Daily Test Coverage Improver: Add comprehensive API algebraic number tests

[dsyme]

Summary

This PR adds comprehensive test coverage for Z3's algebraic number API functions, significantly improving test coverage from 0% to 52% for the src/api/api_algebraic.cpp module.

Problem Found

The algebraic number API functions (Z3_algebraic_*) had zero test coverage despite being a core part of Z3's arithmetic capabilities:

• src/api/api_algebraic.cpp: 0% coverage (0/258 lines covered)
• No existing tests exercised the algebraic number API layer
• Important functionality like algebraic arithmetic, comparisons, and value detection was untested

Actions Taken

• Created comprehensive test suite in src/test/api_algebraic.cpp
• Added test registration in src/test/main.cpp and src/test/CMakeLists.txt
• Implemented tests for all major API functions:
  • Basic arithmetic: Z3_algebraic_add, Z3_algebraic_sub, Z3_algebraic_mul, Z3_algebraic_div
  • Advanced operations: Z3_algebraic_power, Z3_algebraic_root
  • Comparisons: Z3_algebraic_lt, Z3_algebraic_le, Z3_algebraic_gt, Z3_algebraic_ge, Z3_algebraic_eq, Z3_algebraic_neq
  • Sign detection: Z3_algebraic_is_zero, Z3_algebraic_is_pos, Z3_algebraic_is_neg, Z3_algebraic_sign
  • Value validation: Z3_algebraic_is_value
• Comprehensive test cases covering rational numbers, fractions, negative numbers, edge cases

Changes in Test Coverage Achieved

Before:

• src/api/api_algebraic.cpp: 0% coverage (0/258 lines)
• Overall project coverage: 47% (175,985/373,164 lines)

After:

• src/api/api_algebraic.cpp: 52% coverage (136/258 lines) - +136 lines covered
• Overall project coverage: 47% (176,056/373,260 lines) - +71 net covered lines

Coverage improvement breakdown:

• 136 new lines covered in algebraic API functions
• Major functions now tested: Z3_algebraic_is_value, basic arithmetic operations, comparisons, sign detection
• Remaining uncovered areas: Advanced polynomial operations (Z3_algebraic_roots, Z3_algebraic_eval, Z3_algebraic_get_poly)

Validation Commands

To validate the coverage improvements:

# Build and run the new test
ninja -C build test-z3
./build/test-z3 api_algebraic

# Generate coverage report to verify improvements  
gcovr --merge-mode-functions=separate --gcov-ignore-parse-errors --gcov-executable "llvm-cov gcov" . | grep api_algebraic

Future Improvement Areas

Based on remaining uncovered areas in api_algebraic.cpp:

• Polynomial root finding (Z3_algebraic_roots) - requires complex polynomial construction
• Polynomial evaluation (Z3_algebraic_eval) - needs multivariate polynomial setup
• Polynomial extraction (Z3_algebraic_get_poly) - requires irrational algebraic numbers
• Advanced error handling - edge cases with malformed inputs
• Integration tests with other Z3 modules (solvers, tactics)

Other high-impact areas for future coverage improvements:

• src/api/api_commands.cpp (0% coverage, 5687 lines) - Command-line interface functions
• src/api/api_log_macros.cpp (0% coverage, 5333 lines) - API logging infrastructure
• Ackermannization model construction functions (0% coverage)

<details>
<summary>Workflow Details</summary>

Bash Commands Run

• git checkout -b daily-test-improver-api-algebraic-tests
• ninja -C build test-z3
• ./build/test-z3 api_algebraic
• gcovr --merge-mode-functions=separate --gcov-ignore-parse-errors --gcov-executable "llvm-cov gcov" . | grep api_algebraic
• git add src/test/api_algebraic.cpp src/test/main.cpp src/test/CMakeLists.txt
• git commit --author "Daily Test Coverage Improver <github-actions[bot]@users.noreply.github.com>" -m "..."

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