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| ### Normal Trees | ||
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| In order to find the primary and secondary variables a normal tree can be constructed. | ||
| In order to find the primary and secondary variables **REVIEW: You have not yet defined primary and secondary variables**, a normal tree can be constructed. |
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These are defined in the next section. It would be difficult to define these terms without first discussing the normal tree.
| # Mathematica Package | ||
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| The Mathematica package `StateMint` can be installed as described in the [documentation](https://github.com/CameronDevine/StateMint/blob/master/mathematica/README.md). The central function of the package is `stateEquations`, which uses an algorithm similar to that of the Python package, above, to derive the state equations. It takes as arguments lists of elemental equations, constraint equations, primary variables, and input variables and returns the vector state equation, state variables, and the time-derivative of the state variables. | ||
| The Mathematica package `StateMint` can be installed as described in the [documentation](https://github.com/CameronDevine/StateMint/blob/master/mathematica/README.md). The central function of the package is `stateEquations`, which uses an algorithm similar **REVIEW: Not exactly the same? Why not?** to that of the Python package, above, to derive the state equations. It takes as arguments lists of elemental equations, constraint equations, primary variables, and input variables and returns the vector state equation, state variables, and the time-derivative of the state variables. |
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The functions available in Mathematica allow a simpler and more elegant package to be written.
| The next step is to form a set of $N$ constraint equations that describe the topology of the system defined by the interconnection of the $N$ elements. | ||
| A set of $2N$ differential and algebraic equations and $2N$ unknown variables result. | ||
| If properly constructed (e.g. with the linear graph technique), $N$ of the unknown variables can be immediately eliminated through direct substitution. | ||
| A set of $2N$ differential and algebraic equations and $2N$ unknown variables result **REVIEW: Add a citation for why this is the case?**. |
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This is the case because each element has its elemental equation, along with a continuity or compatibility (a constraint) equation. Each element also has a through and across-variable associated with it. I have not seen this explicitly stated anywhere, but it can be derived from the linear graph methods. If you would like I could reference Rowell and Wormley here.
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| A detailed example of how to use the Mathematica StateMint package is [included](https://github.com/CameronDevine/StateMint/blob/master/mathematica/Example.nb) in the StateMint repository. | ||
| This package is best used by those who are already familiar with Mathematica, or for more complex problems where Mathematica may perform better than SymPy. | ||
| This package is best used by those who are already familiar with Mathematica, or for more complex problems where Mathematica may perform better than SymPy **REVIEW: Do you have any evidence or citations for this claim?**. |
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We do not have any evidence or citations for this claim.
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I made all of the grammatical changes suggested here. I also addressed most of the review comments by making the requested modifications, or responding to the comments in the pull request. A PDF copy of the most recent version of the paper is available here, https://github.com/openjournals/jose-papers/blob/jose.00044/jose.00044/10.21105.jose.00044.pdf |
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Hey Cameron. This PR is part of the JOSE pre-review.