# Solving a large system of non-linear equations

I am new to Mathematica, and I am currently trying to use it to solve a large symbolic system of non-linear equations. I began the code below about 30 hrs ago, and the Mathematica Kernal has been using between 4 and 7GB of RAM since that time.

Is there any chance (at this point) that a solution is still forthcoming? That is, should I continue to let this thing run?

If so, is there any time threshold beyond which a solution is unlikely?

There are currently 22 unknowns, and a bunch of other parameters. An alternative specification of the problem could drop this to 16 unknowns with 16 equations. Would Mathematica be significantly more likely to solve this formulation in a reasonable amount of time?

Here is my code:

Solve[{F1^γ1 L1^(-1 + α1)
P1 R1^η1 S1^β1 T1^ζ1 α1 - λ - P1 r (S1 θ1 + F1 S1 ι1 + S1 TV1 κ1 + RV1 S1 μ1) == 0,
-Cs + F1^γ1 L1^α1 P1 R1^η1 S1^(-1 + β1) T1^ζ1 β1 -
L1 P1 r (θ1 + F1 ι1 + TV1 κ1 + RV1 μ1) == 0,
-Cf + F1^(-1 + γ1) L1^α1 P1 R1^η1 S1^β1 T1^ζ1 γ1 - L1 P1 r S1 ι1 == 0,
F2^γ2 L2^(-1 + α2) P2 R2^η2 S2^β2 T2^ζ2 α2 - λ -
P2 r (S2 θ2 + F2 S2 ι2 + S2 TV2 κ2 + RV2 S2 μ2) == 0,
-Cs + F2^γ2 L2^α2 P2 R2^η2 S2^(-1 + β2) T2^ζ2 β2 -
L2 P2 r (θ2 + F2 ι2 + TV2 κ2 + RV2 μ2) == 0,
-Cf + F2^(-1 + γ2) L2^α2 P2 R2^η2 S2^β2 T2^ζ2 γ2 - L2 P2 r S2 ι2 == 0,
F3^γ3 L3^(-1 + α3) P3 R3^η3 S3^β3 T3^ζ3 α3 - λ -
P3 r (S3 θ3 + F3 S3 ι3 + S3 TV3 κ3 + RV3 S3 μ3) == 0,
-Cs + F3^γ3 L3^α3 P3 R3^η3 S3^(-1 + β3) T3^ζ3 β3 -
L3 P3 r (θ3 + F3 ι3 + TV3 κ3 + RV3 μ3) == 0,
-Cf + F3^(-1 + γ3) L3^α3 P3 R3^η3 S3^β3 T3^ζ3 γ3 - L3 P3 r S3 ι3 == 0,
F4^γ4 L4^(-1 + α4) P4 R4^η4 S4^β4 T4^ζ4 α4 - λ -
P4 r (S4 θ4 + F4 S4 ι4 + S4 TV4 κ4 + RV4 S4 μ4) == 0,
-Cs + F4^γ4 L4^α4 P4 R4^η4 S4^(-1 + β4) T4^ζ4 β4 -
L4 P4 r (θ4 + F4 ι4 + TV4 κ4 + RV4 μ4) == 0,
-Cf + F4^(-1 + γ4) L4^α4 P4 R4^η4 S4^β4 T4^ζ4 γ4 - L4 P4 r S4 ι4 == 0,
F5^γ5 L5^(-1 + α5) P5 R5^η5 S5^β5 T5^ζ5 α5 - λ -
P5 r (S5 θ5 + F5 S5 ι5 + S5 TV5 κ5 + RV5 S5 μ5) == 0,
-Cs + F5^γ5 L5^α5 P5 R5^η5 S5^(-1 + β5) T5^ζ5 β5 -
L5 P5 r (θ5 + F5 ι5 + TV5 κ5 + RV5 μ5) == 0,
-Cf + F5^(-1 + γ5) L5^α5 P5 R5^η5 S5^β5 T5^ζ5 γ5 - L5 P5 r S5 ι5 == 0,
F6^γ6 L6^(-1 + α6) P6 R6^η6 S6^β6 T6^ζ6 α6 - λ -
P6 r (S6 θ6 + F6 S6 ι6 + S6 TV6 κ6 + RV6 S6 μ6) == 0,
-Cs + F6^γ6 L6^α6 P6 R6^η6 S6^(-1 + β6) T6^ζ6 β6 -
L6 P6 r (θ6 + F6 ι6 + TV6 κ6 + RV6 μ6) == 0,
-Cf + F6^(-1 + γ6) L6^α6 P6 R6^η6 S6^β6 T6^ζ6 γ6 - L6 P6 r S6 ι6 == 0,
F7^γ7 L7^(-1 + α7) P7 R7^η7 S7^β7 T7^ζ7 α7 - λ -
P7 r (S7 θ7 + F7 S7 ι7 + S7 TV7 κ7 + RV7 S7 μ7) == 0,
-Cs + F7^γ7 L7^α7 P7 R7^η7 S7^(-1 + β7) T7^ζ7 β7 -
L7 P7 r (θ7 + F7 ι7 + TV7 κ7 + RV7 μ7) == 0,
-Cf + F7^(-1 + γ7) L7^α7 P7 R7^η7 S7^β7 T7^ζ7 γ7 - L7 P7 r S7 ι7 == 0,
-L1 - L2 - L3 - L4 - L5 - L6 - L7 + ℒ == 0},
{L1, L2, L3, L4, L5, L6, L7, S1, S2, S3, S4, S5, S6, S7, F1, F2, F3, F4, F5, F6, F7}]

• I directly copied your posted code and pasted into a new Mathematica notebook. It has a syntax error: Syntax::sntxf: "F3^(-1+\[Gamma]3)L3^\[Alpha]3P3 R3^\[Eta]3S3^\[Beta]3T3^\[Zeta]3" cannot be followed by "\[Gamma]3 -L3P3 r S3 \[Iota]3". Commented Apr 25, 2014 at 18:48
• I had a bit of an issue pasting the code into the box, so I editted in the post. Perhaps I deleted something important, but the code is definitely running in Mathematica... at least the menu bar on the notebook window says "Running..." and it is taking up 25% of my CPU (I have a 4-core processor)and a variable but approximately 7GB section of my ram. Commented Apr 26, 2014 at 5:41