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docs/src/examples/modelingtoolkitize_index_reduction.md

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@@ -115,7 +115,7 @@ But that's not a satisfying answer, so what do you do about it?
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It turns out that higher order DAEs can be transformed into lower order DAEs.
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[If you differentiate the last equation two times and perform a substitution,
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you can arrive at the following set of equations](https://people.math.wisc.edu/~chr/am205/g_act/DAE_slides.pdf):
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you can arrive at the following set of equations](https://people.math.wisc.edu/%7Echr/am205/g_act/DAE_slides.pdf):
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```math
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\begin{aligned}

src/clock.jl

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@@ -14,6 +14,7 @@ Symbolics.option_to_metadata_type(::Val{:timedomain}) = TimeDomain
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"""
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is_continuous_domain(x)
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true if `x` contains only continuous-domain signals.
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See also [`has_continuous_domain`](@ref)
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"""
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"""
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has_time_domain(x)
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Determine if variable `x` has a time-domain attributed to it.
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"""
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function has_time_domain(x::Symbolic)

src/structural_transformation/pantelides.jl

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@@ -76,18 +76,18 @@ Computes which variables are the "highest-differentiated" for purposes of
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pantelides. Ordinarily this is relatively straightforward. However, in our
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case, there are two complicating conditions:
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1. We allow variables in the structure graph that don't appear in the
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system at all. What we are interested in is the highest-differentiated
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variable that actually appears in the system.
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1. We allow variables in the structure graph that don't appear in the
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system at all. What we are interested in is the highest-differentiated
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variable that actually appears in the system.
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2. We have an alias graph. The alias graph implicitly contributes an
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alias equation, so it doesn't actually whitelist any additional variables,
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but it may change which variable is considered the highest differentiated one.
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Consider the following situation:
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2. We have an alias graph. The alias graph implicitly contributes an
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alias equation, so it doesn't actually whitelist any additional variables,
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but it may change which variable is considered the highest differentiated one.
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Consider the following situation:
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Vars: x, y
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Eqs: 0 = f(x)
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Alias: ẋ = ẏ
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Vars: x, y
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Eqs: 0 = f(x)
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Alias: ẋ = ẏ
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In the absence of the alias, we would consider `x` to be the highest
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differentiated variable. However, because of the alias (and because there

src/systems/discrete_system/discrete_system.jl

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"""
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```julia
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SciMLBase.DiscreteFunction{iip}(sys::DiscreteSystem, dvs=states(sys),
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ps=parameters(sys);
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version=nothing,
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SciMLBase.DiscreteFunction{iip}(sys::DiscreteSystem, dvs = states(sys),
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ps = parameters(sys);
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version = nothing,
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kwargs...) where {iip}
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```
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"""
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```julia
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DiscreteFunctionExpr{iip}(sys::DiscreteSystem, dvs = states(sys),
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ps = parameters(sys);
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version = nothing,
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kwargs...) where {iip}
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DiscreteFunctionExpr{iip}(sys::DiscreteSystem, dvs = states(sys),
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ps = parameters(sys);
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version = nothing,
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kwargs...) where {iip}
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```
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Create a Julia expression for an `DiscreteFunction` from the [`DiscreteSystem`](@ref).

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