Simplify printing

[ChrisRackauckas]

With the changes downstream, this makes var"mysymbol.x" just print as mysymbol.x, which makes all of the use cases look so much nicer and gets rid of unicode.

julia> rc_model
Model rc_model with 1 equations
Unknowns (1):
  capacitor.v
Parameters (3):
  resistor.R [defaults to 2.0]
  capacitor.C [defaults to 1.0]
⋮
Incidence matrix:1×2 SparseArrays.SparseMatrixCSC{Num, Int64} with 2 stored entries:
 ×  ×

julia> equations(rc_model)
1-element Vector{Equation}:
 Differential(t)(capacitor.v) ~ capacitor.i / capacitor.C

julia> unknowns(rc_model)
1-element Vector{SymbolicUtils.BasicSymbolic{Real}}:
 capacitor.v

julia> parameters(rc_model)
3-element Vector{SymbolicUtils.BasicSymbolic{Real}}:
 resistor.R
 capacitor.C
 source.V

julia> observed(rc_model)
19-element Vector{Equation}:
 source.v ~ source.V
 capacitor.p.v ~ capacitor.v
 capacitor.n.v ~ -0.0
 ground.g.v ~ 0.0
 ⋮
 source.p.i ~ source.i
 capacitor.p.i ~ -capacitor.n.i
 source.n.i ~ -source.p.i

[github-actions[bot]]

Benchmark Results

	master	7515cfa7951353...	master/7515cfa7951353...
overhead/acrule/a+2	0.767 ± 0.023 μs	0.733 ± 0.023 μs	1.05
overhead/acrule/a+2+b	0.743 ± 0.023 μs	0.71 ± 0.023 μs	1.05
overhead/acrule/a+b	0.265 ± 0.0082 μs	0.256 ± 0.0075 μs	1.04
overhead/acrule/noop:Int	25.9 ± 0.05 ns	25.9 ± 0.92 ns	1
overhead/acrule/noop:Sym	0.0359 ± 0.0058 μs	0.0372 ± 0.0055 μs	0.965
overhead/rule/noop:Int	0.0463 ± 0.0022 μs	0.0446 ± 0.00056 μs	1.04
overhead/rule/noop:Sym	0.057 ± 0.0032 μs	0.0575 ± 0.0035 μs	0.992
overhead/rule/noop:Term	0.0566 ± 0.003 μs	0.0564 ± 0.0039 μs	1
overhead/ruleset/noop:Int	0.134 ± 0.0034 μs	0.128 ± 0.0028 μs	1.05
overhead/ruleset/noop:Sym	0.165 ± 0.0073 μs	0.15 ± 0.0069 μs	1.1
overhead/ruleset/noop:Term	3.82 ± 0.21 μs	3.85 ± 0.19 μs	0.992
overhead/simplify/noop:Int	0.152 ± 0.003 μs	0.14 ± 0.002 μs	1.09
overhead/simplify/noop:Sym	0.164 ± 0.0077 μs	0.161 ± 0.0045 μs	1.01
overhead/simplify/noop:Term	0.0393 ± 0.0025 ms	0.0402 ± 0.0028 ms	0.979
overhead/simplify/randterm (+, *):serial	0.126 ± 0.002 s	0.13 ± 0.0022 s	0.97
overhead/simplify/randterm (+, *):thread	0.0762 ± 0.026 s	0.0773 ± 0.027 s	0.985
overhead/simplify/randterm (/, *):serial	0.234 ± 0.0091 ms	0.235 ± 0.011 ms	0.993
overhead/simplify/randterm (/, *):thread	0.266 ± 0.011 ms	0.27 ± 0.012 ms	0.987
overhead/substitute/a	0.0582 ± 0.002 ms	0.0585 ± 0.002 ms	0.995
overhead/substitute/a,b	0.0515 ± 0.0021 ms	0.0525 ± 0.0023 ms	0.982
overhead/substitute/a,b,c	17.3 ± 0.87 μs	18 ± 0.97 μs	0.966
polyform/easy_iszero	0.0338 ± 0.0023 ms	0.0352 ± 0.0025 ms	0.962
polyform/isone	2.79 ± 0.01 ns	2.79 ± 0.01 ns	1
polyform/iszero	1.84 ± 0.047 ms	1.88 ± 0.065 ms	0.978
polyform/simplify_fractions	2.58 ± 0.071 ms	2.63 ± 0.091 ms	0.979
time_to_load	4.87 ± 0.017 s	4.89 ± 0.045 s	0.995

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR. Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).

[YingboMa]

This will break model text serialization.

[ChrisRackauckas]

This would make copy-paste work, which would mean directly writing to a file would reconstruct the same expressions. I presume you must mean something different by text serialization?

[YingboMa]

@variables t x.y isn't valid syntax.

[YingboMa]

I meant something like

julia> rc_model
Model rc_model with 14 (22) equations
Unknowns (22):
  resistor₊v(t) [defaults to 0.0]
  resistor₊i(t) [defaults to 0.0]
  resistor₊p₊v(t)
  resistor₊p₊i(t)
  resistor₊n₊v(t)
  resistor₊n₊i(t)
  capacitor₊v(t) [defaults to 0.0]
  capacitor₊i(t) [defaults to 0.0]
  capacitor₊p₊v(t)
  capacitor₊p₊i(t)
  capacitor₊n₊v(t)
  capacitor₊n₊i(t)
  input₊output₊u(t): Inner variable in RealOutput output
⋮
Parameters (7):
  resistor₊R [defaults to 1.0]: Resistance
  capacitor₊C [defaults to 1.0]: Capacitance
  input₊offset [defaults to 1]
  input₊start_time [defaults to 1]
  input₊amplitude [defaults to 1]
  input₊frequency [defaults to 1]
  input₊phase [defaults to 1]

julia> toexpr(rc_model)
:(let
      begin
          var"##iv#14121" = (#= /Users/schemescheme/src/julia/ModelingToolkit/src/systems/abstractsystem.jl:1250 =# @variables(t))[1]
          var"##sts#14122" = (collect)(@variables(resistor₊v(t), resistor₊i(t), resistor₊p₊v(t), resistor₊p₊i(t), resistor₊n₊v(t), resistor₊n₊i(t), capacitor₊v(t), capacitor₊i(t), capacitor₊p₊v(t), capacitor₊p₊i(t), capacitor₊n₊v(t), capacitor₊n₊i(t), input₊output₊u(t), source₊v(t), source₊i(t), source₊p₊v(t), source₊p₊i(t), source₊n₊v(t), source₊n₊i(t), source₊V₊u(t), ground₊g₊v(t), ground₊g₊i(t)))
          var"##ps#14123" = (collect)(@parameters(resistor₊R, capacitor₊C, input₊offset, input₊start_time, input₊amplitude, input₊frequency, input₊phase))
          var"##eqs#14125" = [(Symbolics.connect)(input.output, source.V); (Symbolics.connect)(source.p, resistor.p); (Symbolics.connect)(resistor.n, capacitor.p); (Symbolics.connect)(capacitor.n, source.n, ground.g); (~)(resistor₊v, (+)((*)(-1, resistor₊n₊v), resistor₊p₊v)); (~)(0, (+)(resistor₊p₊i, resistor₊n₊i)); (~)(resistor₊i, resistor₊p₊i); (~)(resistor₊v, (*)(resistor₊R, resistor₊i)); (~)(capacitor₊v, (+)(capacitor₊p₊v, (*)(-1, capacitor₊n₊v))); (~)(0, (+)(capacitor₊p₊i, capacitor₊n₊i)); (~)(capacitor₊i, capacitor₊p₊i); (~)((Differential(t))(capacitor₊v), (/)(capacitor₊i, capacitor₊C)); (~)(input₊output₊u, (+)(input₊offset, (ifelse)((<)(t, input₊start_time), 0, (*)(input₊amplitude, (sin)((+)(input₊phase, (*)(6.283185307179586, input₊frequency, (+)((*)(-1, input₊start_time), t)))))))); (~)(source₊v, (+)((*)(-1, source₊n₊v), source₊p₊v)); (~)(0, (+)(source₊p₊i, source₊n₊i)); (~)(source₊i, source₊p₊i); (~)(source₊v, source₊V₊u); (~)(ground₊g₊v, 0)]
          var"##defs#14126" = (Dict)((Pair)(resistor₊v, 0.0), (Pair)(input₊frequency, 1), (Pair)(input₊offset, 1), (Pair)(capacitor₊i, 0.0), (Pair)(resistor₊i, 0.0), (Pair)(input₊start_time, 1), (Pair)(resistor₊R, 1.0), (Pair)(source₊v, 0.0), (Pair)(input₊phase, 1), (Pair)(capacitor₊v, 0.0), (Pair)(input₊amplitude, 1), (Pair)(source₊i, 0.0), (Pair)(capacitor₊C, 1.0))
          var"##eqs#14127" = [;]
          var"##iv#14128" = (#= /Users/schemescheme/src/julia/ModelingToolkit/src/systems/abstractsystem.jl:1276 =# @variables(t))[1]
          (ODESystem)(var"##eqs#14125", var"##iv#14128", var"##sts#14122", var"##ps#14123"; defaults = var"##defs#14126", observed = var"##eqs#14127", name = :rc_model, checks = false)
      end
  end)

[ChrisRackauckas]

I see, so we should specialize the display of systems and equations specifically?

[YingboMa]

Yeah, I think we should decouple display of models further. We can add a PrettyPrint struct and overload show for PrettyPrint(model, :eqs) etc.