscript[a, 11])*
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$2$$]\) Subscript[b,
13]) + (Subscript[a, 11] Subscript[b,
15]) - ((Subscript[K, 2 L]*Subscript[a, 11])*
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$4$$]\) Subscript[b,
21]) - (2 *(Subscript[K, 1 L]*Subscript[a, 21])* Subscript[b, 11]
Subscript[b, 13] Subscript[b,
21]) + (2 *(Subscript[K, 2 R]*Subscript[a, 11])*
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$3$$]\)
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$2$$]\)) + ((Subscript[K,
1 R]*Subscript[a, 11])* Subscript[b, 13]
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$2$$]\)) - (2 *(Subscript[K,
2 L]*Subscript[a, 11])*
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$2$$]\)
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$3$$]\)) + ((Subscript[K,
2 R]*Subscript[a, 11])* Subscript[b, 11]
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$4$$]\)) - ((Subscript[K,
2 L]*Subscript[a, 11])*
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$5$$]\)) - ((Subscript[K,
1 L]*Subscript[a, 21])*
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$2$$]\) Subscript[b,
23]) - (2 *(Subscript[K, 1 R]*Subscript[a, 11])* Subscript[b, 11]
Subscript[b, 21] Subscript[b,
23]) + ((Subscript[K, 1 L]*Subscript[a, 21])*
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$2$$]\) Subscript[b,
23]) - (Subscript[a, 21] Subscript[b, 25]);
y25 = ((Subscript[K, 2 L]*Subscript[a, 11])*
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$5$$]\)) + (3* (Subscript[K,
1 L]*Subscript[a, 21])*
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$2$$]\) Subscript[b,
13]) + (Subscript[a, 21] Subscript[b,
15]) + ((Subscript[K, 2 R]*Subscript[a, 11])*
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$4$$]\) Subscript[b,
21]) + (2 * (Subscript[K, 1 R]*Subscript[a, 11])* Subscript[b,
11] Subscript[b, 13] Subscript[b,
21]) - (2*(Subscript[K, 2 L]*Subscript[a, 11])*
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$3$$]\)
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$2$$]\)) + ((Subscript[K,
1 L]*Subscript[a, 21])* Subscript[b, 13]
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$2$$]\)) + (2  *(Subscript[K,
2 R]*Subscript[a, 11])*
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$2$$]\)
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$3$$]\)) + ((Subscript[K,
2 L]*Subscript[a, 11])* Subscript[b, 11]
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$4$$]\)) + ((Subscript[K,
2 R]*Subscript[a, 11])*
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$5$$]\)) - ((Subscript[K,
2 L]*Subscript[a, 11])*
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$5$$]\)) + ((Subscript[K,
1 R]*Subscript[a, 11])*
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$2$$]\) Subscript[b,
23]) - (2 * (Subscript[K, 1 L]*Subscript[a, 21])* Subscript[b,
11] Subscript[b, 21] Subscript[b,
23]) - ((Subscript[K, 1 R]*Subscript[a, 11])*
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$2$$]\) Subscript[b,
23]) + (Subscript[a, 11] Subscript[b, 25]);

h11 = A1*y11 + ((3/4)*(A1)^3*y13) + ((5/8)*(A1)^5*y15) +
I*(A1*y21 + ((3/4)*(A1)^3*y23) + ((5/8)*(A1)^5*y25));

h31 = ((A1^3)/4)*y13 + ((5/16)*(A1)^5*y15) +
I*(((A1^3)/4)*y23 + ((5/16)*(A1)^5*y25));

h51 = ((A1^5)/16)*y15 + I*((A1^5/16)*y25);

h12 = A2*y11 + ((3/4)*(A2)^3*y13) + ((5/8)*(A2)^5*y15) +
I*(A2*y21 + ((3/4)*(A2)^3*y23) + ((5/8)*(A2)^5*y25));

h32 = ((A2^3)/4)*y13 + ((5/16)*(A2)^5*y15) +
I*(((A2^3)/4)*y23 + ((5/16)*(A2)^5*y25));

h52 = ((A2^5)/16)*y15 + I*((A2^5/16)*y25);

h11g = Expand[(A1*
y11 + ((3/4)*(A1)^3*y13) + ((5/8)*(A1)^5*y15))^2 + (A1*
y21 + ((3/4)*(A1)^3*y23) + ((5/8)*(A1)^5*y25))^2];
h12g = Expand[(A2*
y11 + ((3/4)*(A2)^3*y13) + ((5/8)*(A2)^5*y15))^2 + (A2*
y21 + ((3/4)*(A2)^3*y23) + ((5/8)*(A2)^5*y25))^2];
h31g = Expand[(((A1^3)/4)*
y13 + ((5/16)*(A1)^5*y15))^2 + (((A1^3)/4)*
y23 + ((5/16)*(A1)^5*y25))^2];
h32g = Expand[(((A2^3)/4)*
y13 + ((5/16)*(A2)^5*y15))^2 + (((A2^3)/4)*
y23 + ((5/16)*(A2)^5*y25))^2];
h51g = Expand[(((A1^5)/16)*y15)^2 + ((A1^5/16)*y25)^2];
h52g = Expand[(((A2^5)/16)*y15)^2 + ((A2^5/16)*y25)^2];

Solve[{h11g - (A1^2
\!$$\*SubsuperscriptBox[\(a$$, $$11$$, $$2$$]\)
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$2$$]\) + A1^2
\!$$\*SubsuperscriptBox[\(a$$, $$21$$, $$2$$]\)
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$2$$]\) + A1^2
\!$$\*SubsuperscriptBox[\(a$$, $$11$$, $$2$$]\)
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$2$$]\) + A1^2
\!$$\*SubsuperscriptBox[\(a$$, $$21$$, $$2$$]\)
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$2$$]\)) == 0,
h12g - (A1^2
\!$$\*SubsuperscriptBox[\(a$$, $$11$$, $$2$$]\)
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$2$$]\) + A1^2
\!$$\*SubsuperscriptBox[\(a$$, $$21$$, $$2$$]\)
\!$$\*SubsuperscriptBox[\(b$$, $$11$$, $$2$$]\) + A1^2
\!$$\*SubsuperscriptBox[\(a$$, $$11$$, $$2$$]\)
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$2$$]\) + A1^2
\!$$\*SubsuperscriptBox[\(a$$, $$21$$, $$2$$]\)
\!$$\*SubsuperscriptBox[\(b$$, $$21$$, $$2$$]\)) == 0,
h31g == 0, h32g == 0, h51g == 0, h52g == 0}, {Subscript[a,
11], Subscript[a, 21], Subscript[b, 13], Subscript[b, 23],
Subscript[b, 15], Subscript[b, 25]}]

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## migrated from scicomp.stackexchange.comSep 4 '13 at 16:48

This question came from our site for scientists using computers to solve scientific problems.

Yes please go ahead and migrate the question there. –  user5087 Sep 4 '13 at 7:06
Welcome to the site. If you could just add the code of the equations you are running someone might be able to help you. At the moment only God knows what the problem could be, and he is not registered at Mathematica.SE. –  István Zachar Sep 5 '13 at 8:23
This is still very difficult to read. I'm not sure what the Subsuperscript boxes do but I would get rid of them. While you're at it you should get rid of the asterisks for multiplication. They are not needed. –  JEP Jun 7 at 1:56
I see now what the subscripts do. Your equations still don't make sense to me. You are looking for symbolic formulae for Subscript[a, 11], Subscript[a, 21], Subscript[b, 13], Subscript[b, 23], Subscript[b, 15], Subscript[b, 25] but these equations: h31g == 0, h32g == 0, h51g == 0, h52g == 0 do not depend on the subscripted quantities. –  JEP Jun 8 at 2:52
It seems quite possible that your equations are intractable in their current form. Do you have any reason to believe otherwise? –  m_goldberg Aug 27 at 23:24