A sub-package for efficiently dealing with polynomials.

Within the documentation for this sub-package, a “finite power series,”
i.e., a polynomial (also referred to simply as a “series”) is represented
by a 1-D numpy array of the polynomial’s coefficients, ordered from lowest
order term to highest. For example, array([1,2,3]) represents
`P_0 + 2*P_1 + 3*P_2`

, where P_n is the n-th order basis polynomial
applicable to the specific module in question, e.g., `polynomial`

(which
“wraps” the “standard” basis) or `chebyshev`

. For optimal performance,
all operations on polynomials, including evaluation at an argument, are
implemented as operations on the coefficients. Additional (module-specific)
information can be found in the docstring for the module of interest.

This package provides *convenience classes* for each of six different kinds
of polynomials:

Name

ProvidesPolynomial

Power series

Chebyshev

Chebyshev series

Legendre

Legendre series

Laguerre

Laguerre series

Hermite

Hermite series

HermiteE

HermiteE series

These *convenience classes* provide a consistent interface for creating,
manipulating, and fitting data with polynomials of different bases.
The convenience classes are the preferred interface for the `polynomial`

package, and are available from the `numpy.polynomial`

namespace.
This eliminates the need to
navigate to the corresponding submodules, e.g. `np.polynomial.Polynomial`

or `np.polynomial.Chebyshev`

instead of
`np.polynomial.polynomial.Polynomial`

or
`np.polynomial.chebyshev.Chebyshev`

, respectively.
The classes provide a more consistent and concise interface than the
type-specific functions defined in the submodules for each type of polynomial.
For example, to fit a Chebyshev polynomial with degree `1`

to data given
by arrays `xdata`

and `ydata`

, the
`fit`

class method:

```
>>> from numpy.polynomial import Chebyshev
>>> c = Chebyshev.fit(xdata, ydata, deg=1)
```

is preferred over the `chebyshev.chebfit`

function from the
`numpy.polynomial.chebyshev`

module:

```
>>> from numpy.polynomial.chebyshev import chebfit
>>> c = chebfit(xdata, ydata, deg=1)
```

See Using the Convenience Classes for more details.

# Convenience Classes¶

The following lists the various constants and methods common to all of
the classes representing the various kinds of polynomials. In the following,
the term `Poly`

represents any one of the convenience classes (e.g.
`Polynomial`

, `Chebyshev`

, `Hermite`

, etc.) while the lowercase `p`

represents an **instance** of a polynomial class.

## Constants¶

`Poly.domain`

– Default domain`Poly.window`

– Default window`Poly.basis_name`

– String used to represent the basis`Poly.maxpower`

– Maximum value`n`

such that`p**n`

is allowed`Poly.nickname`

– String used in printing

## Creation¶

Methods for creating polynomial instances.

`Poly.basis(degree)`

– Basis polynomial of given degree`Poly.identity()`

–`p`

where`p(x) = x`

for all`x`

`Poly.fit(x, y, deg)`

–`p`

of degree`deg`

with coefficients determined by the least-squares fit to the data`x`

,`y`

`Poly.fromroots(roots)`

–`p`

with specified roots`p.copy()`

– Create a copy of`p`

## Conversion¶

Methods for converting a polynomial instance of one kind to another.

`p.cast(Poly)`

– Convert`p`

to instance of kind`Poly`

`p.convert(Poly)`

– Convert`p`

to instance of kind`Poly`

or map between`domain`

and`window`

## Calculus¶

`p.deriv()`

– Take the derivative of`p`

`p.integ()`

– Integrate`p`

## Validation¶

`Poly.has_samecoef(p1, p2)`

– Check if coefficients match`Poly.has_samedomain(p1, p2)`

– Check if domains match`Poly.has_sametype(p1, p2)`

– Check if types match`Poly.has_samewindow(p1, p2)`

– Check if windows match

## Misc¶

`p.linspace()`

– Return`x, p(x)`

at equally-spaced points in`domain`

`p.mapparms()`

– Return the parameters for the linear mapping between`domain`

and`window`

.`p.roots()`

– Return the roots of*p*.`p.trim()`

– Remove trailing coefficients.`p.cutdeg(degree)`

– Truncate p to given degree`p.truncate(size)`

– Truncate p to given size

# Configuration¶

Set the default format for the string representation of polynomials. |