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✨ imaginary number

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This commit is contained in:
LittleSheep
2025-09-13 21:05:42 +08:00
parent 65c595461d
commit 4a5749a1f4
2 changed files with 31 additions and 13 deletions
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42
lib/solver.dart
View File

@@ -243,11 +243,29 @@ class SolverService {
CalculationStep( CalculationStep(
stepNumber: 4, stepNumber: 4,
title: '判断解', title: '判断解',
explanation: r'因为 $\Delta < 0$，该方程在实数范围内无解。', explanation: r'因为 $\Delta < 0$，该方程在实数范围内无解，但有虚数解。',
formula: '无实数解', formula: '无实数解，有虚数解',
), ),
); );
return CalculationResult(steps: steps, finalAnswer: '无实数解');
final sqrtDelta = sqrt(-delta);
final realPart = -b / (2 * a);
final imagPart = sqrtDelta / (2 * a);
steps.add(
CalculationStep(
stepNumber: 5,
title: '计算虚数根',
explanation: '使用求根公式计算虚数根。',
formula: r'$$x = \frac{-b \pm \sqrt{-\Delta} i}{2a}$$',
),
);
return CalculationResult(
steps: steps,
finalAnswer:
'\$\$x_1 = ${realPart.toStringAsFixed(4)} + ${imagPart.toStringAsFixed(4)}i, \\quad x_2 = ${realPart.toStringAsFixed(4)} - ${imagPart.toStringAsFixed(4)}i\$\$',
);
} }
} }
@@ -270,12 +288,12 @@ class SolverService {
explanation: '这是一个二元一次方程组，我们将使用加减消元法求解。', explanation: '这是一个二元一次方程组，我们将使用加减消元法求解。',
formula: formula:
''' '''
\$\$
\\begin{cases} \\begin{cases}
${a1}x ${b1 >= 0 ? '+' : ''} ${b1}y = $c1 & (1) \\ ${a1}x ${b1 >= 0 ? '+' : ''} ${b1}y = $c1 & (1) \\\\
${a2}x ${b2 >= 0 ? '+' : ''} ${b2}y = $c2 & (2) ${a2}x ${b2 >= 0 ? '+' : ''} ${b2}y = $c2 & (2)
\\end{cases} \\end{cases}
\$\$
''', ''',
), ),
); );
@@ -344,9 +362,9 @@ ${newA2}x ${b1 * b2 >= 0 ? '+' : ''} ${b1 * b2}y = $newC2 & (4)
''' '''
\\begin{aligned} \\begin{aligned}
$a2($x) + ${b2}y &= $c2 \\ $a2($x) + ${b2}y &= $c2 \\\\
${a2 * x} + ${b2}y &= $c2 \\ ${a2 * x} + ${b2}y &= $c2 \\\\
${b2}y &= $c2 - ${a2 * x} \\ ${b2}y &= $c2 - ${a2 * x} \\\\
${b2}y &= ${c2 - a2 * x} ${b2}y &= ${c2 - a2 * x}
\\end{aligned} \\end{aligned}
@@ -378,9 +396,9 @@ ${b2}y &= ${c2 - a2 * x}
''' '''
\\begin{aligned} \\begin{aligned}
$a1($x) + ${b1}y &= $c1 \\ $a1($x) + ${b1}y &= $c1 \\\\
${a1 * x} + ${b1}y &= $c1 \\ ${a1 * x} + ${b1}y &= $c1 \\\\
${b1}y &= $c1 - ${a1 * x} \\ ${b1}y &= $c1 - ${a1 * x} \\\\
${b1}y &= ${c1 - a1 * x} ${b1}y &= ${c1 - a1 * x}
\\end{aligned} \\end{aligned}

2
pubspec.yaml
View File

@@ -16,7 +16,7 @@ publish_to: "none" # Remove this line if you wish to publish to pub.dev
# https://developer.apple.com/library/archive/documentation/General/Reference/InfoPlistKeyReference/Articles/CoreFoundationKeys.html # https://developer.apple.com/library/archive/documentation/General/Reference/InfoPlistKeyReference/Articles/CoreFoundationKeys.html
# In Windows, build-name is used as the major, minor, and patch parts # In Windows, build-name is used as the major, minor, and patch parts
# of the product and file versions while build-number is used as the build suffix. # of the product and file versions while build-number is used as the build suffix.
version: 1.0.0+2 version: 1.0.0+3
environment: environment:
sdk: ^3.9.2 sdk: ^3.9.2