# symbolic solution for a system of nonlinear equations in mathematica [closed]

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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## migration rejected from scicomp.stackexchange.comSep 29 '15 at 20:34

This question came from our site for scientists using computers to solve scientific problems. Votes, comments, and answers are locked due to the question being closed here, but it may be eligible for editing and reopening on the site where it originated.

## closed as off-topic by MarcoB, Yves Klett, blochwave, C. E., marchSep 29 '15 at 20:34

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – MarcoB, Yves Klett, blochwave, C. E., march
If this question can be reworded to fit the rules in the help center, please edit the question.

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 '15 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 '15 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 '15 at 23:24