Draft - InvRing for SLn (#2823)

* added cayley-omega.jl

* made omegap a separate function

* updates reynolds__ - need to fix det denominator

* First attempt for SLn

* fixed the bug

* Added direct product and tensor

* removed a loop from generators

* small fix - reduce_gens_

* deleted cayley omega

* coefficient bug fixed

* Created object Reductive Groups in file InvariantRings_ReductiveGroups

* small fixes in InvariantRings_ReductiveGroups.jl

* callable derksen_ideal and hilbert_ideal in InvariantRings_ReductiveGroups

* export functions in InvariantRings_ReductiveGroups

* printing of direct sum of vector stpaces in InvariantRings_ReductiveGroups

* mu_star, reynolds_operator added to Inv Rings Red Grps

* added file InvariantRings_ReductiveGroups

* deleted redundant folder

* Some tweaks

* edits to make the code more efficient in InvariantTheory.jl

* minor edits in InvariantTheory.jl

* fixed coefficient problem in InvariantTheory.jl

* added comments and minor edits. Lazy computation of InvariantRing in InvariantTheory.jl

* minor edits to InvariantTheory.jl

* added export functions in InvariantTheory.jl

* typo in InvariantTheory.jl

* minor edits in InvaraintTheory.jl, few tests in tests.jl

* finished tests.jl for invariant theory of SLm

* removed factorise in InvariantTheory.jl

* more efficient rep_mat_ function in InvariantTheory.jl

* chenged degree_basis function

* pretty(io) in InvariantTheory.jl

* minor change in reductive group constructor

* evaluate func in generators func in InvariantTheory.jl

* started with adding Torus to reductive groups

* incorporating tori with fast algorithm to InvariantTheory.jl

* removed show functions, added test in invariant theory

* field error for reductive groups

* minor type changes

* added test for invariants of tori

* direct product and tensor for representations

* tests for direct sum, tensor of representaions, minor fix in construction function of reductive groups

* minor modification

* minor edits in InvariantTheory.jl

* Update experimental/InvariantTheory/src/InvariantTheory.jl

Co-authored-by: Max Horn <[email protected]>

* Update experimental/InvariantTheory/src/InvariantTheory.jl

Co-authored-by: Max Horn <[email protected]>

* minor changes discussed in pull request

* removed goto in torus invariants function

* removed import statement

* changed name of representation_from_forms

* torus of rank

* minor changes from pull request

* minor edits from pr comments

* minor changes in show commands

* started file for torus fast

* shifted torus to new file TorusInvariantsFast

* minor change in fundtion degree basis

* fixed typo

* added comments, removed extra output of generators(..)

* renamed InvariantRing to RedGrpInvRing

* minor changes

* fixed all texts except torus

* no internal constructor needed

* fixed tests, changed names

* print field for LinearlyReductiveGroup

* changed RedGrpInvRing to attributes. Other minor changes

* added error messages for @Req, fixed typo

* added export functions to torus groups

* fixed export functions in InvariantTheory.jl

* minor changes suggested in pr implemented

* fixed test

* exported direct_sum, tensor

* included file TorusInvariantsFast.jl

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Co-authored-by: Max Horn <[email protected]>