Use closures in enforce_constraints and new_lc

[Pratyush]

Description

Corresponds to arkworks-rs/snark#405

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• Targeted PR against correct branch (master)
• Linked to Github issue with discussion and accepted design OR have an explanation in the PR that describes this work.
• Wrote unit tests
• Updated relevant documentation in the code
• Added a relevant changelog entry to the Pending section in CHANGELOG.md
• Re-reviewed Files changed in the Github PR explorer

[Copilot]

Pull Request Overview

This PR refactors linear combination construction to defer computation via closures and updates related APIs accordingly.

• Replaced eager cs.new_lc(...) calls with closure-based invocations (|| …) throughout the code.
• Refactored add_many, linear_combination, and inner-product methods to build LinearCombination lazily.
• Adjusted dependency sourcing in Cargo.toml to use a git reference for ark-relations.

Reviewed Changes

Copilot reviewed 7 out of 7 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
src/fields/fp/mod.rs	Swapped cs.new_lc to use closures; updated signatures for batching and linear-comb methods.
src/eq.rs	Converted enforce_r1cs_constraint calls to closure form.
src/boolean/select.rs	Updated constraint invocations to use closures and lc_diff!.
src/boolean/mod.rs	Enhanced lc for Constant(true) and added a variable() helper.
src/boolean/eq.rs	Refactored conditional equality methods to closures and lc_diff!.
src/boolean/allocated.rs	Switched R1CS constraints to closure syntax and lc_diff!.
Cargo.toml	Pointed ark-relations to a git repo and commented out patch entries.

Comments suppressed due to low confidence (2)

src/fields/fp/mod.rs:159

• [nitpick] The signature change from a generic IntoIterator to a slice &[B] is a breaking API change. To maintain flexibility, consider re-introducing an overload or supporting IntoIterator directly.

pub fn add_many<B: Borrow<Self>>(iter: &[B]) -> Option<Self> {

src/fields/fp/mod.rs:207

• The generic bound I1: IntoIterator<Item = B1, IntoIter: Clone> is invalid Rust syntax. Split it into separate bounds: I1: IntoIterator<Item = B1>, I1::IntoIter: Clone to compile successfully.

pub fn linear_combination<B1, B2, I1>(this: I1, other: &[B2]) -> Option<Self>