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Update change_independent_variable docstring
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src/systems/diffeqs/basic_transformations.jl

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@@ -60,30 +60,30 @@ This or other additional equations can also be specified through `eqs`.
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The transformation is well-defined when the mapping between the new and old independent variables are one-to-one.
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This is satisfied if one is a strictly increasing function of the other (e.g. ``du(t)/dt > 0`` or ``du(t)/dt < 0``).
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Keyword arguments
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=================
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If `dummies`, derivatives of the new independent variable with respect to the old one are expressed through dummy equations; otherwise they are explicitly inserted into the equations.
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If `simplify`, these dummy expressions are simplified and often give a tidier transformation.
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If `fold`, internal substitutions will evaluate numerical expressions.
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# Keyword arguments
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- `dummies`: Whether derivatives of the new independent variable with respect to the old one are expressed through dummy equations or explicitly inserted into the equations.
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- `simplify`: Whether expanded derivative expressions are simplified. This can give a tidier transformation.
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- `fold`: Whether internal substitutions will evaluate numerical expressions.
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Additional keyword arguments `kwargs...` are forwarded to the constructor that rebuilds `sys`.
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Usage before structural simplification
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======================================
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# Usage before structural simplification
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The variable change must take place before structural simplification.
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Subsequently, consider passing `allow_symbolic = true` to `structural_simplify(sys)` to reduce the number of unknowns, with the understanding that the transformation is well-defined.
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Usage with non-autonomous systems
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=================================
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If `sys` is autonomous (i.e. ``t`` appears explicitly in its equations), it is often desirable to also pass an algebraic equation relating the new and old independent variables (e.g. ``t = f(u(t))``).
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# Usage with non-autonomous systems
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If `sys` is non-autonomous (i.e. ``t`` appears explicitly in its equations), it is often desirable to also pass an algebraic equation relating the new and old independent variables (e.g. ``t = f(u(t))``).
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Otherwise the transformed system will be underdetermined and cannot be structurally simplified without additional changes.
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Usage with hierarchical systems
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===============================
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# Usage with hierarchical systems
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It is recommended that `iv` is a non-namespaced variable in `sys`.
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This means it can belong to the top-level system or be a variable in a subsystem declared with `GlobalScope`.
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Example
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=======
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# Example
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Consider a free fall with constant horizontal velocity.
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Physics naturally describes position as a function of time.
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By changing the independent variable, it can be reformulated for vertical position as a function of horizontal position:

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