Docs For Class Math_PolynomialOp

add [line 115]

object &add(
mixed
$p1, mixed
$p2)

Add two Polynomials together and return the result

 $p = new Polynomial("x + 2");

 $res = PolynomialOp::add("x + 3", $p);
 print($res->toString()); // Prints 2x + 5 ( sum of the two )

See: Math_Polynomial::subtract()
Access: public

Parameters:

mixed	`$p1`	—	String representation or Polynomial object
mixed	`$p2`	—

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create [line 93]

object create(
string
$str)

Create a Polynomial object from a string/integer/float

Access: public

Parameters:

string $str —

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createFromRoots [line 367]

object &createFromRoots(
array
$arr)

Create a Polynomial object which has roots (zeros) provided as parameters

The roots can be passed in as either a variable length parameter list or a single array of float values.

Access: public

Parameters:

array $arr — An array of roots

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createFunction [line 846]

string createFunction(
object
$p)

Create a lambda-style anonymous function from the Polynomial

Creates an anonymous function representing the Polynomial which takes one parameter, an x value to evaluate at, and returns a unique name for the function.

See: http://www.php.net/create_function, Math_PolynomialOp::evaluate(), Math_PolynomialOp::createTangentFunction()
Access: public

Parameters:

object $p — Polynomial object or string representing a Polynomial

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createTangentFunction [line 987]

string createTangentFunction(
object
$p, float
$x)

Create a lambda-style function representing the tangent line at a point

See: http://www.php.net/create_function, Math_PolynomialOp::createFunction()
Access: public

Parameters:

object	`$p`	—
float	`$x`	—

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div [line 240]

object &div(
object
$p1, object
$p2, [object
$rem = null])

Divide one Polynomial by another, returning the result

Divide the first polynomial by another polynomial object or a string represention of another polynomial. Optionally, you can pass another Polynomial object by reference to store the remainder of the division operator.

 $a = new Polynomial("4x^2 + 2x");

 $b = new Polynomial("2x");
 $remainder = new Polynomial();
 $result = PolynomialOp::div($a, $b, $remainder);
 print("A divided by B is: " . $result->toString() . " with a remainder of " . $remainder->toString() . "\n");

Access: public

Parameters:

object	`$p1`	—
object	`$p2`	—
object	`$rem`	—

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equals [line 737]

bool equals(
object
$p1, object
$p2)

Tell whether or not two Polynomials/string representations are equal

Access: public

Parameters:

object	`$p1`	—
object	`$p2`	—

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evaluate [line 339]

float evaluate(

$p, float
$x, object
$m1)

Evaluate the polynomial for a given x value

Return: The resulting value ( y value, or value of function f(x) )
Access: public

Parameters:

object	`$m1`	—
float	`$x`	—	The x to evaluate the polynomial at
	`$p`	—

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getCriticalPoints [line 823]

array getCriticalPoints(
object
$p)

Calculate and return an array of critical points for the Polynomial

Critical points of a Polynomial are where something 'important' happens in the Polynomial (inflection point, maximum, minumum, etc.)

Access: public

Parameters:

object $p —

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getDerivative [line 1082]

object A &getDerivative(
object
$p, [
$n = 1], integer
$der_num)

Get the nth derivative of the Polynomial

Returns the nth derivative of the Polynomial. Derivatives are commonly used in calculus as they represent slopes or acceleration. To get the first derivative, the second parameter should be a 1. For the second derivative parameter should be a two, etc. etc.

Return: polynomial object representing the nth derivative
Access: public

Parameters:

object	`$p`	—	The Polynomial object
integer	`$der_num`	—	The derivative you want (1 = 1st, 2 = 2nd, etc.)
	`$n`	—

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getLocalMaximums [line 884]

array getLocalMaximums(
object
$p, [float
$x_min = null], [float
$x_max = null])

Find and return an array of the local maximums of the Polynomial

By default the function returns all local maximums for the Polynomial. If you want just maximums on an interval, pass in the $x_min and $x_max parameters.

See: Math_PolynomialOp::getLocalMaximums()
Access: public

Parameters:

object	`$p`	—
float	`$x_min`	—
float	`$x_max`	—

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getLocalMinimums [line 925]

array getLocalMinimums(
object
$p, [float
$x_min = null], [float
$x_max = null])

Find and return an array of the minimums of the Polynomial

By default the method returns all minimums, if you want the minimums within an interval, pass in the $x_min and $x_max parameters.

See: Math_PolynomialOp::getLocalMaximums()
Access: public

Parameters:

object	`$p`	—
float	`$x_min`	—
float	`$x_max`	—

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getRoots [line 418]

array getRoots(
object
$p, [array
$guesses = array()])

Get the roots of this Polynomial

For Polynomials of degree less than or equal to 4, the exact value of any real roots (zeros) of the Polynomial are returned. For Polynomials of higher degrees, the roots are estimated using the Newton-Raphson method from the Math_Numerical_RootFinding package. Remember that these roots are *estimates* and for high-degree polynomials all of the roots may not be calculated and returned!

If you're calculating roots for a higher-degree Polynomial and want to provide the initial guesses for the roots, you can pass them in as an array parameter.

If possible, this function will return integers instead of floats.

Return: An array of roots ( points where y = 0 )
See: Math_PolynomialOp::getRootsLinear(), Math_PolynomialOp::getRootsQuadratic(), Math_PolynomialOp::getRootsCubic(), Math_PolynomialOp::getRootsQuartic(), Math_PolynomialOp::getRootsHighDegree(), Math_Numerical_RootFinding
Access: public

Parameters:

object	`$p`	—
array	`$guesses`	—

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getRootsCubic [line 553]

array getRootsCubic(

$p, object
$m)

Find and return the real roots of a cubic Polynomial using the cubic formula

See: Math_PolynomialOp::getRoots()
Access: public

Parameters:

object	`$m`	—
	`$p`	—

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getRootsHighDegree [line 770]

array getRootsHighDegree(

$p, [array
$guesses = array()], object
$m)

Estimate and return the roots of a high-degree Polynomial ( degree 5 or greater )

This function uses Newton's method using the Math_Numerical_RootFinding PEAR package to estimate the real roots of high-degree Polynomials. If you already have estimates of where the roots might be, you can pass in an array of guesses. Otherwise, the method will try to calculate some good initial guesses for you.

You must have the Math_Numerical_RootFinding package installed for this method to work!

See: Math_PolynomialOp::getRoots(), Math_Numerical_RootFinding
Access: public

Parameters:

object	`$m`	—
array	`$guesses`	—
	`$p`	—

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getRootsLinear [line 472]

array getRootsLinear(

$p, object
$m)

Get the roots of a linear Polynomial

See: Math_PolynomialOp::getRoots()
Access: public

Parameters:

object	`$m`	—
	`$p`	—

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getRootsQuadratic [line 508]

array getRootsQuadratic(

$p, object
$m)

Get the roots of a quadratic Polynomial (using the Quadratic Formula)

See: Math_Polynomial::getRoots()
Access: public

Parameters:

object	`$m`	—
	`$p`	—

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getRootsQuartic [line 632]

array getRootsQuartic(
object
$p)

Find and return the roots of a Quartic Polynomial (degree 4) with the Quartic formula

See: Math_PolynomialOp::getRoots()
Access: public

Parameters:

object $p —

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getSlopeAt [line 1027]

float getSlopeAt(
object
$p, float
$x)

Get the slope of the Polynomial at a given x value

See: Math_PolynomialOp::getTangentAt()

Parameters:

object	`$p`	—
float	`$x`	—

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getTangentAt [line 962]

object getTangentAt(
object
$p, float
$x)

Get a Polynomial object representing a tangent to the given Polynomial at the given point

See: Math_PolynomialOp::getSlopeAt()
Access: public

Parameters:

object	`$p`	—
float	`$x`	—

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getTangentSlopeAt [line 1039]

float getTangentSlopeAt(
object
$p, float
$x)

Alias of Math_PolynomialOp::getSlopeAt()

Parameters:

object	`$p`	—
float	`$x`	—

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isConstant [line 1142]

bool isConstant(
object
$p)

Tell whether or not a Polynomial is constant (degree 0)

Access: public

Parameters:

object $p —

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isMath_Polynomial [line 723]

bool isMath_Polynomial(
object
$p)

Tell whether or not an object is a Polynomial or not

Access: public

Parameters:

object $p —

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isZero [line 1116]

bool isZero(
object
$p)

Tells whether or not the Polynomial is equivalent to zero

Return: TRUE if its equal to 0, FALSE if it is not
Access: public

Parameters:

object $p —

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mod [line 322]

object &mod(
object
$p1, object
$p2)

Calculate the mod (%) $p1 of $p2 and return the result as a Polynomial

 print('p1 % p2 is: ');

 $mod = Math_PolynomialOp::mod($p1, $p2);
 print($mod->toString());

Parameters:

object	`$p1`	—
object	`$p2`	—

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mul [line 184]

object &mul(

$p1, 
$p2, object
$m1, object
$m2)

Multiply two Polynomials together

The parameters may be either a Polynomial object or a string representation of a polynomial.

Access: public

Parameters:

object	`$m1`	—	Polynomial object or string representing polynomial
object	`$m2`	—
	`$p1`	—
	`$p2`	—

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sub [line 151]

object &sub(
mixed
$p1, mixed
$p2)

Subtract one Polynomial from another Polynomial

See: Math_PolynomialOp::add()
Access: public

Parameters:

mixed	`$p1`	—	The initial Polynomial
mixed	`$p2`	—	The Polynomial to subtract from the initial one

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_round [line 447]

mixed _round(
mixed
$mixed)

Round an array of integers or single integer if its within the round boundary

Access: protected

Parameters:

mixed $mixed —

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Class: Math_PolynomialOp

Class Overview

Author(s):

Methods

Inherited Variables

Inherited Methods

Class Details

Method Detail

add [line 115]

Parameters:

create [line 93]

Parameters:

createFromRoots [line 367]

Parameters:

createFunction [line 846]

Parameters:

createTangentFunction [line 987]

Parameters:

div [line 240]

Parameters:

equals [line 737]

Parameters:

evaluate [line 339]

Parameters:

getCriticalPoints [line 823]

Parameters:

getDerivative [line 1082]

Parameters:

getLocalMaximums [line 884]

Parameters:

getLocalMinimums [line 925]

Parameters:

getRoots [line 418]

Parameters:

getRootsCubic [line 553]

Parameters:

getRootsHighDegree [line 770]

Parameters:

getRootsLinear [line 472]

Parameters:

getRootsQuadratic [line 508]

Parameters:

getRootsQuartic [line 632]

Parameters:

getSlopeAt [line 1027]

Parameters:

getTangentAt [line 962]

Parameters:

getTangentSlopeAt [line 1039]

Parameters:

isConstant [line 1142]

Parameters:

isMath_Polynomial [line 723]

Parameters:

isZero [line 1116]

Parameters:

mod [line 322]

Parameters:

mul [line 184]

Parameters:

sub [line 151]

Parameters:

_round [line 447]

Parameters: