MAINT: Remove the polytemplate.py file.

1 files changed, 0 insertions, 927 deletions

diff --git a/numpy/polynomial/polytemplate.py b/numpy/polynomial/polytemplate.py
deleted file mode 100644
index e68dd18ef..000000000
--- a/numpy/polynomial/polytemplate.py
+++ /dev/null
@@ -1,927 +0,0 @@
-"""
-Template for the Chebyshev and Polynomial classes.
-
-This module houses a Python string module Template object (see, e.g.,
-http://docs.python.org/library/string.html#template-strings) used by
-the `polynomial` and `chebyshev` modules to implement their respective
-`Polynomial` and `Chebyshev` classes.  It provides a mechanism for easily
-creating additional specific polynomial classes (e.g., Legendre, Jacobi,
-etc.) in the future, such that all these classes will have a common API.
-
-"""
-from __future__ import division, absolute_import, print_function
-
-import string
-import sys
-import warnings
-from number import Number
-
-from numpy import ModuleDeprecationWarning
-
-warnings.warn("The polytemplate module will be removed in Numpy 1.10.0.",
-              ModuleDeprecationWarning)
-
-polytemplate = string.Template('''
-from __future__ import division, absolute_import, print_function
-import numpy as np
-import warnings
-from . import polyutils as pu
-
-class $name(pu.PolyBase) :
-    """A $name series class.
-
-    $name instances provide the standard Python numerical methods '+',
-    '-', '*', '//', '%', 'divmod', '**', and '()' as well as the listed
-    methods.
-
-    Parameters
-    ----------
-    coef : array_like
-        $name coefficients, in increasing order.  For example,
-        ``(1, 2, 3)`` implies ``P_0 + 2P_1 + 3P_2`` where the
-        ``P_i`` are a graded polynomial basis.
-    domain : (2,) array_like, optional
-        Domain to use. The interval ``[domain[0], domain[1]]`` is mapped to
-        the interval ``[window[0], window[1]]`` by shifting and scaling.
-        The default value is $domain.
-    window : (2,) array_like, optional
-        Window, see ``domain`` for its use. The default value is $domain.
-        .. versionadded:: 1.6.0
-
-    Attributes
-    ----------
-    coef : (N,) ndarray
-        $name coefficients, from low to high.
-    domain : (2,) ndarray
-        Domain that is mapped to ``window``.
-    window : (2,) ndarray
-        Window that ``domain`` is mapped to.
-
-    Class Attributes
-    ----------------
-    maxpower : int
-        Maximum power allowed, i.e., the largest number ``n`` such that
-        ``p(x)**n`` is allowed. This is to limit runaway polynomial size.
-    domain : (2,) ndarray
-        Default domain of the class.
-    window : (2,) ndarray
-        Default window of the class.
-
-    Notes
-    -----
-    It is important to specify the domain in many cases, for instance in
-    fitting data, because many of the important properties of the
-    polynomial basis only hold in a specified interval and consequently
-    the data must be mapped into that interval in order to benefit.
-
-    Examples
-    --------
-
-    """
-    # Limit runaway size. T_n^m has degree n*2^m
-    maxpower = 16
-    # Default domain
-    domain = np.array($domain)
-    # Default window
-    window = np.array($domain)
-    # Don't let participate in array operations. Value doesn't matter.
-    __array_priority__ = 1000
-    # Not hashable
-    __hash__ = None
-
-    def has_samecoef(self, other):
-        """Check if coefficients match.
-
-        Parameters
-        ----------
-        other : class instance
-            The other class must have the ``coef`` attribute.
-
-        Returns
-        -------
-        bool : boolean
-            True if the coefficients are the same, False otherwise.
-
-        Notes
-        -----
-        .. versionadded:: 1.6.0
-
-        """
-        if len(self.coef) != len(other.coef):
-            return False
-        elif not np.all(self.coef == other.coef):
-            return False
-        else:
-            return True
-
-    def has_samedomain(self, other):
-        """Check if domains match.
-
-        Parameters
-        ----------
-        other : class instance
-            The other class must have the ``domain`` attribute.
-
-        Returns
-        -------
-        bool : boolean
-            True if the domains are the same, False otherwise.
-
-        Notes
-        -----
-        .. versionadded:: 1.6.0
-
-        """
-        return np.all(self.domain == other.domain)
-
-    def has_samewindow(self, other):
-        """Check if windows match.
-
-        Parameters
-        ----------
-        other : class instance
-            The other class must have the ``window`` attribute.
-
-        Returns
-        -------
-        bool : boolean
-            True if the windows are the same, False otherwise.
-
-        Notes
-        -----
-        .. versionadded:: 1.6.0
-
-        """
-        return np.all(self.window == other.window)
-
-    def has_sametype(self, other):
-        """Check if types match.
-
-        Parameters
-        ----------
-        other : object
-            Class instance.
-
-        Returns
-        -------
-        bool : boolean
-            True if other is same class as self
-
-        Notes
-        -----
-        .. versionadded:: 1.7.0
-
-        """
-        return isinstance(other, self.__class__)
-
-    def __init__(self, coef, domain=$domain, window=$domain) :
-        [coef, dom, win] = pu.as_series([coef, domain, window], trim=False)
-        if len(dom) != 2 :
-            raise ValueError("Domain has wrong number of elements.")
-        if len(win) != 2 :
-            raise ValueError("Window has wrong number of elements.")
-        self.coef = coef
-        self.domain = dom
-        self.window = win
-
-    def __repr__(self):
-        format = "%s(%s, %s, %s)"
-        coef = repr(self.coef)[6:-1]
-        domain = repr(self.domain)[6:-1]
-        window = repr(self.window)[6:-1]
-        return format % ('$name', coef, domain, window)
-
-    def __str__(self) :
-        format = "%s(%s)"
-        coef = str(self.coef)
-        return format % ('$nick', coef)
-
-    # Pickle and copy
-
-    def __getstate__(self) :
-        ret = self.__dict__.copy()
-        ret['coef'] = self.coef.copy()
-        ret['domain'] = self.domain.copy()
-        ret['window'] = self.window.copy()
-        return ret
-
-    def __setstate__(self, dict) :
-        self.__dict__ = dict
-
-    # Call
-
-    def __call__(self, arg) :
-        off, scl = pu.mapparms(self.domain, self.window)
-        arg = off + scl*arg
-        return ${nick}val(arg, self.coef)
-
-    def __iter__(self) :
-        return iter(self.coef)
-
-    def __len__(self) :
-        return len(self.coef)
-
-    # Numeric properties.
-
-    def __neg__(self) :
-        return self.__class__(-self.coef, self.domain, self.window)
-
-    def __pos__(self) :
-        return self
-
-    def __add__(self, other) :
-        """Returns sum"""
-        if isinstance(other, pu.PolyBase):
-            if not self.has_sametype(other):
-                raise TypeError("Polynomial types differ")
-            elif not self.has_samedomain(other):
-                raise TypeError("Domains differ")
-            elif not self.has_samewindow(other):
-                raise TypeError("Windows differ")
-            else:
-                coef = ${nick}add(self.coef, other.coef)
-        else :
-            try :
-                coef = ${nick}add(self.coef, other)
-            except :
-                return NotImplemented
-        return self.__class__(coef, self.domain, self.window)
-
-    def __sub__(self, other) :
-        """Returns difference"""
-        if isinstance(other, pu.PolyBase):
-            if not self.has_sametype(other):
-                raise TypeError("Polynomial types differ")
-            elif not self.has_samedomain(other):
-                raise TypeError("Domains differ")
-            elif not self.has_samewindow(other):
-                raise TypeError("Windows differ")
-            else:
-                coef = ${nick}sub(self.coef, other.coef)
-        else :
-            try :
-                coef = ${nick}sub(self.coef, other)
-            except :
-                return NotImplemented
-        return self.__class__(coef, self.domain, self.window)
-
-    def __mul__(self, other) :
-        """Returns product"""
-        if isinstance(other, pu.PolyBase):
-            if not self.has_sametype(other):
-                raise TypeError("Polynomial types differ")
-            elif not self.has_samedomain(other):
-                raise TypeError("Domains differ")
-            elif not self.has_samewindow(other):
-                raise TypeError("Windows differ")
-            else:
-                coef = ${nick}mul(self.coef, other.coef)
-        else :
-            try :
-                coef = ${nick}mul(self.coef, other)
-            except :
-                return NotImplemented
-        return self.__class__(coef, self.domain, self.window)
-
-    def __div__(self, other):
-        # set to __floordiv__,  /, for now.
-        return self.__floordiv__(other)
-
-    def __truediv__(self, other) :
-        # there is no true divide if the rhs is not a Number, although it
-        # could return the first n elements of an infinite series.
-        # It is hard to see where n would come from, though.
-        if not isinstance(other, Number) or isinstance(other, bool):
-            form = "unsupported types for true division: '%s', '%s'"
-            raise TypeError(form % (type(self), type(other)))
-        return self.__floordiv__(other)
-
-    def __floordiv__(self, other) :
-        """Returns the quotient."""
-        if isinstance(other, pu.PolyBase):
-            if not self.has_sametype(other):
-                raise TypeError("Polynomial types differ")
-            elif not self.has_samedomain(other):
-                raise TypeError("Domains differ")
-            elif not self.has_samewindow(other):
-                raise TypeError("Windows differ")
-            else:
-                quo, rem = ${nick}div(self.coef, other.coef)
-        else :
-            try :
-                quo, rem = ${nick}div(self.coef, other)
-            except :
-                return NotImplemented
-        return self.__class__(quo, self.domain, self.window)
-
-    def __mod__(self, other) :
-        """Returns the remainder."""
-        if isinstance(other, pu.PolyBase):
-            if not self.has_sametype(other):
-                raise TypeError("Polynomial types differ")
-            elif not self.has_samedomain(other):
-                raise TypeError("Domains differ")
-            elif not self.has_samewindow(other):
-                raise TypeError("Windows differ")
-            else:
-                quo, rem = ${nick}div(self.coef, other.coef)
-        else :
-            try :
-                quo, rem = ${nick}div(self.coef, other)
-            except :
-                return NotImplemented
-        return self.__class__(rem, self.domain, self.window)
-
-    def __divmod__(self, other) :
-        """Returns quo, remainder"""
-        if isinstance(other, self.__class__) :
-            if not self.has_samedomain(other):
-                raise TypeError("Domains are not equal")
-            elif not self.has_samewindow(other):
-                raise TypeError("Windows are not equal")
-            else:
-                quo, rem = ${nick}div(self.coef, other.coef)
-        else :
-            try :
-                quo, rem = ${nick}div(self.coef, other)
-            except :
-                return NotImplemented
-        quo = self.__class__(quo, self.domain, self.window)
-        rem = self.__class__(rem, self.domain, self.window)
-        return quo, rem
-
-    def __pow__(self, other) :
-        try :
-            coef = ${nick}pow(self.coef, other, maxpower = self.maxpower)
-        except :
-            raise
-        return self.__class__(coef, self.domain, self.window)
-
-    def __radd__(self, other) :
-        try :
-            coef = ${nick}add(other, self.coef)
-        except :
-            return NotImplemented
-        return self.__class__(coef, self.domain, self.window)
-
-    def __rsub__(self, other):
-        try :
-            coef = ${nick}sub(other, self.coef)
-        except :
-            return NotImplemented
-        return self.__class__(coef, self.domain, self.window)
-
-    def __rmul__(self, other) :
-        try :
-            coef = ${nick}mul(other, self.coef)
-        except :
-            return NotImplemented
-        return self.__class__(coef, self.domain, self.window)
-
-    def __rdiv__(self, other):
-        # set to __floordiv__ /.
-        return self.__rfloordiv__(other)
-
-    def __rtruediv__(self, other) :
-        # An instance of PolyBase is not considered a
-        # Number.
-        return NotImplemented
-
-    def __rfloordiv__(self, other) :
-        try :
-            quo, rem = ${nick}div(other, self.coef)
-        except:
-            return NotImplemented
-        return self.__class__(quo, self.domain, self.window)
-
-    def __rmod__(self, other) :
-        try :
-            quo, rem = ${nick}div(other, self.coef)
-        except :
-            return NotImplemented
-        return self.__class__(rem, self.domain, self.window)
-
-    def __rdivmod__(self, other) :
-        try :
-            quo, rem = ${nick}div(other, self.coef)
-        except :
-            return NotImplemented
-        quo = self.__class__(quo, self.domain, self.window)
-        rem = self.__class__(rem, self.domain, self.window)
-        return quo, rem
-
-    # Enhance me
-    # some augmented arithmetic operations could be added here
-
-    def __eq__(self, other) :
-        res = isinstance(other, self.__class__) \
-                and self.has_samecoef(other) \
-                and self.has_samedomain(other) \
-                and self.has_samewindow(other)
-        return res
-
-    def __ne__(self, other) :
-        return not self.__eq__(other)
-
-    #
-    # Extra methods.
-    #
-
-    def copy(self) :
-        """Return a copy.
-
-        Return a copy of the current $name instance.
-
-        Returns
-        -------
-        new_instance : $name
-            Copy of current instance.
-
-        """
-        return self.__class__(self.coef, self.domain, self.window)
-
-    def degree(self) :
-        """The degree of the series.
-
-        Notes
-        -----
-        .. versionadded:: 1.5.0
-
-        """
-        return len(self) - 1
-
-    def cutdeg(self, deg) :
-        """Truncate series to the given degree.
-
-        Reduce the degree of the $name series to `deg` by discarding the
-        high order terms. If `deg` is greater than the current degree a
-        copy of the current series is returned. This can be useful in least
-        squares where the coefficients of the high degree terms may be very
-        small.
-
-        Parameters
-        ----------
-        deg : non-negative int
-            The series is reduced to degree `deg` by discarding the high
-            order terms. The value of `deg` must be a non-negative integer.
-
-        Returns
-        -------
-        new_instance : $name
-            New instance of $name with reduced degree.
-
-        Notes
-        -----
-        .. versionadded:: 1.5.0
-
-        """
-        return self.truncate(deg + 1)
-
-    def trim(self, tol=0) :
-        """Remove small leading coefficients
-
-        Remove leading coefficients until a coefficient is reached whose
-        absolute value greater than `tol` or the beginning of the series is
-        reached. If all the coefficients would be removed the series is set to
-        ``[0]``. A new $name instance is returned with the new coefficients.
-        The current instance remains unchanged.
-
-        Parameters
-        ----------
-        tol : non-negative number.
-            All trailing coefficients less than `tol` will be removed.
-
-        Returns
-        -------
-        new_instance : $name
-            Contains the new set of coefficients.
-
-        """
-        coef = pu.trimcoef(self.coef, tol)
-        return self.__class__(coef, self.domain, self.window)
-
-    def truncate(self, size) :
-        """Truncate series to length `size`.
-
-        Reduce the $name series to length `size` by discarding the high
-        degree terms. The value of `size` must be a positive integer. This
-        can be useful in least squares where the coefficients of the
-        high degree terms may be very small.
-
-        Parameters
-        ----------
-        size : positive int
-            The series is reduced to length `size` by discarding the high
-            degree terms. The value of `size` must be a positive integer.
-
-        Returns
-        -------
-        new_instance : $name
-            New instance of $name with truncated coefficients.
-
-        """
-        isize = int(size)
-        if isize != size or isize < 1 :
-            raise ValueError("size must be a positive integer")
-        if isize >= len(self.coef) :
-            coef = self.coef
-        else :
-            coef = self.coef[:isize]
-        return self.__class__(coef, self.domain, self.window)
-
-    def convert(self, domain=None, kind=None, window=None) :
-        """Convert to different class and/or domain.
-
-        Parameters
-        ----------
-        domain : array_like, optional
-            The domain of the converted series. If the value is None,
-            the default domain of `kind` is used.
-        kind : class, optional
-            The polynomial series type class to which the current instance
-            should be converted. If kind is None, then the class of the
-            current instance is used.
-        window : array_like, optional
-            The window of the converted series. If the value is None,
-            the default window of `kind` is used.
-
-        Returns
-        -------
-        new_series_instance : `kind`
-            The returned class can be of different type than the current
-            instance and/or have a different domain.
-
-        Notes
-        -----
-        Conversion between domains and class types can result in
-        numerically ill defined series.
-
-        Examples
-        --------
-
-        """
-        if kind is None:
-            kind = $name
-        if domain is None:
-            domain = kind.domain
-        if window is None:
-            window = kind.window
-        return self(kind.identity(domain, window=window))
-
-    def mapparms(self) :
-        """Return the mapping parameters.
-
-        The returned values define a linear map ``off + scl*x`` that is
-        applied to the input arguments before the series is evaluated. The
-        map depends on the ``domain`` and ``window``; if the current
-        ``domain`` is equal to the ``window`` the resulting map is the
-        identity.  If the coefficients of the ``$name`` instance are to be
-        used by themselves outside this class, then the linear function
-        must be substituted for the ``x`` in the standard representation of
-        the base polynomials.
-
-        Returns
-        -------
-        off, scl : floats or complex
-            The mapping function is defined by ``off + scl*x``.
-
-        Notes
-        -----
-        If the current domain is the interval ``[l_1, r_1]`` and the window
-        is ``[l_2, r_2]``, then the linear mapping function ``L`` is
-        defined by the equations::
-
-            L(l_1) = l_2
-            L(r_1) = r_2
-
-        """
-        return pu.mapparms(self.domain, self.window)
-
-    def integ(self, m=1, k=[], lbnd=None) :
-        """Integrate.
-
-        Return an instance of $name that is the definite integral of the
-        current series. Refer to `${nick}int` for full documentation.
-
-        Parameters
-        ----------
-        m : non-negative int
-            The number of integrations to perform.
-        k : array_like
-            Integration constants. The first constant is applied to the
-            first integration, the second to the second, and so on. The
-            list of values must less than or equal to `m` in length and any
-            missing values are set to zero.
-        lbnd : Scalar
-            The lower bound of the definite integral.
-
-        Returns
-        -------
-        integral : $name
-            The integral of the series using the same domain.
-
-        See Also
-        --------
-        ${nick}int : similar function.
-        ${nick}der : similar function for derivative.
-
-        """
-        off, scl = self.mapparms()
-        if lbnd is None :
-            lbnd = 0
-        else :
-            lbnd = off + scl*lbnd
-        coef = ${nick}int(self.coef, m, k, lbnd, 1./scl)
-        return self.__class__(coef, self.domain, self.window)
-
-    def deriv(self, m=1):
-        """Differentiate.
-
-        Return an instance of $name that is the derivative of the current
-        series.  Refer to `${nick}der` for full documentation.
-
-        Parameters
-        ----------
-        m : non-negative int
-            The number of integrations to perform.
-
-        Returns
-        -------
-        derivative : $name
-            The derivative of the series using the same domain.
-
-        See Also
-        --------
-        ${nick}der : similar function.
-        ${nick}int : similar function for integration.
-
-        """
-        off, scl = self.mapparms()
-        coef = ${nick}der(self.coef, m, scl)
-        return self.__class__(coef, self.domain, self.window)
-
-    def roots(self) :
-        """Return list of roots.
-
-        Return ndarray of roots for this series. See `${nick}roots` for
-        full documentation. Note that the accuracy of the roots is likely to
-        decrease the further outside the domain they lie.
-
-        See Also
-        --------
-        ${nick}roots : similar function
-        ${nick}fromroots : function to go generate series from roots.
-
-        """
-        roots = ${nick}roots(self.coef)
-        return pu.mapdomain(roots, self.window, self.domain)
-
-    def linspace(self, n=100, domain=None):
-        """Return x,y values at equally spaced points in domain.
-
-        Returns x, y values at `n` linearly spaced points across domain.
-        Here y is the value of the polynomial at the points x. By default
-        the domain is the same as that of the $name instance.  This method
-        is intended mostly as a plotting aid.
-
-        Parameters
-        ----------
-        n : int, optional
-            Number of point pairs to return. The default value is 100.
-        domain : {None, array_like}
-            If not None, the specified domain is used instead of that of
-            the calling instance. It should be of the form ``[beg,end]``.
-            The default is None.
-
-        Returns
-        -------
-        x, y : ndarrays
-            ``x`` is equal to linspace(self.domain[0], self.domain[1], n)
-            ``y`` is the polynomial evaluated at ``x``.
-
-        .. versionadded:: 1.5.0
-
-        """
-        if domain is None:
-            domain = self.domain
-        x = np.linspace(domain[0], domain[1], n)
-        y = self(x)
-        return x, y
-
-
-
-    @staticmethod
-    def fit(x, y, deg, domain=None, rcond=None, full=False, w=None,
-        window=$domain):
-        """Least squares fit to data.
-
-        Return a `$name` instance that is the least squares fit to the data
-        `y` sampled at `x`. Unlike `${nick}fit`, the domain of the returned
-        instance can be specified and this will often result in a superior
-        fit with less chance of ill conditioning. Support for NA was added
-        in version 1.7.0. See `${nick}fit` for full documentation of the
-        implementation.
-
-        Parameters
-        ----------
-        x : array_like, shape (M,)
-            x-coordinates of the M sample points ``(x[i], y[i])``.
-        y : array_like, shape (M,) or (M, K)
-            y-coordinates of the sample points. Several data sets of sample
-            points sharing the same x-coordinates can be fitted at once by
-            passing in a 2D-array that contains one dataset per column.
-        deg : int
-            Degree of the fitting polynomial.
-        domain : {None, [beg, end], []}, optional
-            Domain to use for the returned $name instance. If ``None``,
-            then a minimal domain that covers the points `x` is chosen.  If
-            ``[]`` the default domain ``$domain`` is used. The default
-            value is $domain in numpy 1.4.x and ``None`` in later versions.
-            The ``[]`` value was added in numpy 1.5.0.
-        rcond : float, optional
-            Relative condition number of the fit. Singular values smaller
-            than this relative to the largest singular value will be
-            ignored. The default value is len(x)*eps, where eps is the
-            relative precision of the float type, about 2e-16 in most
-            cases.
-        full : bool, optional
-            Switch determining nature of return value. When it is False
-            (the default) just the coefficients are returned, when True
-            diagnostic information from the singular value decomposition is
-            also returned.
-        w : array_like, shape (M,), optional
-            Weights. If not None the contribution of each point
-            ``(x[i],y[i])`` to the fit is weighted by `w[i]`. Ideally the
-            weights are chosen so that the errors of the products
-            ``w[i]*y[i]`` all have the same variance.  The default value is
-            None.
-            .. versionadded:: 1.5.0
-        window : {[beg, end]}, optional
-            Window to use for the returned $name instance. The default
-            value is ``$domain``
-            .. versionadded:: 1.6.0
-
-        Returns
-        -------
-        least_squares_fit : instance of $name
-            The $name instance is the least squares fit to the data and
-            has the domain specified in the call.
-
-        [residuals, rank, singular_values, rcond] : only if `full` = True
-            Residuals of the least squares fit, the effective rank of the
-            scaled Vandermonde matrix and its singular values, and the
-            specified value of `rcond`. For more details, see
-            `linalg.lstsq`.
-
-        See Also
-        --------
-        ${nick}fit : similar function
-
-        """
-        if domain is None:
-            domain = pu.getdomain(x)
-        elif type(domain) is list and len(domain) == 0:
-            domain = $domain
-
-        if type(window) is list and len(window) == 0:
-            window = $domain
-
-        xnew = pu.mapdomain(x, domain, window)
-        res = ${nick}fit(xnew, y, deg, w=w, rcond=rcond, full=full)
-        if full :
-            [coef, status] = res
-            return $name(coef, domain=domain, window=window), status
-        else :
-            coef = res
-            return $name(coef, domain=domain, window=window)
-
-    @staticmethod
-    def fromroots(roots, domain=$domain, window=$domain) :
-        """Return $name instance with specified roots.
-
-        Returns an instance of $name representing the product
-        ``(x - r[0])*(x - r[1])*...*(x - r[n-1])``, where ``r`` is the
-        list of roots.
-
-        Parameters
-        ----------
-        roots : array_like
-            List of roots.
-        domain : {array_like, None}, optional
-            Domain for the resulting instance of $name. If none the domain
-            is the interval from the smallest root to the largest. The
-            default is $domain.
-        window : array_like, optional
-            Window for the resulting instance of $name. The default value
-            is $domain.
-
-        Returns
-        -------
-        object : $name instance
-            Series with the specified roots.
-
-        See Also
-        --------
-        ${nick}fromroots : equivalent function
-
-        """
-        [roots] = pu.as_series([roots], trim=False)
-        if domain is None :
-            domain = pu.getdomain(roots)
-        deg = len(roots)
-        off, scl = pu.mapparms(domain, window)
-        rnew = off + scl*roots
-        coef = ${nick}fromroots(rnew) / scl**deg
-        return $name(coef, domain=domain, window=window)
-
-    @staticmethod
-    def identity(domain=$domain, window=$domain) :
-        """Identity function.
-
-        If ``p`` is the returned $name object, then ``p(x) == x`` for all
-        values of x.
-
-        Parameters
-        ----------
-        domain : array_like
-            The resulting array must be of the form ``[beg, end]``, where
-            ``beg`` and ``end`` are the endpoints of the domain.
-        window : array_like
-            The resulting array must be if the form ``[beg, end]``, where
-            ``beg`` and ``end`` are the endpoints of the window.
-
-        Returns
-        -------
-        identity : $name instance
-
-        """
-        off, scl = pu.mapparms(window, domain)
-        coef = ${nick}line(off, scl)
-        return $name(coef, domain, window)
-
-    @staticmethod
-    def basis(deg, domain=$domain, window=$domain):
-        """$name polynomial of degree `deg`.
-
-        Returns an instance of the $name polynomial of degree `d`.
-
-        Parameters
-        ----------
-        deg : int
-            Degree of the $name polynomial. Must be >= 0.
-        domain : array_like
-            The resulting array must be of the form ``[beg, end]``, where
-            ``beg`` and ``end`` are the endpoints of the domain.
-        window : array_like
-            The resulting array must be if the form ``[beg, end]``, where
-            ``beg`` and ``end`` are the endpoints of the window.
-
-        Returns
-        p : $name instance
-
-        Notes
-        -----
-        .. versionadded:: 1.7.0
-
-        """
-        ideg = int(deg)
-        if ideg != deg or ideg < 0:
-            raise ValueError("deg must be non-negative integer")
-        return $name([0]*ideg + [1], domain, window)
-
-    @staticmethod
-    def cast(series, domain=$domain, window=$domain):
-        """Convert instance to equivalent $name series.
-
-        The `series` is expected to be an instance of some polynomial
-        series of one of the types supported by by the numpy.polynomial
-        module, but could be some other class that supports the convert
-        method.
-
-        Parameters
-        ----------
-        series : series
-            The instance series to be converted.
-        domain : array_like
-            The resulting array must be of the form ``[beg, end]``, where
-            ``beg`` and ``end`` are the endpoints of the domain.
-        window : array_like
-            The resulting array must be if the form ``[beg, end]``, where
-            ``beg`` and ``end`` are the endpoints of the window.
-
-        Returns
-        p : $name instance
-            A $name series equal to the `poly` series.
-
-        See Also
-        --------
-        convert -- similar instance method
-
-        Notes
-        -----
-        .. versionadded:: 1.7.0
-
-        """
-        return series.convert(domain, $name, window)
-
-''')