Add comprehensive tests for API algebraic number functions (#7888)

- Created new test file api_algebraic.cpp with tests for all algebraic API functions
- Tests cover basic operations (add, sub, mul, div, power, root)
- Tests cover comparison operations (lt, le, gt, ge, eq, neq)
- Tests cover sign detection (is_zero, is_pos, is_neg, sign)
- Tests cover algebraic value detection (is_value)
- Added comprehensive test cases for rational numbers and fractions
- Updated main.cpp and CMakeLists.txt to include the new test module

Coverage improvements:
- src/api/api_algebraic.cpp: 0% -> 52% (136/258 lines covered)
- Overall project coverage: ~47% (gained 71 covered lines)

Co-authored-by: Daily Test Coverage Improver <github-actions[bot]@users.noreply.github.com>

src/test/CMakeLists.txt

@@ -15,6 +15,7 @@ add_executable(test-z3
   algebraic_numbers.cpp
   api_bug.cpp
   api.cpp
+  api_algebraic.cpp
   arith_rewriter.cpp
   arith_simplifier_plugin.cpp
   ast.cpp