Replace BackendSelection with dedicated contraction algorithm types#123
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## Summary Replaces the string-based `BackendSelection.Algorithm"..."` selection for tensor-network contraction with dedicated algorithm types, and drops `BackendSelection`, `TypeParameterAccessors`, and `FunctionImplementations` as dependencies. Contraction order is now chosen with types instead of `Algorithm` strings: `Greedy` and `Optimal` (the `optimize_contraction_order` strategies, with `Optimal` provided by the TensorOperations extension), `Flat` and `LeftAssociative` (the `contraction_order` strategies), and `Exact` (the `contract_network` algorithm, carrying its `order`/`order_alg` as fields rather than as `Algorithm` parameters). `Greedy` replaces the old `"eager"` name, the standard term for the cost-minimizing pairwise heuristic. `TypeParameterAccessors` was unused. The lone `FunctionImplementations.zero!` call becomes `fill!(a, zero(eltype(a)))`. The structure-aware `zero!` it relied on is worth keeping as a shared overloadable primitive, but where that should live is a separate question, and the dense path `delta` actually uses is unaffected. Also un-breaks the `show`/`printnode`/`print_tree` tests for the lazy and symbolic tensors: the rendered output was already correct, the expected strings just predated ITensorBase's index-name display. This sets up moving the `LazyITensors` submodule into ITensorBase, which its `BackendSelection` use had stood in the way of.
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) ## Summary Adds the lazy and symbolic tensor types and the contraction-order machinery to ITensorBase, in the top-level namespace: `LazyITensor` and `SymbolicITensor` expression leaves, `lazy` / `Mul` / `symnameddims` / `substitute` for building lazy contraction expressions, and `optimize_evaluation_order` with the `Greedy` and `Optimal` order algorithms. This code was moved from ITensorNetworksNext's `LazyITensors` submodule, most recently reworked in ITensor/ITensorNetworksNext.jl#123 to use dedicated contraction-order algorithm types and fewer dependencies. It moves down to ITensorBase so it sits alongside the `ITensor` type it builds on, and a follow-up will switch ITensorNetworksNext to consume it instead of carrying its own copy. `AbstractTrees` becomes a regular dependency rather than a weakdep: the lazy and symbolic `show` and tree rendering use it throughout, and the `printnode(::AbstractITensor)` method that was in `ITensorBaseAbstractTreesExt` moves into the package. `TermInterface`, `WrappedUnions`, and `Combinatorics` are new dependencies. The `Optimal` order, which uses `TensorOperations.optimaltree`, is provided by a new `TensorOperations` extension. `SymbolicITensor` is a placeholder that gets substituted with a real tensor before contraction, so it stores only what contraction-order selection needs: `name`, the index `size`s, and `dimnames`, with `inds` reconstructed as plain ranges of those sizes. It is parameterized by the dimension-name type and the name type, the latter matching how the tensor network types parameterize by vertex type.
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Summary
Replaces the string-based
BackendSelection.Algorithm"..."selection for tensor-network contraction with dedicated algorithm types, and dropsBackendSelection,TypeParameterAccessors, andFunctionImplementationsas dependencies.Contraction order is now chosen with types instead of
Algorithmstrings:GreedyandOptimal(theoptimize_contraction_orderstrategies, withOptimalprovided by the TensorOperations extension),FlatandLeftAssociative(thecontraction_orderstrategies), andExact(thecontract_networkalgorithm, carrying itsorder/order_algas fields rather than asAlgorithmparameters).Greedyreplaces the old"eager"name, the standard term for the cost-minimizing pairwise heuristic.TypeParameterAccessorswas unused. The loneFunctionImplementations.zero!call becomesfill!(a, zero(eltype(a))). The structure-awarezero!it relied on is worth keeping as a shared overloadable primitive, but where that should live is a separate question, and the dense pathdeltaactually uses is unaffected.Also un-breaks the
show/printnode/print_treetests for the lazy and symbolic tensors: the rendered output was already correct, the expected strings just predated ITensorBase's index-name display.This sets up moving the
LazyITensorssubmodule into ITensorBase, which itsBackendSelectionuse had stood in the way of.