Heads up about changes in Julia LinearAlgebra stdlib affecting this package

[KristofferC]

Pivoting in the LU factorization is now used in more cases after: JuliaLang/julia#32989

This means that the line https://github.com/JuliaLang/julia/blame/master/stdlib/LinearAlgebra/src/lu.jl#L143 gets executed which breaks this package tests:

Tests for Taylor1 expansions: Error During Test at /root/.julia/packages/TaylorSeries/STRph/test/onevariable.jl:10
  Got exception outside of a @test
  ArgumentError: The 0th order Taylor1 coefficient must be non-zero
  (abs(x) is not differentiable at x=0).
  Stacktrace:
   [1] abs at /root/.julia/packages/TaylorSeries/STRph/src/other_functions.jl:88 [inlined]
   [2] #generic_lufact!#134(::Bool, ::typeof(LinearAlgebra.generic_lufact!), ::Array{Taylor1{Float64},2}, ::Val{true}) at /workspace/srcdir/julia/usr/share/julia/stdlib/v1.3/LinearAlgebra/src/lu.jl:143
   [3] #generic_lufact! at ./none:0 [inlined]
   [4] #lu!#133 at /workspace/srcdir/julia/usr/share/julia/stdlib/v1.3/LinearAlgebra/src/lu.jl:130 [inlined]
   [5] #lu! at ./none:0 [inlined]
   [6] #lu#135 at /workspace/srcdir/julia/usr/share/julia/stdlib/v1.3/LinearAlgebra/src/lu.jl:273 [inlined]
   [7] lu at /workspace/srcdir/julia/usr/share/julia/stdlib/v1.3/LinearAlgebra/src/lu.jl:272 [inlined] (repeats 2 times)
   [8] inv(::Array{Taylor1{Float64},2}) at /workspace/srcdir/julia/usr/share/julia/stdlib/v1.3/LinearAlgebra/src/dense.jl:770
   [9] top-level scope at /root/.julia/packages/TaylorSeries/STRph/test/onevariable.jl:509
   [10] top-level scope at /workspace/srcdir/julia/usr/share/julia/stdlib/v1.3/Test/src/Test.jl:1107
   [11] top-level scope at /root/.julia/packages/TaylorSeries/STRph/test/onevariable.jl:11
   [12] include at ./boot.jl:328 [inlined]
   [13] include_relative(::Module, ::String) at ./loading.jl:1105
   [14] include(::Module, ::String) at ./Base.jl:31
   [15] include(::String) at ./client.jl:432
   [16] top-level scope at /root/.julia/packages/TaylorSeries/STRph/test/runtests.jl:17
   [17] include at ./boot.jl:328 [inlined]
   [18] include_relative(::Module, ::String) at ./loading.jl:1105
   [19] include(::Module, ::String) at ./Base.jl:31
   [20] include(::String) at ./client.jl:432
   [21] top-level scope at none:6
   [22] eval(::Module, ::Any) at ./boot.jl:330
   [23] exec_options(::Base.JLOptions) at ./client.jl:271
   [24] _start() at ./client.jl:468

[lbenet]

Thanks for reporting. I'll take a look on this.

[lbenet]

The problem is indeed the fact that abs(zero(T)) for T::Taylor1 is not defined, throws actually an error; polynomials do not form an ordered field, which is required for pivoting.

A possible solution could be to extend lu(A::AbstractMatrix{T}, ...) for T::Taylor1 so it uses the old method without pivoting. Does that make sense? Would that be a good solution?

cc @andreasnoack