Printing of PolyRing uses wrong variable identifiers

[mjrodgers]

Describe the bug
Singular.jl has a method to rename "bad" identifiers before sending them to the Singular libraries, and maintains the list of original symbols in Julia to use. But printing of PolyRing uses a strange mix of old and new symbols.\

To Reproduce
We see here using "bad" variable names that we get sort of nonsense output involving the renamed variables.

julia> R, (x, y, z) = polynomial_ring(QQ, ["[x]", "[y]", "[z]"])
(Singular Polynomial Ring (QQ),(x,x@1,x@2),(dp(3),C), spoly{n_Q}[[x], [y], [z]])

Expected behavior
I would expect the output to be more informative, and to only use the originally supplied Julia identifiers for the variables.

We can see this carries over to other contexts, such as defining an Ideal we see a mix of the old and new identifiers:

julia> I = Ideal(R, x+z, y+z)
Singular ideal over Singular Polynomial Ring (QQ),(x,x@1,x@2),(dp(3),C) with generators ([x] + [z], [y] + [z])

Information about your setup:
julia> versioninfo()
Julia Version 1.9.1
Commit 147bdf428cd (2023-06-07 08:27 UTC)
Platform Info:
OS: macOS (x86_64-apple-darwin22.4.0)
CPU: 8 × Intel(R) Core(TM) i7-1068NG7 CPU @ 2.30GHz
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-14.0.6 (ORCJIT, icelake-client)
Threads: 1 on 8 virtual cores

julia> using Pkg; Pkg.status(mode=PKGMODE_MANIFEST)
Status ~/.julia/environments/v1.9/Manifest.toml
[c3fe647b] AbstractAlgebra v0.30.9
[66b61cbe] AlgebraicSolving v0.3.2
[6e4b80f9] BenchmarkTools v1.3.2
[f01c122e] BinaryWrappers v0.1.2
[da1fd8a2] CodeTracking v1.3.1
[34da2185] Compat v4.6.1
[1f15a43c] CxxWrap v0.13.4
[9a962f9c] DataAPI v1.15.0
[e2d170a0] DataValueInterfaces v1.0.0
[55939f99] DecFP v1.3.1
[ffbed154] DocStringExtensions v0.9.3
[e2ba6199] ExprTools v0.1.9
[c863536a] GAP v0.9.6
[d5909c97] GroupsCore v0.4.0
[3e1990a7] Hecke v0.18.14
[92d709cd] IrrationalConstants v0.2.2
[82899510] IteratorInterfaceExtensions v1.0.0
[692b3bcd] JLLWrappers v1.4.1
[682c06a0] JSON v0.21.4
[aa1ae85d] JuliaInterpreter v0.9.23
[2ab3a3ac] LogExpFunctions v0.3.24
[6f1432cf] LoweredCodeUtils v2.3.0
[1914dd2f] MacroTools v0.5.10
[6fafb56a] Memoization v0.2.1
[78c3b35d] Mocking v0.7.7
[4fe8b98c] Mongoc v0.9.0
[ffc61752] Mustache v1.0.17
[2edaba10] Nemo v0.34.6
[bac558e1] OrderedCollections v1.6.0
[f1435218] Oscar v0.12.1
[d96e819e] Parameters v0.12.3
[69de0a69] Parsers v2.7.0
[fa939f87] Pidfile v1.3.0
[14b8a8f1] PkgTemplates v0.7.38
[d720cf60] Polymake v0.9.2
[aea7be01] PrecompileTools v1.1.2
[21216c6a] Preferences v1.4.0
[fb686558] RandomExtensions v0.4.3
[3cdcf5f2] RecipesBase v1.3.4
[ae029012] Requires v1.3.0
[295af30f] Revise v3.5.3
[6c6a2e73] Scratch v1.2.0
[bcd08a7b] Singular v0.18.6
[276daf66] SpecialFunctions v2.2.0
[3783bdb8] TableTraits v1.0.1
[bd369af6] Tables v1.10.1
[3a884ed6] UnPack v1.0.2
[ae81ac8f] ASL_jll v0.1.3+0
[e21ec000] Antic_jll v0.201.500+0
[d9960996] Arb_jll v200.2300.0+0
[6e34b625] Bzip2_jll v1.0.8+0
[fcfa6d1b] Calcium_jll v0.401.100+0
[47200ebd] DecFP_jll v2.0.3+1
[e134572f] FLINT_jll v200.900.6+0
[5cd7a574] GAP_jll v400.1200.200+2
[de1ad85e] GAP_lib_jll v400.1201.200+0
[ba154793] GAP_pkg_juliainterface_jll v0.800.202+2
[e8aa6df9] GLPK_jll v5.0.1+0
[e33a78d0] Hwloc_jll v2.9.1+0
[9cc047cb] Ipopt_jll v300.1400.1300+0
[1d63c593] LLVMOpenMP_jll v15.0.4+0
[dd4b983a] LZO_jll v2.10.1+0
[d00139f3] METIS_jll v5.1.2+0
[d7ed1dd3] MUMPS_seq_jll v500.600.0+0
[90100e71] MongoC_jll v1.19.1+0
[68e3532b] Ncurses_jll v6.2.0+0
[76642167] Ninja_jll v1.11.1+0
⌅ [656ef2d0] OpenBLAS32_jll v0.3.21+0
⌅ [458c3c95] OpenSSL_jll v1.1.21+0
[efe28fd5] OpenSpecFun_jll v0.5.5+0
[80dd9cbb] PPL_jll v1.2.1+0
[83958c19] Perl_jll v5.34.0+2
[05236dd9] Readline_jll v8.1.1+1
[e5ac4fe4] SCIP_jll v800.0.301+0
[319450e9] SPRAL_jll v2023.3.29+0
[43d676ae] Singular_jll v403.203.202+0
[36f60fef] TOPCOM_jll v0.17.8+0
[3161d3a3] Zstd_jll v1.5.5+0
[508c9074] bliss_jll v0.77.0+1
⌅ [28df3c45] boost_jll v1.76.0+1
[f07e07eb] cddlib_jll v0.94.13+0
[5558cf25] cohomCalg_jll v0.32.0+0
[1493ae25] lib4ti2_jll v1.6.10+0
[3eaa8342] libcxxwrap_julia_jll v0.9.7+1
[4d8266f6] libpolymake_julia_jll v0.9.2+0
[ae4fbd8f] libsingular_julia_jll v0.34.0+0
[3873f7d0] lrslib_jll v0.3.3+0
[6d01cc9a] msolve_jll v0.4.9+0
[55c6dc9b] nauty_jll v2.6.13+1
[6690c6e9] normaliz_jll v300.900.301+0
⌅ [7c209550] polymake_jll v400.900.0+0
[fe1e1685] snappy_jll v1.1.9+1
[0dad84c5] ArgTools v1.1.1
[56f22d72] Artifacts
[2a0f44e3] Base64
[ade2ca70] Dates
[8ba89e20] Distributed
[f43a241f] Downloads v1.6.0
[7b1f6079] FileWatching
[b77e0a4c] InteractiveUtils
[4af54fe1] LazyArtifacts
[b27032c2] LibCURL v0.6.3
[76f85450] LibGit2
[8f399da3] Libdl
[37e2e46d] LinearAlgebra
[56ddb016] Logging
[d6f4376e] Markdown
[a63ad114] Mmap
[ca575930] NetworkOptions v1.2.0
[44cfe95a] Pkg v1.9.0
[de0858da] Printf
[9abbd945] Profile
[3fa0cd96] REPL
[9a3f8284] Random
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization
[6462fe0b] Sockets
[2f01184e] SparseArrays
[10745b16] Statistics v1.9.0
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[8dfed614] Test
[cf7118a7] UUIDs
[4ec0a83e] Unicode
[e66e0078] CompilerSupportLibraries_jll v1.0.2+0
[781609d7] GMP_jll v6.2.1+2
[deac9b47] LibCURL_jll v7.84.0+0
[29816b5a] LibSSH2_jll v1.10.2+0
[3a97d323] MPFR_jll v4.1.1+4
[c8ffd9c3] MbedTLS_jll v2.28.2+0
[14a3606d] MozillaCACerts_jll v2022.10.11
[4536629a] OpenBLAS_jll v0.3.21+4
[05823500] OpenLibm_jll v0.8.1+0
[bea87d4a] SuiteSparse_jll v5.10.1+6
[83775a58] Zlib_jll v1.2.13+0
[8e850b90] libblastrampoline_jll v5.8.0+0
[8e850ede] nghttp2_jll v1.48.0+0
[3f19e933] p7zip_jll v17.4.0+0