1126 lines
27 KiB
Dart
1126 lines
27 KiB
Dart
// === 在 abstract class Expr 中添加声明 ===
|
||
import 'dart:math' show sqrt, cos, sin, tan, pow, log, exp, asin, acos, atan;
|
||
import 'parser.dart';
|
||
|
||
abstract class Expr {
|
||
Expr simplify();
|
||
|
||
/// 新增：对表达式进行“求值/数值化”——尽可能把可算的部分算出来
|
||
Expr evaluate();
|
||
|
||
/// Substitute variable with value
|
||
Expr substitute(String varName, Expr value);
|
||
|
||
@override
|
||
String toString();
|
||
|
||
MulExpr operator *(Expr other) => MulExpr(this, other);
|
||
AddExpr operator +(Expr other) => AddExpr(this, other);
|
||
SubExpr operator -(Expr other) => SubExpr(this, other);
|
||
DivExpr operator /(Expr other) => DivExpr(this, other);
|
||
}
|
||
|
||
// === IntExpr ===
|
||
class IntExpr extends Expr {
|
||
final int value;
|
||
IntExpr(this.value);
|
||
|
||
@override
|
||
Expr simplify() => this;
|
||
|
||
@override
|
||
Expr evaluate() => this;
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) => this;
|
||
|
||
@override
|
||
String toString() => value.toString();
|
||
}
|
||
|
||
// === DoubleExpr ===
|
||
class DoubleExpr extends Expr {
|
||
final double value;
|
||
DoubleExpr(this.value);
|
||
|
||
@override
|
||
Expr simplify() => this;
|
||
|
||
@override
|
||
Expr evaluate() => this;
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) => this;
|
||
|
||
@override
|
||
String toString() => value.toString();
|
||
}
|
||
|
||
// === VarExpr ===
|
||
class VarExpr extends Expr {
|
||
final String name;
|
||
VarExpr(this.name);
|
||
|
||
@override
|
||
Expr simplify() => this;
|
||
|
||
@override
|
||
Expr evaluate() => this;
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) => name == varName ? value : this;
|
||
|
||
@override
|
||
String toString() => name;
|
||
}
|
||
|
||
// === FractionExpr.evaluate ===
|
||
class FractionExpr extends Expr {
|
||
final int numerator;
|
||
final int denominator;
|
||
|
||
FractionExpr(this.numerator, this.denominator) {
|
||
if (denominator == 0) throw Exception("分母不能为0");
|
||
}
|
||
|
||
@override
|
||
Expr simplify() {
|
||
int g = _gcd(numerator.abs(), denominator.abs());
|
||
int n = numerator ~/ g;
|
||
int d = denominator ~/ g;
|
||
|
||
// 分母负数转移到分子
|
||
if (d < 0) {
|
||
n = -n;
|
||
d = -d;
|
||
}
|
||
|
||
if (d == 1) return IntExpr(n); // 化简成整数
|
||
return FractionExpr(n, d);
|
||
}
|
||
|
||
@override
|
||
Expr evaluate() => simplify();
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) => this;
|
||
|
||
@override
|
||
String toString() => "$numerator/$denominator";
|
||
}
|
||
|
||
// === AddExpr.evaluate: 把可算的合并（整数、分数、以及同类 sqrt 项） ===
|
||
class AddExpr extends Expr {
|
||
final Expr left, right;
|
||
AddExpr(this.left, this.right);
|
||
|
||
@override
|
||
Expr simplify() {
|
||
var l = left.simplify();
|
||
var r = right.simplify();
|
||
|
||
if (l is FractionExpr && r is FractionExpr) {
|
||
return FractionExpr(
|
||
l.numerator * r.denominator + r.numerator * l.denominator,
|
||
l.denominator * r.denominator,
|
||
).simplify();
|
||
}
|
||
if (l is IntExpr && r is FractionExpr) {
|
||
return FractionExpr(
|
||
l.value * r.denominator + r.numerator,
|
||
r.denominator,
|
||
).simplify();
|
||
}
|
||
if (l is FractionExpr && r is IntExpr) {
|
||
return FractionExpr(
|
||
l.numerator + r.value * l.denominator,
|
||
l.denominator,
|
||
).simplify();
|
||
}
|
||
|
||
return AddExpr(l, r);
|
||
}
|
||
|
||
@override
|
||
Expr evaluate() {
|
||
var l = left.evaluate();
|
||
var r = right.evaluate();
|
||
|
||
// 纯整数相加 -> 整数
|
||
if (l is IntExpr && r is IntExpr) {
|
||
return IntExpr(l.value + r.value);
|
||
}
|
||
|
||
// 小数相加
|
||
if (l is DoubleExpr && r is DoubleExpr) {
|
||
return DoubleExpr(l.value + r.value);
|
||
}
|
||
if (l is IntExpr && r is DoubleExpr) {
|
||
return DoubleExpr(l.value + r.value);
|
||
}
|
||
if (l is DoubleExpr && r is IntExpr) {
|
||
return DoubleExpr(l.value + r.value);
|
||
}
|
||
|
||
// 分数相加 / 分数与整数相加
|
||
if (l is FractionExpr && r is FractionExpr) {
|
||
return FractionExpr(
|
||
l.numerator * r.denominator + r.numerator * l.denominator,
|
||
l.denominator * r.denominator,
|
||
).simplify();
|
||
}
|
||
if (l is IntExpr && r is FractionExpr) {
|
||
return FractionExpr(
|
||
l.value * r.denominator + r.numerator,
|
||
r.denominator,
|
||
).simplify();
|
||
}
|
||
if (l is FractionExpr && r is IntExpr) {
|
||
return FractionExpr(
|
||
l.numerator + r.value * l.denominator,
|
||
l.denominator,
|
||
).simplify();
|
||
}
|
||
|
||
// 分数与小数相加
|
||
if (l is FractionExpr && r is DoubleExpr) {
|
||
return DoubleExpr(l.numerator / l.denominator + r.value);
|
||
}
|
||
if (l is DoubleExpr && r is FractionExpr) {
|
||
return DoubleExpr(l.value + r.numerator / r.denominator);
|
||
}
|
||
|
||
// 合并同类的 sqrt 项: a*sqrt(X) + b*sqrt(X) = (a+b)*sqrt(X)
|
||
var a = _asSqrtTerm(l);
|
||
var b = _asSqrtTerm(r);
|
||
if (a != null && b != null && a.inner.toString() == b.inner.toString()) {
|
||
return MulExpr(IntExpr(a.coef + b.coef), SqrtExpr(a.inner)).simplify();
|
||
}
|
||
|
||
return AddExpr(l, r);
|
||
}
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) => AddExpr(
|
||
left.substitute(varName, value),
|
||
right.substitute(varName, value),
|
||
);
|
||
|
||
@override
|
||
String toString() => "($left + $right)";
|
||
}
|
||
|
||
// === SubExpr.evaluate 类似 AddExpr，但做减法 ===
|
||
class SubExpr extends Expr {
|
||
final Expr left, right;
|
||
SubExpr(this.left, this.right);
|
||
|
||
@override
|
||
Expr simplify() {
|
||
var l = left.simplify();
|
||
var r = right.simplify();
|
||
|
||
if (l is IntExpr && r is IntExpr) {
|
||
return IntExpr(l.value - r.value);
|
||
}
|
||
if (l is FractionExpr && r is FractionExpr) {
|
||
return FractionExpr(
|
||
l.numerator * r.denominator - r.numerator * l.denominator,
|
||
l.denominator * r.denominator,
|
||
).simplify();
|
||
}
|
||
return SubExpr(l, r);
|
||
}
|
||
|
||
@override
|
||
Expr evaluate() {
|
||
var l = left.evaluate();
|
||
var r = right.evaluate();
|
||
|
||
if (l is IntExpr && r is IntExpr) {
|
||
return IntExpr(l.value - r.value);
|
||
}
|
||
|
||
// 小数相减
|
||
if (l is DoubleExpr && r is DoubleExpr) {
|
||
return DoubleExpr(l.value - r.value);
|
||
}
|
||
if (l is IntExpr && r is DoubleExpr) {
|
||
return DoubleExpr(l.value - r.value);
|
||
}
|
||
if (l is DoubleExpr && r is IntExpr) {
|
||
return DoubleExpr(l.value - r.value);
|
||
}
|
||
|
||
if (l is FractionExpr && r is FractionExpr) {
|
||
return FractionExpr(
|
||
l.numerator * r.denominator - r.numerator * l.denominator,
|
||
l.denominator * r.denominator,
|
||
).simplify();
|
||
}
|
||
if (l is IntExpr && r is FractionExpr) {
|
||
return FractionExpr(
|
||
l.value * r.denominator - r.numerator,
|
||
r.denominator,
|
||
).simplify();
|
||
}
|
||
if (l is FractionExpr && r is IntExpr) {
|
||
return FractionExpr(
|
||
l.numerator - r.value * l.denominator,
|
||
l.denominator,
|
||
).simplify();
|
||
}
|
||
|
||
// 分数与小数相减
|
||
if (l is FractionExpr && r is DoubleExpr) {
|
||
return DoubleExpr(l.numerator / l.denominator - r.value);
|
||
}
|
||
if (l is DoubleExpr && r is FractionExpr) {
|
||
return DoubleExpr(l.value - r.numerator / r.denominator);
|
||
}
|
||
|
||
// 处理同类 sqrt 项: a*sqrt(X) - b*sqrt(X) = (a-b)*sqrt(X)
|
||
var a = _asSqrtTerm(l);
|
||
var b = _asSqrtTerm(r);
|
||
if (a != null && b != null && a.inner.toString() == b.inner.toString()) {
|
||
return MulExpr(IntExpr(a.coef - b.coef), SqrtExpr(a.inner)).simplify();
|
||
}
|
||
|
||
return SubExpr(l, r);
|
||
}
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) => SubExpr(
|
||
left.substitute(varName, value),
|
||
right.substitute(varName, value),
|
||
);
|
||
|
||
@override
|
||
String toString() => "($left - $right)";
|
||
}
|
||
|
||
// === MulExpr.evaluate ===
|
||
class MulExpr extends Expr {
|
||
final Expr left, right;
|
||
MulExpr(this.left, this.right);
|
||
|
||
@override
|
||
Expr simplify() {
|
||
var l = left.simplify();
|
||
var r = right.simplify();
|
||
|
||
if (l is IntExpr && l.value == 1) return r;
|
||
if (r is IntExpr && r.value == 1) return l;
|
||
if (l is IntExpr && l.value == -1) return SubExpr(IntExpr(0), r).simplify();
|
||
if (r is IntExpr && r.value == -1) return SubExpr(IntExpr(0), l).simplify();
|
||
|
||
if (l is IntExpr && r is IntExpr) {
|
||
return IntExpr(l.value * r.value);
|
||
}
|
||
if (l is FractionExpr && r is IntExpr) {
|
||
return FractionExpr(l.numerator * r.value, l.denominator).simplify();
|
||
}
|
||
if (l is IntExpr && r is FractionExpr) {
|
||
return FractionExpr(l.value * r.numerator, r.denominator).simplify();
|
||
}
|
||
if (l is FractionExpr && r is FractionExpr) {
|
||
return FractionExpr(
|
||
l.numerator * r.numerator,
|
||
l.denominator * r.denominator,
|
||
).simplify();
|
||
}
|
||
if (l is SqrtExpr && r is FractionExpr) {
|
||
return FractionExpr(1, r.denominator).simplify() *
|
||
MulExpr(l, IntExpr(r.numerator)).simplify();
|
||
}
|
||
|
||
return MulExpr(l, r);
|
||
}
|
||
|
||
@override
|
||
Expr evaluate() {
|
||
var l = left.evaluate();
|
||
var r = right.evaluate();
|
||
|
||
if (l is IntExpr && l.value == 1) return r;
|
||
if (r is IntExpr && r.value == 1) return l;
|
||
if (l is IntExpr && l.value == -1) return SubExpr(IntExpr(0), r).simplify();
|
||
if (r is IntExpr && r.value == -1) return SubExpr(IntExpr(0), l).simplify();
|
||
|
||
if (l is IntExpr && r is IntExpr) {
|
||
return IntExpr(l.value * r.value);
|
||
}
|
||
|
||
// 小数相乘
|
||
if (l is DoubleExpr && r is DoubleExpr) {
|
||
return DoubleExpr(l.value * r.value);
|
||
}
|
||
if (l is IntExpr && r is DoubleExpr) {
|
||
return DoubleExpr(l.value * r.value);
|
||
}
|
||
if (l is DoubleExpr && r is IntExpr) {
|
||
return DoubleExpr(l.value * r.value);
|
||
}
|
||
|
||
if (l is FractionExpr && r is IntExpr) {
|
||
return FractionExpr(l.numerator * r.value, l.denominator).simplify();
|
||
}
|
||
if (l is IntExpr && r is FractionExpr) {
|
||
return FractionExpr(l.value * r.numerator, r.denominator).simplify();
|
||
}
|
||
if (l is FractionExpr && r is FractionExpr) {
|
||
return FractionExpr(
|
||
l.numerator * r.numerator,
|
||
l.denominator * r.denominator,
|
||
).simplify();
|
||
}
|
||
|
||
// 分数与小数相乘
|
||
if (l is FractionExpr && r is DoubleExpr) {
|
||
return DoubleExpr(l.numerator / l.denominator * r.value);
|
||
}
|
||
if (l is DoubleExpr && r is FractionExpr) {
|
||
return DoubleExpr(l.value * r.numerator / r.denominator);
|
||
}
|
||
|
||
// sqrt * sqrt: sqrt(a)*sqrt(a) = a
|
||
if (l is SqrtExpr &&
|
||
r is SqrtExpr &&
|
||
l.inner.toString() == r.inner.toString()) {
|
||
return l.inner.simplify();
|
||
}
|
||
|
||
// int * sqrt -> 保留形式，之后 simplify() 再处理约分
|
||
if ((l is IntExpr && r is SqrtExpr) || (l is SqrtExpr && r is IntExpr)) {
|
||
return MulExpr(l, r).simplify();
|
||
}
|
||
|
||
return MulExpr(l, r);
|
||
}
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) => MulExpr(
|
||
left.substitute(varName, value),
|
||
right.substitute(varName, value),
|
||
);
|
||
|
||
@override
|
||
String toString() => "($left * $right)";
|
||
}
|
||
|
||
// === DivExpr.evaluate ===
|
||
class DivExpr extends Expr {
|
||
final Expr left, right;
|
||
DivExpr(this.left, this.right);
|
||
|
||
@override
|
||
Expr simplify() {
|
||
var l = left.simplify();
|
||
var r = right.simplify();
|
||
|
||
if (l is IntExpr && r is IntExpr) {
|
||
return FractionExpr(l.value, r.value).simplify();
|
||
}
|
||
if (l is FractionExpr && r is IntExpr) {
|
||
return FractionExpr(l.numerator, l.denominator * r.value).simplify();
|
||
}
|
||
if (l is IntExpr && r is FractionExpr) {
|
||
return FractionExpr(l.value * r.denominator, r.numerator).simplify();
|
||
}
|
||
if (l is FractionExpr && r is FractionExpr) {
|
||
return FractionExpr(
|
||
l.numerator * r.denominator,
|
||
l.denominator * r.numerator,
|
||
).simplify();
|
||
}
|
||
if (l is MulExpr &&
|
||
l.left is IntExpr &&
|
||
l.right is SqrtExpr &&
|
||
r is IntExpr) {
|
||
int coeff = (l.left as IntExpr).value;
|
||
int denom = r.value;
|
||
int g = _gcd(coeff.abs(), denom.abs());
|
||
return MulExpr(
|
||
IntExpr(coeff ~/ g),
|
||
DivExpr(l.right, IntExpr(denom ~/ g)).simplify(),
|
||
).simplify();
|
||
}
|
||
return DivExpr(l, r);
|
||
}
|
||
|
||
@override
|
||
Expr evaluate() {
|
||
var l = left.evaluate();
|
||
var r = right.evaluate();
|
||
|
||
if (l is IntExpr && r is IntExpr) {
|
||
return FractionExpr(l.value, r.value).simplify();
|
||
}
|
||
if (l is FractionExpr && r is IntExpr) {
|
||
return FractionExpr(l.numerator, l.denominator * r.value).simplify();
|
||
}
|
||
if (l is IntExpr && r is FractionExpr) {
|
||
return FractionExpr(l.value * r.denominator, r.numerator).simplify();
|
||
}
|
||
if (l is FractionExpr && r is FractionExpr) {
|
||
return FractionExpr(
|
||
l.numerator * r.denominator,
|
||
l.denominator * r.numerator,
|
||
).simplify();
|
||
}
|
||
|
||
// handle (k * sqrt(X)) / d 约分
|
||
if (l is MulExpr &&
|
||
l.left is IntExpr &&
|
||
l.right is SqrtExpr &&
|
||
r is IntExpr) {
|
||
int coeff = (l.left as IntExpr).value;
|
||
int denom = r.value;
|
||
int g = _gcd(coeff.abs(), denom.abs());
|
||
return MulExpr(
|
||
IntExpr(coeff ~/ g),
|
||
DivExpr(l.right, IntExpr(denom ~/ g)).evaluate(),
|
||
).evaluate();
|
||
}
|
||
|
||
return DivExpr(l, r);
|
||
}
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) => DivExpr(
|
||
left.substitute(varName, value),
|
||
right.substitute(varName, value),
|
||
);
|
||
|
||
@override
|
||
String toString() => "($left / $right)";
|
||
}
|
||
|
||
// === SqrtExpr.evaluate ===
|
||
class SqrtExpr extends Expr {
|
||
final Expr inner;
|
||
SqrtExpr(this.inner);
|
||
|
||
@override
|
||
Expr simplify() {
|
||
var i = inner.simplify();
|
||
if (i is IntExpr) {
|
||
int n = i.value;
|
||
int root = sqrt(n).floor();
|
||
if (root * root == n) {
|
||
return IntExpr(root); // 完全平方数
|
||
}
|
||
// 尝试拆分 sqrt，比如 sqrt(8) = 2*sqrt(2)
|
||
for (int k = root; k > 1; k--) {
|
||
if (n % (k * k) == 0) {
|
||
return MulExpr(
|
||
IntExpr(k),
|
||
SqrtExpr(IntExpr(n ~/ (k * k))),
|
||
).simplify();
|
||
}
|
||
}
|
||
}
|
||
return SqrtExpr(i);
|
||
}
|
||
|
||
@override
|
||
Expr evaluate() {
|
||
var i = inner.evaluate();
|
||
if (i is IntExpr) {
|
||
int n = i.value;
|
||
int root = sqrt(n).floor();
|
||
if (root * root == n) return IntExpr(root);
|
||
// 拆平方因子并返回 k * sqrt(remain)
|
||
for (int k = root; k > 1; k--) {
|
||
if (n % (k * k) == 0) {
|
||
return MulExpr(
|
||
IntExpr(k),
|
||
SqrtExpr(IntExpr(n ~/ (k * k))),
|
||
).evaluate();
|
||
}
|
||
}
|
||
}
|
||
return SqrtExpr(i);
|
||
}
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) =>
|
||
SqrtExpr(inner.substitute(varName, value));
|
||
|
||
@override
|
||
String toString() => "\\sqrt{${inner.toString()}}";
|
||
}
|
||
|
||
// === CosExpr ===
|
||
class CosExpr extends Expr {
|
||
final Expr inner;
|
||
CosExpr(this.inner);
|
||
|
||
@override
|
||
Expr simplify() => CosExpr(inner.simplify());
|
||
|
||
@override
|
||
Expr evaluate() {
|
||
var i = inner.evaluate();
|
||
if (i is IntExpr) {
|
||
return DoubleExpr(cos(i.value.toDouble()));
|
||
}
|
||
if (i is FractionExpr) {
|
||
return DoubleExpr(cos(i.numerator / i.denominator));
|
||
}
|
||
if (i is DoubleExpr) {
|
||
return DoubleExpr(cos(i.value));
|
||
}
|
||
return CosExpr(i);
|
||
}
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) =>
|
||
CosExpr(inner.substitute(varName, value));
|
||
|
||
@override
|
||
String toString() => "cos($inner)";
|
||
}
|
||
|
||
// === SinExpr ===
|
||
class SinExpr extends Expr {
|
||
final Expr inner;
|
||
SinExpr(this.inner);
|
||
|
||
@override
|
||
Expr simplify() => SinExpr(inner.simplify());
|
||
|
||
@override
|
||
Expr evaluate() {
|
||
var i = inner.evaluate();
|
||
if (i is IntExpr) {
|
||
return DoubleExpr(sin(i.value.toDouble()));
|
||
}
|
||
if (i is FractionExpr) {
|
||
return DoubleExpr(sin(i.numerator / i.denominator));
|
||
}
|
||
if (i is DoubleExpr) {
|
||
return DoubleExpr(sin(i.value));
|
||
}
|
||
return SinExpr(i);
|
||
}
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) =>
|
||
SinExpr(inner.substitute(varName, value));
|
||
|
||
@override
|
||
String toString() => "sin($inner)";
|
||
}
|
||
|
||
// === TanExpr ===
|
||
class TanExpr extends Expr {
|
||
final Expr inner;
|
||
TanExpr(this.inner);
|
||
|
||
@override
|
||
Expr simplify() => TanExpr(inner.simplify());
|
||
|
||
@override
|
||
Expr evaluate() {
|
||
var i = inner.evaluate();
|
||
if (i is IntExpr) {
|
||
return DoubleExpr(tan(i.value.toDouble()));
|
||
}
|
||
if (i is FractionExpr) {
|
||
return DoubleExpr(tan(i.numerator / i.denominator));
|
||
}
|
||
if (i is DoubleExpr) {
|
||
return DoubleExpr(tan(i.value));
|
||
}
|
||
return TanExpr(i);
|
||
}
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) =>
|
||
TanExpr(inner.substitute(varName, value));
|
||
|
||
@override
|
||
String toString() => "tan($inner)";
|
||
}
|
||
|
||
// === PowExpr ===
|
||
class PowExpr extends Expr {
|
||
final Expr left, right;
|
||
PowExpr(this.left, this.right);
|
||
|
||
@override
|
||
Expr simplify() {
|
||
var l = left.simplify();
|
||
var r = right.simplify();
|
||
|
||
// x^0 = 1
|
||
if (r is IntExpr && r.value == 0) return IntExpr(1);
|
||
// x^1 = x
|
||
if (r is IntExpr && r.value == 1) return l;
|
||
// 1^x = 1
|
||
if (l is IntExpr && l.value == 1) return IntExpr(1);
|
||
// 0^x = 0 (for x != 0)
|
||
if (l is IntExpr && l.value == 0 && !(r is IntExpr && r.value == 0)) {
|
||
return IntExpr(0);
|
||
}
|
||
|
||
return PowExpr(l, r);
|
||
}
|
||
|
||
@override
|
||
Expr evaluate() {
|
||
var l = left.evaluate();
|
||
var r = right.evaluate();
|
||
|
||
// x^0 = 1
|
||
if (r is IntExpr && r.value == 0) return IntExpr(1);
|
||
// x^1 = x
|
||
if (r is IntExpr && r.value == 1) return l;
|
||
// 1^x = 1
|
||
if (l is IntExpr && l.value == 1) return IntExpr(1);
|
||
// 0^x = 0 (for x != 0)
|
||
if (l is IntExpr && l.value == 0 && !(r is IntExpr && r.value == 0)) {
|
||
return IntExpr(0);
|
||
}
|
||
|
||
// If both are numbers, compute
|
||
if (l is IntExpr && r is IntExpr) {
|
||
return DoubleExpr(pow(l.value.toDouble(), r.value.toDouble()).toDouble());
|
||
}
|
||
if (l is DoubleExpr && r is IntExpr) {
|
||
return DoubleExpr(pow(l.value, r.value.toDouble()).toDouble());
|
||
}
|
||
if (l is IntExpr && r is DoubleExpr) {
|
||
return DoubleExpr(pow(l.value.toDouble(), r.value).toDouble());
|
||
}
|
||
if (l is DoubleExpr && r is DoubleExpr) {
|
||
return DoubleExpr(pow(l.value, r.value).toDouble());
|
||
}
|
||
|
||
return PowExpr(l, r);
|
||
}
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) => PowExpr(
|
||
left.substitute(varName, value),
|
||
right.substitute(varName, value),
|
||
);
|
||
|
||
@override
|
||
String toString() {
|
||
String leftStr = left.toString();
|
||
String rightStr = right.toString();
|
||
|
||
// Remove outer parentheses
|
||
if (leftStr.startsWith('(') && leftStr.endsWith(')')) {
|
||
leftStr = leftStr.substring(1, leftStr.length - 1);
|
||
}
|
||
if (rightStr.startsWith('(') && rightStr.endsWith(')')) {
|
||
rightStr = rightStr.substring(1, rightStr.length - 1);
|
||
}
|
||
|
||
// Add parentheses around base if it's a complex expression
|
||
bool needsParens =
|
||
!(left is VarExpr || left is IntExpr || left is DoubleExpr);
|
||
String base = needsParens ? '($leftStr)' : leftStr;
|
||
|
||
return '$base^{$rightStr}';
|
||
}
|
||
}
|
||
|
||
// === LogExpr ===
|
||
class LogExpr extends Expr {
|
||
final Expr inner;
|
||
LogExpr(this.inner);
|
||
|
||
@override
|
||
Expr simplify() => LogExpr(inner.simplify());
|
||
|
||
@override
|
||
Expr evaluate() {
|
||
var i = inner.evaluate();
|
||
if (i is IntExpr) {
|
||
return DoubleExpr(log(i.value.toDouble()));
|
||
}
|
||
if (i is FractionExpr) {
|
||
return DoubleExpr(log(i.numerator / i.denominator));
|
||
}
|
||
if (i is DoubleExpr) {
|
||
return DoubleExpr(log(i.value));
|
||
}
|
||
return LogExpr(i);
|
||
}
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) =>
|
||
LogExpr(inner.substitute(varName, value));
|
||
|
||
@override
|
||
String toString() => "log($inner)";
|
||
}
|
||
|
||
// === ExpExpr ===
|
||
class ExpExpr extends Expr {
|
||
final Expr inner;
|
||
ExpExpr(this.inner);
|
||
|
||
@override
|
||
Expr simplify() => ExpExpr(inner.simplify());
|
||
|
||
@override
|
||
Expr evaluate() {
|
||
var i = inner.evaluate();
|
||
if (i is IntExpr) {
|
||
return DoubleExpr(exp(i.value.toDouble()));
|
||
}
|
||
if (i is FractionExpr) {
|
||
return DoubleExpr(exp(i.numerator / i.denominator));
|
||
}
|
||
if (i is DoubleExpr) {
|
||
return DoubleExpr(exp(i.value));
|
||
}
|
||
return ExpExpr(i);
|
||
}
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) =>
|
||
ExpExpr(inner.substitute(varName, value));
|
||
|
||
@override
|
||
String toString() => "exp($inner)";
|
||
}
|
||
|
||
// === AsinExpr ===
|
||
class AsinExpr extends Expr {
|
||
final Expr inner;
|
||
AsinExpr(this.inner);
|
||
|
||
@override
|
||
Expr simplify() => AsinExpr(inner.simplify());
|
||
|
||
@override
|
||
Expr evaluate() {
|
||
var i = inner.evaluate();
|
||
if (i is IntExpr) {
|
||
return DoubleExpr(asin(i.value.toDouble()));
|
||
}
|
||
if (i is FractionExpr) {
|
||
return DoubleExpr(asin(i.numerator / i.denominator));
|
||
}
|
||
if (i is DoubleExpr) {
|
||
return DoubleExpr(asin(i.value));
|
||
}
|
||
return AsinExpr(i);
|
||
}
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) =>
|
||
AsinExpr(inner.substitute(varName, value));
|
||
|
||
@override
|
||
String toString() => "asin($inner)";
|
||
}
|
||
|
||
// === AcosExpr ===
|
||
class AcosExpr extends Expr {
|
||
final Expr inner;
|
||
AcosExpr(this.inner);
|
||
|
||
@override
|
||
Expr simplify() => AcosExpr(inner.simplify());
|
||
|
||
@override
|
||
Expr evaluate() {
|
||
var i = inner.evaluate();
|
||
if (i is IntExpr) {
|
||
return DoubleExpr(acos(i.value.toDouble()));
|
||
}
|
||
if (i is FractionExpr) {
|
||
return DoubleExpr(acos(i.numerator / i.denominator));
|
||
}
|
||
if (i is DoubleExpr) {
|
||
return DoubleExpr(acos(i.value));
|
||
}
|
||
return AcosExpr(i);
|
||
}
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) =>
|
||
AcosExpr(inner.substitute(varName, value));
|
||
|
||
@override
|
||
String toString() => "acos($inner)";
|
||
}
|
||
|
||
// === AtanExpr ===
|
||
class AtanExpr extends Expr {
|
||
final Expr inner;
|
||
AtanExpr(this.inner);
|
||
|
||
@override
|
||
Expr simplify() => AtanExpr(inner.simplify());
|
||
|
||
@override
|
||
Expr evaluate() {
|
||
var i = inner.evaluate();
|
||
if (i is IntExpr) {
|
||
return DoubleExpr(atan(i.value.toDouble()));
|
||
}
|
||
if (i is FractionExpr) {
|
||
return DoubleExpr(atan(i.numerator / i.denominator));
|
||
}
|
||
if (i is DoubleExpr) {
|
||
return DoubleExpr(atan(i.value));
|
||
}
|
||
return AtanExpr(i);
|
||
}
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) =>
|
||
AtanExpr(inner.substitute(varName, value));
|
||
|
||
@override
|
||
String toString() => "atan($inner)";
|
||
}
|
||
|
||
// === AbsExpr ===
|
||
class AbsExpr extends Expr {
|
||
final Expr inner;
|
||
AbsExpr(this.inner);
|
||
|
||
@override
|
||
Expr simplify() => AbsExpr(inner.simplify());
|
||
|
||
@override
|
||
Expr evaluate() {
|
||
var i = inner.evaluate();
|
||
if (i is IntExpr) {
|
||
return IntExpr(i.value.abs());
|
||
}
|
||
if (i is FractionExpr) {
|
||
return FractionExpr(i.numerator.abs(), i.denominator);
|
||
}
|
||
if (i is DoubleExpr) {
|
||
return DoubleExpr(i.value.abs());
|
||
}
|
||
return AbsExpr(i);
|
||
}
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) =>
|
||
AbsExpr(inner.substitute(varName, value));
|
||
|
||
@override
|
||
String toString() => "|$inner|";
|
||
}
|
||
|
||
// === PercentExpr ===
|
||
class PercentExpr extends Expr {
|
||
final Expr inner;
|
||
PercentExpr(this.inner);
|
||
|
||
@override
|
||
Expr simplify() => PercentExpr(inner.simplify());
|
||
|
||
@override
|
||
Expr evaluate() {
|
||
var i = inner.evaluate();
|
||
if (i is IntExpr) {
|
||
return DoubleExpr(i.value / 100.0);
|
||
}
|
||
if (i is DoubleExpr) {
|
||
return DoubleExpr(i.value / 100.0);
|
||
}
|
||
if (i is FractionExpr) {
|
||
return DoubleExpr(i.numerator / (i.denominator * 100.0));
|
||
}
|
||
return PercentExpr(i);
|
||
}
|
||
|
||
@override
|
||
Expr substitute(String varName, Expr value) =>
|
||
PercentExpr(inner.substitute(varName, value));
|
||
|
||
@override
|
||
String toString() => "$inner%";
|
||
}
|
||
|
||
// === 辅助：识别 a * sqrt(X) 形式 ===
|
||
class _SqrtTerm {
|
||
final int coef;
|
||
final Expr inner;
|
||
_SqrtTerm(this.coef, this.inner);
|
||
}
|
||
|
||
_SqrtTerm? _asSqrtTerm(Expr e) {
|
||
if (e is SqrtExpr) return _SqrtTerm(1, e.inner);
|
||
if (e is MulExpr) {
|
||
// 可能为 Int * Sqrt or Sqrt * Int
|
||
if (e.left is IntExpr && e.right is SqrtExpr) {
|
||
return _SqrtTerm((e.left as IntExpr).value, (e.right as SqrtExpr).inner);
|
||
}
|
||
if (e.right is IntExpr && e.left is SqrtExpr) {
|
||
return _SqrtTerm((e.right as IntExpr).value, (e.left as SqrtExpr).inner);
|
||
}
|
||
}
|
||
return null;
|
||
}
|
||
|
||
/// 获取精确三角函数结果
|
||
String? getExactTrigResult(String input) {
|
||
final cleanInput = input.replaceAll(' ', '').toLowerCase();
|
||
|
||
// 匹配 sin(角度) 模式
|
||
final sinMatch = RegExp(r'^sin\((\d+(?:\+\d+)*)\)$').firstMatch(cleanInput);
|
||
if (sinMatch != null) {
|
||
final angleExpr = sinMatch.group(1)!;
|
||
final angle = evaluateAngleExpression(angleExpr);
|
||
if (angle != null) {
|
||
return getSinExactValue(angle);
|
||
}
|
||
}
|
||
|
||
// 匹配 cos(角度) 模式
|
||
final cosMatch = RegExp(r'^cos\((\d+(?:\+\d+)*)\)$').firstMatch(cleanInput);
|
||
if (cosMatch != null) {
|
||
final angleExpr = cosMatch.group(1)!;
|
||
final angle = evaluateAngleExpression(angleExpr);
|
||
if (angle != null) {
|
||
return getCosExactValue(angle);
|
||
}
|
||
}
|
||
|
||
// 匹配 tan(角度) 模式
|
||
final tanMatch = RegExp(r'^tan\((\d+(?:\+\d+)*)\)$').firstMatch(cleanInput);
|
||
if (tanMatch != null) {
|
||
final angleExpr = tanMatch.group(1)!;
|
||
final angle = evaluateAngleExpression(angleExpr);
|
||
if (angle != null) {
|
||
return getTanExactValue(angle);
|
||
}
|
||
}
|
||
|
||
return null;
|
||
}
|
||
|
||
/// 获取 sin 的精确值
|
||
String? getSinExactValue(int angle) {
|
||
// 标准化角度到 0-360 度
|
||
final normalizedAngle = angle % 360;
|
||
|
||
switch (normalizedAngle) {
|
||
case 0:
|
||
case 360:
|
||
return '0';
|
||
case 30:
|
||
return '\\frac{1}{2}';
|
||
case 45:
|
||
return '\\frac{\\sqrt{2}}{2}';
|
||
case 60:
|
||
return '\\frac{\\sqrt{3}}{2}';
|
||
case 75:
|
||
return '1 + \\frac{\\sqrt{2}}{2}';
|
||
case 90:
|
||
return '1';
|
||
case 120:
|
||
return '\\frac{\\sqrt{3}}{2}';
|
||
case 135:
|
||
return '\\frac{\\sqrt{2}}{2}';
|
||
case 150:
|
||
return '\\frac{1}{2}';
|
||
case 180:
|
||
return '0';
|
||
case 210:
|
||
return '-\\frac{1}{2}';
|
||
case 225:
|
||
return '-\\frac{\\sqrt{2}}{2}';
|
||
case 240:
|
||
return '-\\frac{\\sqrt{3}}{2}';
|
||
case 270:
|
||
return '-1';
|
||
case 300:
|
||
return '-\\frac{\\sqrt{3}}{2}';
|
||
case 315:
|
||
return '-\\frac{\\sqrt{2}}{2}';
|
||
case 330:
|
||
return '-\\frac{1}{2}';
|
||
default:
|
||
return null;
|
||
}
|
||
}
|
||
|
||
/// 获取 cos 的精确值
|
||
String? getCosExactValue(int angle) {
|
||
// cos(angle) = sin(90 - angle)
|
||
final complementaryAngle = 90 - angle;
|
||
return getSinExactValue(complementaryAngle.abs());
|
||
}
|
||
|
||
/// 获取 tan 的精确值
|
||
String? getTanExactValue(int angle) {
|
||
// tan(angle) = sin(angle) / cos(angle)
|
||
final sinValue = getSinExactValue(angle);
|
||
final cosValue = getCosExactValue(angle);
|
||
|
||
if (sinValue != null && cosValue != null) {
|
||
if (cosValue == '0') return null; // 未定义
|
||
return '\\frac{$sinValue}{$cosValue}';
|
||
}
|
||
|
||
return null;
|
||
}
|
||
|
||
/// 将数值结果格式化为几倍根号的形式
|
||
String formatSqrtResult(double result) {
|
||
// 处理负数
|
||
if (result < 0) {
|
||
return '-${formatSqrtResult(-result)}';
|
||
}
|
||
|
||
// 处理零
|
||
if (result == 0) return '0';
|
||
|
||
// 检查是否接近整数
|
||
final rounded = result.round();
|
||
if ((result - rounded).abs() < 1e-10) {
|
||
return rounded.toString();
|
||
}
|
||
|
||
// 计算 result 的平方，看它是否接近整数
|
||
final squared = result * result;
|
||
final squaredRounded = squared.round();
|
||
|
||
// 如果 squared 接近整数，说明 result 是某个数的平方根
|
||
if ((squared - squaredRounded).abs() < 1e-6) {
|
||
// 寻找最大的完全平方数因子
|
||
int maxSquareFactor = 1;
|
||
for (int i = 2; i * i <= squaredRounded; i++) {
|
||
if (squaredRounded % (i * i) == 0) {
|
||
maxSquareFactor = i * i;
|
||
}
|
||
}
|
||
|
||
final coefficient = sqrt(maxSquareFactor).round();
|
||
final remaining = squaredRounded ~/ maxSquareFactor;
|
||
|
||
if (remaining == 1) {
|
||
// 完全平方数，直接返回系数
|
||
return coefficient.toString();
|
||
} else if (coefficient == 1) {
|
||
return '\\sqrt{$remaining}';
|
||
} else {
|
||
return '$coefficient\\sqrt{$remaining}';
|
||
}
|
||
}
|
||
|
||
// 如果不是平方根的结果，返回原始数值（保留几位小数）
|
||
return result
|
||
.toStringAsFixed(6)
|
||
.replaceAll(RegExp(r'\.0+$'), '')
|
||
.replaceAll(RegExp(r'\.$'), '');
|
||
}
|
||
|
||
/// 辗转相除法求 gcd
|
||
int _gcd(int a, int b) => b == 0 ? a : _gcd(b, a % b);
|