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feat: 三角函数化简逻辑
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6 files changed

Lines changed: 253 additions & 11 deletions

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‎CMakeLists.txt‎

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Original file line numberDiff line numberDiff line change
@@ -79,6 +79,9 @@ target_link_libraries(test_complex_arithmetic PRIVATE lmcas LammpCore)
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add_executable(test_calculus tests/test_calculus.cpp)
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target_link_libraries(test_calculus PRIVATE lmcas LammpCore)
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add_executable(test_trig tests/test_trig.cpp)
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target_link_libraries(test_trig PRIVATE lmcas LammpCore)
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enable_testing()
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add_test(NAME TestCAS COMMAND test_cas)
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add_test(NAME TestBigIntDebug COMMAND test_bigint_debug)
@@ -89,3 +92,4 @@ add_test(NAME TestArithmetic COMMAND test_arithmetic)
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add_test(NAME TestNewFeatures COMMAND test_new_features)
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add_test(NAME TestComplexArithmetic COMMAND test_complex_arithmetic)
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add_test(NAME TestCalculus COMMAND test_calculus)
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add_test(NAME TestTrig COMMAND test_trig)

‎notes.txt‎

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@@ -1,21 +1,22 @@
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LMCAS缺少：
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1.线性代数
3-
行列式
4-
矩阵求逆
5-
转置
6-
特征值（特征向量
7-
线性方程组求解（Ax=b 高斯消元法？
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行列式 OK
4+
矩阵求逆 OK
5+
转置 OK
6+
特征值（特征向量
7+
线性方程组求解（Ax=b 高斯消元法？ OK
88
2.微积分
9-
符号积分（不定积分求解算法RISCH
10-
极限计算（洛必达法则、泰勒级数展开
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符号积分（不定积分求解算法RISCH 项式、对数规则、线性性质和部分启发式积分
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极限计算（洛必达法则、泰勒级数展开 代入法和 洛必达法则 启发式算法（针对 0/0 型）
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微分 实现了基础求导法则
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3.高级方程求解
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多项式
13-
方程组
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方程组 OK
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不等式
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4.多项式
16-
展开
17-
因式分解
18-
最大公约数
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展开 OK
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因式分解 OK
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最大公约数 OK
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5.三角函数
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恒等式化简
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‎symbolic.hpp‎

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@@ -531,4 +531,7 @@ class LAMINA_API SymbolicExpr {
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std::shared_ptr<SymbolicExpr> simplify_multiply() const;
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std::shared_ptr<SymbolicExpr> simplify_add() const;
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std::shared_ptr<SymbolicExpr> simplify_power() const;
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std::shared_ptr<SymbolicExpr> simplify_sin() const;
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std::shared_ptr<SymbolicExpr> simplify_cos() const;
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std::shared_ptr<SymbolicExpr> simplify_tan() const;
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};

‎symbolic_core.cpp‎

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@@ -121,6 +121,10 @@ std::shared_ptr<SymbolicExpr> SymbolicExpr::simplify() const {
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return SymbolicExpr::ln(val);
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}
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case Type::Sin: return simplify_sin();
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case Type::Cos: return simplify_cos();
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case Type::Tan: return simplify_tan();
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default:
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// TODO: Recursive simplify for other functions
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return std::make_shared<SymbolicExpr>(*this);

‎symbolic_simplify.cpp‎

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@@ -632,6 +632,177 @@ static std::shared_ptr<SymbolicExpr> expand_power_integer(const std::shared_ptr<
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return distribute_multiply(base, rest);
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}
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// --- Trigonometric Simplifications ---
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// Helper: matches c * pi or pi * c or pi
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// Returns pair {bool matched, Rational c}
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static std::pair<bool, Rational> match_pi_multiple(const std::shared_ptr<SymbolicExpr>& expr) {
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if (expr->type == SymbolicExpr::Type::Variable && (expr->identifier == "π" || expr->identifier == "pi")) {
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return {true, Rational(1)};
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}
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if (expr->type == SymbolicExpr::Type::Multiply && expr->operands.size() == 2) {
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auto left = expr->operands[0];
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auto right = expr->operands[1];
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bool left_is_pi = (left->type == SymbolicExpr::Type::Variable && (left->identifier == "π" || left->identifier == "pi"));
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bool right_is_pi = (right->type == SymbolicExpr::Type::Variable && (right->identifier == "π" || right->identifier == "pi"));
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if (left_is_pi && right->is_number()) return {true, right->convert_rational()};
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if (right_is_pi && left->is_number()) return {true, left->convert_rational()};
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}
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return {false, Rational(0)};
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}
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std::shared_ptr<SymbolicExpr> SymbolicExpr::simplify_sin() const {
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auto arg = operands[0]->simplify();
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// sin(0) = 0
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if (arg->is_number() && arg->convert_rational() == Rational(0)) return SymbolicExpr::number(0);
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// sin(-x) = -sin(x)
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if (arg->type == SymbolicExpr::Type::Multiply && arg->operands.size() == 2) {
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if (arg->operands[0]->is_number() && arg->operands[0]->convert_rational() == Rational(-1)) {
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// sin(-u) -> -sin(u)
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return SymbolicExpr::multiply(SymbolicExpr::number(-1), SymbolicExpr::sin(arg->operands[1]))->simplify();
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}
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}
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// Check for k * pi
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auto pi_match = match_pi_multiple(arg);
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if (pi_match.first) {
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Rational k = pi_match.second;
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// sin(n * pi) = 0 for integer n
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if (k.is_integer()) return SymbolicExpr::number(0);
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// sin( (2n+1)/2 * pi ) = (-1)^n
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// k = n + 1/2 -> 2k = 2n + 1 an odd integer
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Rational two_k = k * Rational(2);
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if (two_k.is_integer()) {
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BigInt bk = two_k.get_numerator(); // This is 2k
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// Check if 2k is odd (not even)
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bool is_even = (bk._size == 0) || !(bk._data[0] & 1);
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if (!is_even) {
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// n = (2k - 1) / 4 ?? No.
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// Let 2k = m (odd). k = m/2.
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// sin(m/2 * pi).
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// m = 1 (pi/2) -> 1
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// m = 3 (3pi/2) -> -1
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// m = 5 -> 1
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// Pattern: (m-1)/2 is even -> 1, odd -> -1 ?
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// m=1 -> 0 -> 1. m=3 -> 1 -> -1.
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// index = (m-1)/2. if index even -> 1.
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// We need m % 4.
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// 1 % 4 = 1 -> 1
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// 3 % 4 = 3 -> -1
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// 5 % 4 = 1 -> 1
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// -1 % 4 = -1 -> 3 -> -1
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BigInt m = bk;
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long long m_ll = 0;
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try { m_ll = std::stoll(m.to_string()); } catch(...) { return SymbolicExpr::sin(arg); } // Too big
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long long rem = m_ll % 4;
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if (rem < 0) rem += 4;
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if (rem == 1) return SymbolicExpr::number(1);
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if (rem == 3) return SymbolicExpr::number(-1);
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}
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}
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// Standard values: pi/6, pi/4, pi/3
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// sin(pi/6) = 1/2
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if (k == Rational(1, 6)) return SymbolicExpr::number(Rational(1, 2));
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// sin(pi/4) = sqrt(2)/2
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if (k == Rational(1, 4)) {
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auto sq2 = SymbolicExpr::sqrt(SymbolicExpr::number(2));
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return SymbolicExpr::multiply(SymbolicExpr::number(Rational(1, 2)), sq2)->simplify();
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}
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// sin(pi/3) = sqrt(3)/2
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if (k == Rational(1, 3)) {
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auto sq3 = SymbolicExpr::sqrt(SymbolicExpr::number(3));
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return SymbolicExpr::multiply(SymbolicExpr::number(Rational(1, 2)), sq3)->simplify();
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}
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}
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return SymbolicExpr::sin(arg);
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}
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std::shared_ptr<SymbolicExpr> SymbolicExpr::simplify_cos() const {
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auto arg = operands[0]->simplify();
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// cos(0) = 1
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if (arg->is_number() && arg->convert_rational() == Rational(0)) return SymbolicExpr::number(1);
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// cos(-x) = cos(x)
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if (arg->type == SymbolicExpr::Type::Multiply && arg->operands.size() == 2) {
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if (arg->operands[0]->is_number() && arg->operands[0]->convert_rational() == Rational(-1)) {
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return SymbolicExpr::cos(arg->operands[1])->simplify();
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}
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}
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auto pi_match = match_pi_multiple(arg);
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if (pi_match.first) {
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Rational k = pi_match.second;
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// cos(pi) = -1, cos(2pi) = 1
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if (k.is_integer()) {
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BigInt num = k.get_numerator();
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bool num_even = (num._size == 0 || !(num._data[0] & 1));
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if (num_even) return SymbolicExpr::number(1);
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else return SymbolicExpr::number(-1);
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}
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// cos(pi/2 + n*pi) = 0
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Rational two_k = k * Rational(2);
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if (two_k.is_integer()) {
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BigInt bk = two_k.get_numerator();
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bool bk_even = (bk._size == 0 || !(bk._data[0] & 1));
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if (!bk_even) return SymbolicExpr::number(0);
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}
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// cos(pi/6) = sqrt(3)/2
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if (k == Rational(1, 6)) {
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auto sq3 = SymbolicExpr::sqrt(SymbolicExpr::number(3));
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return SymbolicExpr::multiply(SymbolicExpr::number(Rational(1, 2)), sq3)->simplify();
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}
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// cos(pi/4) = sqrt(2)/2
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if (k == Rational(1, 4)) {
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auto sq2 = SymbolicExpr::sqrt(SymbolicExpr::number(2));
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return SymbolicExpr::multiply(SymbolicExpr::number(Rational(1, 2)), sq2)->simplify();
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}
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// cos(pi/3) = 1/2
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if (k == Rational(1, 3)) {
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return SymbolicExpr::number(Rational(1, 2));
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}
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}
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return SymbolicExpr::cos(arg);
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}
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std::shared_ptr<SymbolicExpr> SymbolicExpr::simplify_tan() const {
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auto arg = operands[0]->simplify();
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if (arg->is_number() && arg->convert_rational() == Rational(0)) return SymbolicExpr::number(0);
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if (arg->type == SymbolicExpr::Type::Multiply && arg->operands.size() == 2) {
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if (arg->operands[0]->is_number() && arg->operands[0]->convert_rational() == Rational(-1)) {
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return SymbolicExpr::multiply(SymbolicExpr::number(-1), SymbolicExpr::tan(arg->operands[1]))->simplify();
792+
}
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}
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// tan(pi/4) = 1
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auto pi_match = match_pi_multiple(arg);
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if (pi_match.first) {
798+
Rational k = pi_match.second;
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if (k == Rational(1, 4)) return SymbolicExpr::number(1);
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if (k.is_integer()) return SymbolicExpr::number(0);
801+
}
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return SymbolicExpr::tan(arg);
804+
}
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/*
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std::shared_ptr<SymbolicExpr> SymbolicExpr::expand() const {
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// Moved to symbolic_poly.cpp

‎tests/test_trig.cpp‎

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@@ -0,0 +1,59 @@
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#include "test_common.hpp"
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#include "../symbolic.hpp"
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int main() {
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auto x = SymbolicExpr::variable("x");
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auto pi = SymbolicExpr::variable("pi"); // Assuming "pi" or "π" is recognized
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TEST_CASE("Trig Basic Values");
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{
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// sin(0) -> 0
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EXPECT_EQ_STR(SymbolicExpr::sin(SymbolicExpr::number(0))->simplify()->to_string(), "0", "sin(0)");
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// cos(0) -> 1
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EXPECT_EQ_STR(SymbolicExpr::cos(SymbolicExpr::number(0))->simplify()->to_string(), "1", "cos(0)");
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// tan(0) -> 0
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EXPECT_EQ_STR(SymbolicExpr::tan(SymbolicExpr::number(0))->simplify()->to_string(), "0", "tan(0)");
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}
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TEST_CASE("Trig Parity");
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{
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// sin(-x) -> -1*sin(x) or -sin(x) depending on output format
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// The implementation specifically returns -1 * sin(x)
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auto sin_neg = SymbolicExpr::sin(SymbolicExpr::multiply(SymbolicExpr::number(-1), x))->simplify();
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// to_string for -1*sin(x) typically is "-1*sin(x)" or "-sin(x)"?
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// Let's check logic: SymbolicExpr::multiply(SymbolicExpr::number(-1), ... )
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// The toString might be "-1*sin(x)"
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// Let's try to verify if it contains sin(x) and starts with -
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std::string s = sin_neg->to_string();
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bool ok = (s == "-1*sin(x)" || s == "-sin(x)" || s == "-1*(sin(x))");
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if(!ok) std::cout << " Got: " << s << std::endl;
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EXPECT_TRUE(ok, "sin(-x) -> -sin(x)");
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// cos(-x) -> cos(x)
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auto cos_neg = SymbolicExpr::cos(SymbolicExpr::multiply(SymbolicExpr::number(-1), x))->simplify();
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EXPECT_EQ_STR(cos_neg->to_string(), "cos(x)", "cos(-x)");
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}
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TEST_CASE("Trig Pi Values");
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{
39+
// sin(pi) -> 0
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EXPECT_EQ_STR(SymbolicExpr::sin(pi)->simplify()->to_string(), "0", "sin(pi)");
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// cos(pi) -> -1
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EXPECT_EQ_STR(SymbolicExpr::cos(pi)->simplify()->to_string(), "-1", "cos(pi)");
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// sin(pi/6) -> 1/2
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// pi/6 is pi * (1/6)
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auto pi_6 = SymbolicExpr::multiply(SymbolicExpr::number(Rational(1,6)), pi);
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EXPECT_EQ_STR(SymbolicExpr::sin(pi_6)->simplify()->to_string(), "1/2", "sin(pi/6)");
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// cos(pi/3) -> 1/2
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auto pi_3 = SymbolicExpr::multiply(SymbolicExpr::number(Rational(1,3)), pi);
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EXPECT_EQ_STR(SymbolicExpr::cos(pi_3)->simplify()->to_string(), "1/2", "cos(pi/3)");
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// tan(pi/4) -> 1
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auto pi_4 = SymbolicExpr::multiply(SymbolicExpr::number(Rational(1,4)), pi);
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EXPECT_EQ_STR(SymbolicExpr::tan(pi_4)->simplify()->to_string(), "1", "tan(pi/4)");
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}
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return 0;
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}

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