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<?php |
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namespace Samsara\Fermat\Values\Algebra; |
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use Samsara\Exceptions\UsageError\IntegrityConstraint; |
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use Samsara\Fermat\Numbers; |
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use Samsara\Fermat\Types\Base\DecimalInterface; |
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use Samsara\Fermat\Types\Base\ExpressionInterface; |
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use Samsara\Fermat\Types\Base\FunctionInterface; |
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use Samsara\Fermat\Types\Base\NumberInterface; |
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use Samsara\Fermat\Types\Expression; |
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use Samsara\Fermat\Values\ImmutableNumber; |
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class PolynomialFunction extends Expression implements ExpressionInterface, FunctionInterface |
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{ |
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/** @var array */ |
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protected $coefficients = []; |
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/** |
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* PolynomialFunction constructor. |
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* |
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* @param array $coefficients |
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* |
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* @throws IntegrityConstraint |
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*/ |
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public function __construct(array $coefficients) |
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{ |
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parent::__construct(Expression::POLYNOMIAL); |
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$sanitizedCoefficients = []; |
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foreach ($coefficients as $exponent => $coefficient) { |
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if (!is_int($exponent)) { |
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throw new IntegrityConstraint( |
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'Keys in the $coefficients array must be integers', |
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'Only use integer keys for the $coefficients array', |
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'The key '.$exponent.' was found in the $coefficients array; an integer was expected' |
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); |
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} |
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/** @var ImmutableNumber $fermatCoefficient */ |
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$fermatCoefficient = Numbers::make(Numbers::IMMUTABLE, $coefficient); |
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if (!$fermatCoefficient->isEqual(0)) { |
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$sanitizedCoefficients[$exponent] = $fermatCoefficient; |
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} |
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} |
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$this->coefficients = $sanitizedCoefficients; |
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$this->expression = function($x) use ($sanitizedCoefficients): ImmutableNumber { |
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/** @var ImmutableNumber $value */ |
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$value = Numbers::makeZero(); |
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/** @var ImmutableNumber $xPart */ |
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$xPart = Numbers::makeOrDont(Numbers::IMMUTABLE, $x); |
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foreach ($sanitizedCoefficients as $exponent => $coefficient) { |
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if ($exponent == 0) { |
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$value = $value->add($coefficient); |
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} else { |
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$term = $coefficient->multiply($xPart->pow($exponent)); |
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$value = $value->add($term); |
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} |
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} |
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return $value; |
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}; |
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} |
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/** |
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* @param int|float|string|NumberInterface|DecimalInterface $x |
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* |
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* @return ImmutableNumber |
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* @throws IntegrityConstraint |
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*/ |
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public function evaluateAt($x): ImmutableNumber |
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{ |
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/** @var callable $answer */ |
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$answer = $this->expression; |
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return $answer($x); |
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} |
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/** |
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* @return FunctionInterface |
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* @throws IntegrityConstraint |
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*/ |
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public function derivativeExpression(): FunctionInterface |
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{ |
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$newCoefficients = []; |
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/** |
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* @var int $exponent |
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* @var ImmutableNumber $coefficient |
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*/ |
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foreach ($this->coefficients as $exponent => $coefficient) { |
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if ($exponent == 0) { |
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continue; |
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} |
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$newCoefficients[$exponent-1] = $coefficient->multiply($exponent); |
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} |
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return new PolynomialFunction($newCoefficients); |
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} |
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/** |
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* @param int|float|string|NumberInterface|DecimalInterface $C |
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* |
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* @return FunctionInterface |
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* @throws IntegrityConstraint |
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*/ |
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public function integralExpression($C = 0): FunctionInterface |
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{ |
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$C = Numbers::make(Numbers::IMMUTABLE, $C); |
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$newCoefficients = []; |
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if (!$C->isEqual(0)) { |
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$newCoefficients[0] = $C; |
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} |
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/** |
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* @var int $exponent |
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* @var ImmutableNumber $coefficient |
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*/ |
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foreach ($this->coefficients as $exponent => $coefficient) { |
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$newExponent = $exponent+1; |
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$newCoefficients[$newExponent] = $coefficient->divide($newExponent); |
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} |
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return new PolynomialFunction($newCoefficients); |
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} |
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public function describeShape() |
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{ |
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$shape = []; |
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/** |
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* @var int $exponent |
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* @var ImmutableNumber $coefficient |
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*/ |
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foreach ($this->coefficients as $exponent => $coefficient) { |
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$shape[$exponent] = $coefficient->getValue(); |
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} |
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return $shape; |
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} |
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} |
JordanRL /
Fermat
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