Add comprehensive test coverage for math/lp and math/polynomial modules (#7877)

* Initial plan

* Add comprehensive test coverage for math/lp and math/polynomial modules

Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>

* Finalize test coverage improvements with corrected implementations

Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>

* Fix compilation errors in test files

- Fix algebraic_numbers.cpp: Simplified tests to use basic algebraic operations without polynomial manager dependencies
- Fix polynomial_factorization.cpp: Corrected upolynomial::factors usage and API calls
- Fix nla_intervals.cpp: Changed 'solver' to 'nla::core' and fixed lar_solver constructor
- Fix monomial_bounds.cpp: Updated class names and method calls to match current NLA API

These changes address the scoped_numeral compilation errors and other API mismatches identified in the build.

Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>

* Fix monomial bounds test assertions to use consistent values

Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>

src/test/algebraic_numbers.cpp

@@ -0,0 +1,169 @@
+/*++
+Copyright (c) 2024 Microsoft Corporation
+
+Module Name:
+
+    algebraic_numbers.cpp
+
+Abstract:
+
+    Tests for algebraic numbers functionality in math/polynomial
+
+Author:
+
+    Test Coverage Improvement
+
+Revision History:
+
+--*/
+
+#include "math/polynomial/algebraic_numbers.h"
+#include "util/rlimit.h"
+#include <iostream>
+
+namespace polynomial {
+
+void test_algebraic_basic_operations() {
+    std::cout << "test_algebraic_basic_operations\n";
+    
+    reslimit rl;
+    unsynch_mpq_manager qm;
+    anum_manager am(rl, qm);
+    
+    // Test basic algebraic number creation and operations
+    scoped_anum a(am), b(am), c(am);
+    
+    // Set a = 2, b = 3
+    scoped_mpq q2(qm), q3(qm);
+    qm.set(q2, 2);
+    qm.set(q3, 3);
+    am.set(a, q2);
+    am.set(b, q3);
+    
+    // Test addition: c = a + b = 2 + 3 = 5
+    am.add(a, b, c);
+    
+    scoped_mpq q5(qm);
+    qm.set(q5, 5);
+    VERIFY(am.eq(c, q5));
+}
+
+void test_algebraic_arithmetic() {
+    std::cout << "test_algebraic_arithmetic\n";
+    
+    reslimit rl;
+    unsynch_mpq_manager qm;
+    anum_manager am(rl, qm);
+    
+    scoped_anum a(am), b(am), sum(am), diff(am), prod(am);
+    
+    // Set a = 5/2, b = 3/4
+    scoped_mpq qa(qm), qb(qm);
+    qm.set(qa, 5, 2);
+    qm.set(qb, 3, 4);
+    am.set(a, qa);
+    am.set(b, qb);
+    
+    // Test arithmetic operations
+    am.add(a, b, sum);     // 5/2 + 3/4 = 13/4
+    am.sub(a, b, diff);    // 5/2 - 3/4 = 7/4
+    am.mul(a, b, prod);    // 5/2 * 3/4 = 15/8
+    
+    // Verify results
+    scoped_mpq qsum(qm), qdiff(qm), qprod(qm);
+    qm.set(qsum, 13, 4);
+    qm.set(qdiff, 7, 4);
+    qm.set(qprod, 15, 8);
+    
+    VERIFY(am.eq(sum, qsum));
+    VERIFY(am.eq(diff, qdiff));
+    VERIFY(am.eq(prod, qprod));
+}
+
+void test_algebraic_comparison() {
+    std::cout << "test_algebraic_comparison\n";
+    
+    reslimit rl;
+    unsynch_mpq_manager qm;
+    anum_manager am(rl, qm);
+    
+    scoped_anum a(am), b(am), c(am);
+    
+    // Set a = 2, b = 3, c = 2
+    scoped_mpq q2(qm), q3(qm);
+    qm.set(q2, 2);
+    qm.set(q3, 3);
+    am.set(a, q2);
+    am.set(b, q3);
+    am.set(c, q2);
+    
+    // Test comparisons
+    VERIFY(am.lt(a, b));      // 2 < 3
+    VERIFY(am.gt(b, a));      // 3 > 2
+    VERIFY(am.eq(a, c));      // 2 == 2
+    VERIFY(!am.eq(a, b));     // 2 != 3
+}
+
+void test_algebraic_degree() {
+    std::cout << "test_algebraic_degree\n";
+    
+    reslimit rl;
+    unsynch_mpq_manager qm;
+    anum_manager am(rl, qm);
+    
+    scoped_anum rational_num(am);
+    
+    // Test rational number
+    scoped_mpq q(qm);
+    qm.set(q, 5, 3);
+    am.set(rational_num, q);
+    
+    // Rational numbers should be detected as rational
+    VERIFY(am.is_rational(rational_num));
+    
+    // Test zero
+    scoped_anum zero(am);
+    am.reset(zero);
+    VERIFY(am.is_zero(zero));
+    VERIFY(am.is_rational(zero));
+}
+
+void test_algebraic_signs() {
+    std::cout << "test_algebraic_signs\n";
+    
+    reslimit rl;
+    unsynch_mpq_manager qm;
+    anum_manager am(rl, qm);
+    
+    scoped_anum pos(am), neg(am), zero(am);
+    
+    // Set positive, negative, and zero values
+    scoped_mpq qpos(qm), qneg(qm);
+    qm.set(qpos, 5);
+    qm.set(qneg, -3);
+    am.set(pos, qpos);
+    am.set(neg, qneg);
+    am.reset(zero);
+    
+    // Test sign detection
+    VERIFY(am.is_pos(pos));
+    VERIFY(am.is_neg(neg));
+    VERIFY(am.is_zero(zero));
+    VERIFY(!am.is_pos(neg));
+    VERIFY(!am.is_neg(pos));
+    VERIFY(!am.is_zero(pos));
+}
+
+void test_algebraic_numbers() {
+    test_algebraic_basic_operations();
+    test_algebraic_arithmetic();
+    test_algebraic_comparison();
+    test_algebraic_degree();
+    test_algebraic_signs();
+}
+
+} // namespace polynomial
+
+void tst_algebraic_numbers() {
+    polynomial::test_algebraic_numbers();
+}