Mathematica Asked by Guillermo Oliver on March 16, 2021
Due to backwards compatibility issues, I am using Mathematica 8.0 and it seems to have an issue with TimeConstrained.
I am using this function to set a limit to the time elapsed in a FullSimplify call:
FullSimplifyTime[Equation_, TrigSimplify_, TimeConstraint_] :=
(Module[{Result, OriginalEquation},
Print["Starting FullSimplify with ", TimeConstraint ,
" second time constraint."];
OriginalEquation = Equation;
(* Set up a timed constrained equation,
return original equation if time is exceeded*)
Result = TimeConstrained[
FullSimplify[Equation, Trig -> TrigSimplify],
TimeConstraint,
NULL
];
If [Result == NULL,
Result = OriginalEquation;
Print["Time constraint exceeded."];
Return[Result]
];
Print["Simplified within time constraint."];
Return[Result]
]
)
I have used it without any issues, until now.
When trying to simplify this expression:
exp = L1 + (L7 (1 - (4 L7 (L1 - L2 Cos[[CapitalTheta]2]) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2])) (-1 + (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2]))^2) + [Sqrt](-(L1 -
L2 Cos[[CapitalTheta]2] +
2 (L6 - L7) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2])) + (L1 -
L2 Cos[[CapitalTheta]2]) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2]))^2) (L1 -
L2 Cos[[CapitalTheta]2] +
2 (-L6 + L7) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2])) + (L1 -
L2 Cos[[CapitalTheta]2]) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2]))^2) (L1 -
L2 Cos[[CapitalTheta]2] -
2 (L6 + L7) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2])) + (L1 -
L2 Cos[[CapitalTheta]2]) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2]))^2) (L1 -
L2 Cos[[CapitalTheta]2] +
2 (L6 + L7) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2])) + (L1 -
L2 Cos[[CapitalTheta]2]) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2]))^2)))^2/((L1 -
L2 Cos[[CapitalTheta]2])^2 +
2 (L1^2 - 2 L6^2 - 4 L1 L7 + 2 L7^2 +
L2 Cos[[CapitalTheta]2] (-2 L1 + 4 L7 +
L2 Cos[[CapitalTheta]2])) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2]))^2 + (L1 -
L2 Cos[[CapitalTheta]2])^2 (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2]))^4)^2))/(1 + (4 L7 (L1 -
L2 Cos[[CapitalTheta]2]) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2])) (-1 + (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2]))^2) + [Sqrt](-(L1 -
L2 Cos[[CapitalTheta]2] +
2 (L6 - L7) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2])) + (L1 -
L2 Cos[[CapitalTheta]2]) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2]))^2) (L1 -
L2 Cos[[CapitalTheta]2] +
2 (-L6 + L7) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2])) + (L1 -
L2 Cos[[CapitalTheta]2]) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2]))^2) (L1 -
L2 Cos[[CapitalTheta]2] -
2 (L6 + L7) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2])) + (L1 -
L2 Cos[[CapitalTheta]2]) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2]))^2) (L1 -
L2 Cos[[CapitalTheta]2] +
2 (L6 + L7) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2])) + (L1 -
L2 Cos[[CapitalTheta]2]) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2]))^2)))^2/((L1 -
L2 Cos[[CapitalTheta]2])^2 +
2 (L1^2 - 2 L6^2 - 4 L1 L7 + 2 L7^2 +
L2 Cos[[CapitalTheta]2] (-2 L1 + 4 L7 +
L2 Cos[[CapitalTheta]2])) (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2]))^2 + (L1 -
L2 Cos[[CapitalTheta]2])^2 (Sqrt[(
L1^2 + L2^2 -
2 L1 L2 Cos[[CapitalTheta]2])/(L1 -
L2 Cos[[CapitalTheta]2])^2] + (
L2 Sin[[CapitalTheta]2])/(-L1 +
L2 Cos[[CapitalTheta]2]))^4)^2);
It seems to work fine in Mathematica 12.1:
AbsoluteTiming[FullSimplifyTime[exp, True, 10];]
*Starting FullSimplify with 10 second time constraint.*
*Time constraint exceeded.*
{10.0546, Null}
But it gets stuck in Mathematica 8.0, it won’t show the time exceeded message.
Any idea on what is going on or how to fix it? If this is a known issue in Mathematica 8.0, is there any way to constraint an evaluation using absolute timing?
Thank you.
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