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🐛 Fix solver issue on (x+3)^2-(1-2x)^2=0

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LittleSheep
2025-09-13 13:32:53 +08:00
parent 6e444f46fb
commit b420ccca47
2 changed files with 60 additions and 26 deletions
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9
lib/screens/calculator_home_page.dart
View File

@@ -300,6 +300,15 @@ class _CalculatorHomePageState extends State<CalculatorHomePage> {
), ),
), ),
), ),
Expanded(
child: Tooltip(
message: '未知数二号',
child: FilledButton.tonal(
onPressed: () => _insertSymbol('y'),
child: Text('y', style: GoogleFonts.robotoMono()),
),
),
),
], ],
), ),
const SizedBox(height: 8), const SizedBox(height: 8),

77
lib/solver.dart
View File

@@ -529,13 +529,29 @@ ${b1}y &= ${c1 - a1 * x}
({String formula, String solution})? _tryFactorization(int a, int b, int c) { ({String formula, String solution})? _tryFactorization(int a, int b, int c) {
if (a == 0) return null; if (a == 0) return null;
int ac = a * c; int ac = a * c;
for (int i = 1; i <= sqrt(ac.abs()); i++) { int absAc = ac.abs();
if (ac % i == 0) { for (int d = 1; d <= sqrt(absAc).toInt(); d++) {
int j = ac ~/ i; if (absAc % d == 0) {
if (check(i, j, b)) return formatFactor(i, j, a); int d1 = d;
if (check(-i, -j, b)) return formatFactor(-i, -j, a); int d2 = absAc ~/ d;
if (check(i, -j, b)) return formatFactor(i, -j, a); List<int> signs1 = ac >= 0 ? [1, -1] : [1, -1];
if (check(-i, j, b)) return formatFactor(-i, j, a); List<int> signs2 = ac >= 0 ? [1, -1] : [1, -1];
for (int s1 in signs1) {
for (int s2 in signs2) {
int m = s1 * d1;
int n = s2 * d2;
if (check(m, n, b)) return formatFactor(m, n, a);
m = s1 * d1;
n = s2 * (-d2);
if (check(m, n, b)) return formatFactor(m, n, a);
m = s1 * (-d1);
n = s2 * d2;
if (check(m, n, b)) return formatFactor(m, n, a);
m = s1 * (-d1);
n = s2 * (-d2);
if (check(m, n, b)) return formatFactor(m, n, a);
}
}
} }
} }
return null; return null;
@@ -544,32 +560,41 @@ ${b1}y &= ${c1 - a1 * x}
bool check(int m, int n, int b) => m + n == b; bool check(int m, int n, int b) => m + n == b;
({String formula, String solution}) formatFactor(int m, int n, int a) { ({String formula, String solution}) formatFactor(int m, int n, int a) {
int common = gcd(n.abs(), a.abs()); // Roots are -m/a and -n/a
int num = n ~/ common; int g1 = gcd(m.abs(), a.abs());
int den = a ~/ common; int root1Num = -m ~/ g1;
int root1Den = a ~/ g1;
final a1 = den; int g2 = gcd(n.abs(), a.abs());
final c1 = num; int root2Num = -n ~/ g2;
final a2 = a ~/ den; int root2Den = a ~/ g2;
final c2 = m ~/ a2;
final f1Part1 = a1 == 1 ? 'x' : '${a1}x'; String sol1 = root1Den == 1 ? '$root1Num' : '\\frac{$root1Num}{$root1Den}';
final f1 = c1 == 0 ? f1Part1 : '$f1Part1 ${c1 >= 0 ? '+' : ''} $c1'; String sol2 = root2Den == 1 ? '$root2Num' : '\\frac{$root2Num}{$root2Den}';
final f2Part1 = a2 == 1 ? 'x' : '${a2}x'; // For formula, show (a x + m)(x + n/a) or simplified
final f2 = c2 == 0 ? f2Part1 : '$f2Part1 ${c2 >= 0 ? '+' : ''} $c2'; String f1 = a == 1 ? 'x' : '${a}x';
f1 = m == 0 ? f1 : '$f1 ${m >= 0 ? '+' : ''} $m';
final int x1Num = -c1, x1Den = a1; String f2;
final int x2Num = -c2, x2Den = a2; if (n % a == 0) {
int coeff = n ~/ a;
f2 = 'x ${coeff >= 0 ? '+' : ''} $coeff';
if (coeff == 0) f2 = 'x';
} else {
f2 = 'x ${n >= 0 ? '+' : ''} \\frac{$n}{$a}';
}
final sol1 = x1Den == 1 ? '$x1Num' : '\\frac{$x1Num}{$x1Den}'; String formula = '\$\$($f1)($f2) = 0\$\$';
final sol2 = x2Den == 1 ? '$x2Num' : '\\frac{$x2Num}{$x2Den}';
final solution = x1Num * x2Den == x2Num * x1Den String solution;
? 'x_1 = x_2 = $sol1' if (root1Num * root2Den == root2Num * root1Den) {
: 'x_1 = $sol1, \\quad x_2 = $sol2'; solution = '\$\$x_1 = x_2 = $sol1\$\$';
} else {
solution = '\$\$x_1 = $sol1, \\quad x_2 = $sol2\$\$';
}
return (formula: '\$\$($f1)($f2) = 0\$\$', solution: '\$\$$solution\$\$'); return (formula: formula, solution: solution);
} }
int gcd(int a, int b) => b == 0 ? a : gcd(b, a % b); int gcd(int a, int b) => b == 0 ? a : gcd(b, a % b);