neulab/docprompting-conala huggingface dataset:
numpy.poly   numpy.poly(seq_of_zeros)[source]
 
Find the coefficients of a polynomial with the given sequence of roots.  Note This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in numpy.polynomial is preferred. A summary of the differences can be found in the transition guide.  Returns the coefficients of the polynomial whose leading coefficient is one for the given sequence of zeros (multiple roots must be included in the sequence as many times as their multiplicity; see Examples). A square matrix (or array, which will be treated as a matrix) can also be given, in which case the coefficients of the characteristic polynomial of the matrix are returned.  Parameters 
 
seq_of_zerosarray_like, shape (N,) or (N, N)


A sequence of polynomial roots, or a square array or matrix object.    Returns 
 
cndarray


1D array of polynomial coefficients from highest to lowest degree: c[0] * x**(N) + c[1] * x**(N-1) + ... + c[N-1] * x + c[N] where c[0] always equals 1.    Raises 
 ValueError

If input is the wrong shape (the input must be a 1-D or square 2-D array).      See also  polyval

Compute polynomial values.  roots

Return the roots of a polynomial.  polyfit

Least squares polynomial fit.  poly1d

A one-dimensional polynomial class.    Notes Specifying the roots of a polynomial still leaves one degree of freedom, typically represented by an undetermined leading coefficient. [1] In the case of this function, that coefficient - the first one in the returned array - is always taken as one. (If for some reason you have one other point, the only automatic way presently to leverage that information is to use polyfit.) The characteristic polynomial, \(p_a(t)\), of an n-by-n matrix A is given by \(p_a(t) = \mathrm{det}(t\, \mathbf{I} - \mathbf{A})\), where I is the n-by-n identity matrix. [2] References  1 
M. Sullivan and M. Sullivan, III, “Algebra and Trignometry, Enhanced With Graphing Utilities,” Prentice-Hall, pg. 318, 1996.  2 
G. Strang, “Linear Algebra and Its Applications, 2nd Edition,” Academic Press, pg. 182, 1980.   Examples Given a sequence of a polynomial’s zeros: >>> np.poly((0, 0, 0)) # Multiple root example
array([1., 0., 0., 0.])
 The line above represents z**3 + 0*z**2 + 0*z + 0. >>> np.poly((-1./2, 0, 1./2))
array([ 1.  ,  0.  , -0.25,  0.  ])
 The line above represents z**3 - z/4 >>> np.poly((np.random.random(1)[0], 0, np.random.random(1)[0]))
array([ 1.        , -0.77086955,  0.08618131,  0.        ]) # random
 Given a square array object: >>> P = np.array([[0, 1./3], [-1./2, 0]])
>>> np.poly(P)
array([1.        , 0.        , 0.16666667])
 Note how in all cases the leading coefficient is always 1.
numpy.poly1d   class numpy.poly1d(c_or_r, r=False, variable=None)[source]
 
A one-dimensional polynomial class.  Note This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in numpy.polynomial is preferred. A summary of the differences can be found in the transition guide.  A convenience class, used to encapsulate “natural” operations on polynomials so that said operations may take on their customary form in code (see Examples).  Parameters 
 
c_or_rarray_like


The polynomial’s coefficients, in decreasing powers, or if the value of the second parameter is True, the polynomial’s roots (values where the polynomial evaluates to 0). For example, poly1d([1, 2, 3]) returns an object that represents \(x^2 + 2x + 3\), whereas poly1d([1, 2, 3], True) returns one that represents \((x-1)(x-2)(x-3) = x^3 - 6x^2 + 11x -6\).  
rbool, optional


If True, c_or_r specifies the polynomial’s roots; the default is False.  
variablestr, optional


Changes the variable used when printing p from x to variable (see Examples).     Examples Construct the polynomial \(x^2 + 2x + 3\): >>> p = np.poly1d([1, 2, 3])
>>> print(np.poly1d(p))
   2
1 x + 2 x + 3
 Evaluate the polynomial at \(x = 0.5\): >>> p(0.5)
4.25
 Find the roots: >>> p.r
array([-1.+1.41421356j, -1.-1.41421356j])
>>> p(p.r)
array([ -4.44089210e-16+0.j,  -4.44089210e-16+0.j]) # may vary
 These numbers in the previous line represent (0, 0) to machine precision Show the coefficients: >>> p.c
array([1, 2, 3])
 Display the order (the leading zero-coefficients are removed): >>> p.order
2
 Show the coefficient of the k-th power in the polynomial (which is equivalent to p.c[-(i+1)]): >>> p[1]
2
 Polynomials can be added, subtracted, multiplied, and divided (returns quotient and remainder): >>> p * p
poly1d([ 1,  4, 10, 12,  9])
 >>> (p**3 + 4) / p
(poly1d([ 1.,  4., 10., 12.,  9.]), poly1d([4.]))
 asarray(p) gives the coefficient array, so polynomials can be used in all functions that accept arrays: >>> p**2 # square of polynomial
poly1d([ 1,  4, 10, 12,  9])
 >>> np.square(p) # square of individual coefficients
array([1, 4, 9])
 The variable used in the string representation of p can be modified, using the variable parameter: >>> p = np.poly1d([1,2,3], variable='z')
>>> print(p)
   2
1 z + 2 z + 3
 Construct a polynomial from its roots: >>> np.poly1d([1, 2], True)
poly1d([ 1., -3.,  2.])
 This is the same polynomial as obtained by: >>> np.poly1d([1, -1]) * np.poly1d([1, -2])
poly1d([ 1, -3,  2])
  Attributes 
 c

The polynomial coefficients  coef

The polynomial coefficients  coefficients

The polynomial coefficients  coeffs

The polynomial coefficients  o

The order or degree of the polynomial  order

The order or degree of the polynomial  r

The roots of the polynomial, where self(x) == 0  roots

The roots of the polynomial, where self(x) == 0  variable

The name of the polynomial variable     Methods  
__call__(val) Call self as a function.  
deriv([m]) Return a derivative of this polynomial.  
integ([m, k]) Return an antiderivative (indefinite integral) of this polynomial.
numpy.polyadd   numpy.polyadd(a1, a2)[source]
 
Find the sum of two polynomials.  Note This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in numpy.polynomial is preferred. A summary of the differences can be found in the transition guide.  Returns the polynomial resulting from the sum of two input polynomials. Each input must be either a poly1d object or a 1D sequence of polynomial coefficients, from highest to lowest degree.  Parameters 
 
a1, a2array_like or poly1d object


Input polynomials.    Returns 
 
outndarray or poly1d object


The sum of the inputs. If either input is a poly1d object, then the output is also a poly1d object. Otherwise, it is a 1D array of polynomial coefficients from highest to lowest degree.      See also  poly1d

A one-dimensional polynomial class.  
poly, polyadd, polyder, polydiv, polyfit, polyint, polysub, polyval

  Examples >>> np.polyadd([1, 2], [9, 5, 4])
array([9, 6, 6])
 Using poly1d objects: >>> p1 = np.poly1d([1, 2])
>>> p2 = np.poly1d([9, 5, 4])
>>> print(p1)
1 x + 2
>>> print(p2)
   2
9 x + 5 x + 4
>>> print(np.polyadd(p1, p2))
   2
9 x + 6 x + 6
numpy.polyder   numpy.polyder(p, m=1)[source]
 
Return the derivative of the specified order of a polynomial.  Note This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in numpy.polynomial is preferred. A summary of the differences can be found in the transition guide.   Parameters 
 
ppoly1d or sequence


Polynomial to differentiate. A sequence is interpreted as polynomial coefficients, see poly1d.  
mint, optional


Order of differentiation (default: 1)    Returns 
 
derpoly1d


A new polynomial representing the derivative.      See also  polyint

Anti-derivative of a polynomial.  poly1d

Class for one-dimensional polynomials.    Examples The derivative of the polynomial \(x^3 + x^2 + x^1 + 1\) is: >>> p = np.poly1d([1,1,1,1])
>>> p2 = np.polyder(p)
>>> p2
poly1d([3, 2, 1])
 which evaluates to: >>> p2(2.)
17.0
 We can verify this, approximating the derivative with (f(x + h) - f(x))/h: >>> (p(2. + 0.001) - p(2.)) / 0.001
17.007000999997857
 The fourth-order derivative of a 3rd-order polynomial is zero: >>> np.polyder(p, 2)
poly1d([6, 2])
>>> np.polyder(p, 3)
poly1d([6])
>>> np.polyder(p, 4)
poly1d([0])
numpy.polydiv   numpy.polydiv(u, v)[source]
 
Returns the quotient and remainder of polynomial division.  Note This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in numpy.polynomial is preferred. A summary of the differences can be found in the transition guide.  The input arrays are the coefficients (including any coefficients equal to zero) of the “numerator” (dividend) and “denominator” (divisor) polynomials, respectively.  Parameters 
 
uarray_like or poly1d


Dividend polynomial’s coefficients.  
varray_like or poly1d


Divisor polynomial’s coefficients.    Returns 
 
qndarray


Coefficients, including those equal to zero, of the quotient.  
rndarray


Coefficients, including those equal to zero, of the remainder.      See also  
poly, polyadd, polyder, polydiv, polyfit, polyint, polymul, polysub

polyval
  Notes Both u and v must be 0-d or 1-d (ndim = 0 or 1), but u.ndim need not equal v.ndim. In other words, all four possible combinations - u.ndim = v.ndim = 0, u.ndim = v.ndim = 1, u.ndim = 1, v.ndim = 0, and u.ndim = 0, v.ndim = 1 - work. Examples  \[\frac{3x^2 + 5x + 2}{2x + 1} = 1.5x + 1.75, remainder 0.25\] >>> x = np.array([3.0, 5.0, 2.0])
>>> y = np.array([2.0, 1.0])
>>> np.polydiv(x, y)
(array([1.5 , 1.75]), array([0.25]))
numpy.polyint   numpy.polyint(p, m=1, k=None)[source]
 
Return an antiderivative (indefinite integral) of a polynomial.  Note This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in numpy.polynomial is preferred. A summary of the differences can be found in the transition guide.  The returned order m antiderivative P of polynomial p satisfies \(\frac{d^m}{dx^m}P(x) = p(x)\) and is defined up to m - 1 integration constants k. The constants determine the low-order polynomial part  \[\frac{k_{m-1}}{0!} x^0 + \ldots + \frac{k_0}{(m-1)!}x^{m-1}\] of P so that \(P^{(j)}(0) = k_{m-j-1}\).  Parameters 
 
parray_like or poly1d


Polynomial to integrate. A sequence is interpreted as polynomial coefficients, see poly1d.  
mint, optional


Order of the antiderivative. (Default: 1)  
klist of m scalars or scalar, optional


Integration constants. They are given in the order of integration: those corresponding to highest-order terms come first. If None (default), all constants are assumed to be zero. If m = 1, a single scalar can be given instead of a list.      See also  polyder

derivative of a polynomial  poly1d.integ

equivalent method    Examples The defining property of the antiderivative: >>> p = np.poly1d([1,1,1])
>>> P = np.polyint(p)
>>> P
 poly1d([ 0.33333333,  0.5       ,  1.        ,  0.        ]) # may vary
>>> np.polyder(P) == p
True
 The integration constants default to zero, but can be specified: >>> P = np.polyint(p, 3)
>>> P(0)
0.0
>>> np.polyder(P)(0)
0.0
>>> np.polyder(P, 2)(0)
0.0
>>> P = np.polyint(p, 3, k=[6,5,3])
>>> P
poly1d([ 0.01666667,  0.04166667,  0.16666667,  3. ,  5. ,  3. ]) # may vary
 Note that 3 = 6 / 2!, and that the constants are given in the order of integrations. Constant of the highest-order polynomial term comes first: >>> np.polyder(P, 2)(0)
6.0
>>> np.polyder(P, 1)(0)
5.0
>>> P(0)
3.0
numpy.polymul   numpy.polymul(a1, a2)[source]
 
Find the product of two polynomials.  Note This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in numpy.polynomial is preferred. A summary of the differences can be found in the transition guide.  Finds the polynomial resulting from the multiplication of the two input polynomials. Each input must be either a poly1d object or a 1D sequence of polynomial coefficients, from highest to lowest degree.  Parameters 
 
a1, a2array_like or poly1d object


Input polynomials.    Returns 
 
outndarray or poly1d object


The polynomial resulting from the multiplication of the inputs. If either inputs is a poly1d object, then the output is also a poly1d object. Otherwise, it is a 1D array of polynomial coefficients from highest to lowest degree.      See also  poly1d

A one-dimensional polynomial class.  
poly, polyadd, polyder, polydiv, polyfit, polyint, polysub, polyval

convolve

Array convolution. Same output as polymul, but has parameter for overlap mode.    Examples >>> np.polymul([1, 2, 3], [9, 5, 1])
array([ 9, 23, 38, 17,  3])
 Using poly1d objects: >>> p1 = np.poly1d([1, 2, 3])
>>> p2 = np.poly1d([9, 5, 1])
>>> print(p1)
   2
1 x + 2 x + 3
>>> print(p2)
   2
9 x + 5 x + 1
>>> print(np.polymul(p1, p2))
   4      3      2
9 x + 23 x + 38 x + 17 x + 3
numpy.polynomial.chebyshev.Chebyshev   class numpy.polynomial.chebyshev.Chebyshev(coef, domain=None, window=None)[source]
 
A Chebyshev series class. The Chebyshev class provides the standard Python numerical methods ‘+’, ‘-’, ‘*’, ‘//’, ‘%’, ‘divmod’, ‘**’, and ‘()’ as well as the methods listed below.  Parameters 
 
coefarray_like


Chebyshev coefficients in order of increasing degree, i.e., (1, 2, 3) gives 1*T_0(x) + 2*T_1(x) + 3*T_2(x).  
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 [-1, 1].  
window(2,) array_like, optional


Window, see domain for its use. The default value is [-1, 1].  New in version 1.6.0.      Methods  
__call__(arg) Call self as a function.  
basis(deg[, domain, window]) Series basis polynomial of degree deg.  
cast(series[, domain, window]) Convert series to series of this class.  
convert([domain, kind, window]) Convert series to a different kind and/or domain and/or window.  
copy() Return a copy.  
cutdeg(deg) Truncate series to the given degree.  
degree() The degree of the series.  
deriv([m]) Differentiate.  
fit(x, y, deg[, domain, rcond, full, w, window]) Least squares fit to data.  
fromroots(roots[, domain, window]) Return series instance that has the specified roots.  
has_samecoef(other) Check if coefficients match.  
has_samedomain(other) Check if domains match.  
has_sametype(other) Check if types match.  
has_samewindow(other) Check if windows match.  
identity([domain, window]) Identity function.  
integ([m, k, lbnd]) Integrate.  
interpolate(func, deg[, domain, args]) Interpolate a function at the Chebyshev points of the first kind.  
linspace([n, domain]) Return x, y values at equally spaced points in domain.  
mapparms() Return the mapping parameters.  
roots() Return the roots of the series polynomial.  
trim([tol]) Remove trailing coefficients  
truncate(size) Truncate series to length size.
numpy.polynomial.hermite.Hermite   class numpy.polynomial.hermite.Hermite(coef, domain=None, window=None)[source]
 
An Hermite series class. The Hermite class provides the standard Python numerical methods ‘+’, ‘-’, ‘*’, ‘//’, ‘%’, ‘divmod’, ‘**’, and ‘()’ as well as the attributes and methods listed in the ABCPolyBase documentation.  Parameters 
 
coefarray_like


Hermite coefficients in order of increasing degree, i.e, (1, 2, 3) gives 1*H_0(x) + 2*H_1(X) + 3*H_2(x).  
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 [-1, 1].  
window(2,) array_like, optional


Window, see domain for its use. The default value is [-1, 1].  New in version 1.6.0.      Methods  
__call__(arg) Call self as a function.  
basis(deg[, domain, window]) Series basis polynomial of degree deg.  
cast(series[, domain, window]) Convert series to series of this class.  
convert([domain, kind, window]) Convert series to a different kind and/or domain and/or window.  
copy() Return a copy.  
cutdeg(deg) Truncate series to the given degree.  
degree() The degree of the series.  
deriv([m]) Differentiate.  
fit(x, y, deg[, domain, rcond, full, w, window]) Least squares fit to data.  
fromroots(roots[, domain, window]) Return series instance that has the specified roots.  
has_samecoef(other) Check if coefficients match.  
has_samedomain(other) Check if domains match.  
has_sametype(other) Check if types match.  
has_samewindow(other) Check if windows match.  
identity([domain, window]) Identity function.  
integ([m, k, lbnd]) Integrate.  
linspace([n, domain]) Return x, y values at equally spaced points in domain.  
mapparms() Return the mapping parameters.  
roots() Return the roots of the series polynomial.  
trim([tol]) Remove trailing coefficients  
truncate(size) Truncate series to length size.
numpy.polynomial.hermite_e.HermiteE   class numpy.polynomial.hermite_e.HermiteE(coef, domain=None, window=None)[source]
 
An HermiteE series class. The HermiteE class provides the standard Python numerical methods ‘+’, ‘-’, ‘*’, ‘//’, ‘%’, ‘divmod’, ‘**’, and ‘()’ as well as the attributes and methods listed in the ABCPolyBase documentation.  Parameters 
 
coefarray_like


HermiteE coefficients in order of increasing degree, i.e, (1, 2, 3) gives 1*He_0(x) + 2*He_1(X) + 3*He_2(x).  
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 [-1, 1].  
window(2,) array_like, optional


Window, see domain for its use. The default value is [-1, 1].  New in version 1.6.0.      Methods  
__call__(arg) Call self as a function.  
basis(deg[, domain, window]) Series basis polynomial of degree deg.  
cast(series[, domain, window]) Convert series to series of this class.  
convert([domain, kind, window]) Convert series to a different kind and/or domain and/or window.  
copy() Return a copy.  
cutdeg(deg) Truncate series to the given degree.  
degree() The degree of the series.  
deriv([m]) Differentiate.  
fit(x, y, deg[, domain, rcond, full, w, window]) Least squares fit to data.  
fromroots(roots[, domain, window]) Return series instance that has the specified roots.  
has_samecoef(other) Check if coefficients match.  
has_samedomain(other) Check if domains match.  
has_sametype(other) Check if types match.  
has_samewindow(other) Check if windows match.  
identity([domain, window]) Identity function.  
integ([m, k, lbnd]) Integrate.  
linspace([n, domain]) Return x, y values at equally spaced points in domain.  
mapparms() Return the mapping parameters.  
roots() Return the roots of the series polynomial.  
trim([tol]) Remove trailing coefficients  
truncate(size) Truncate series to length size.
numpy.polynomial.laguerre.Laguerre   class numpy.polynomial.laguerre.Laguerre(coef, domain=None, window=None)[source]
 
A Laguerre series class. The Laguerre class provides the standard Python numerical methods ‘+’, ‘-’, ‘*’, ‘//’, ‘%’, ‘divmod’, ‘**’, and ‘()’ as well as the attributes and methods listed in the ABCPolyBase documentation.  Parameters 
 
coefarray_like


Laguerre coefficients in order of increasing degree, i.e, (1, 2, 3) gives 1*L_0(x) + 2*L_1(X) + 3*L_2(x).  
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 [0, 1].  
window(2,) array_like, optional


Window, see domain for its use. The default value is [0, 1].  New in version 1.6.0.      Methods  
__call__(arg) Call self as a function.  
basis(deg[, domain, window]) Series basis polynomial of degree deg.  
cast(series[, domain, window]) Convert series to series of this class.  
convert([domain, kind, window]) Convert series to a different kind and/or domain and/or window.  
copy() Return a copy.  
cutdeg(deg) Truncate series to the given degree.  
degree() The degree of the series.  
deriv([m]) Differentiate.  
fit(x, y, deg[, domain, rcond, full, w, window]) Least squares fit to data.  
fromroots(roots[, domain, window]) Return series instance that has the specified roots.  
has_samecoef(other) Check if coefficients match.  
has_samedomain(other) Check if domains match.  
has_sametype(other) Check if types match.  
has_samewindow(other) Check if windows match.  
identity([domain, window]) Identity function.  
integ([m, k, lbnd]) Integrate.  
linspace([n, domain]) Return x, y values at equally spaced points in domain.  
mapparms() Return the mapping parameters.  
roots() Return the roots of the series polynomial.  
trim([tol]) Remove trailing coefficients  
truncate(size) Truncate series to length size.
numpy.polynomial.legendre.Legendre   class numpy.polynomial.legendre.Legendre(coef, domain=None, window=None)[source]
 
A Legendre series class. The Legendre class provides the standard Python numerical methods ‘+’, ‘-’, ‘*’, ‘//’, ‘%’, ‘divmod’, ‘**’, and ‘()’ as well as the attributes and methods listed in the ABCPolyBase documentation.  Parameters 
 
coefarray_like


Legendre coefficients in order of increasing degree, i.e., (1, 2, 3) gives 1*P_0(x) + 2*P_1(x) + 3*P_2(x).  
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 [-1, 1].  
window(2,) array_like, optional


Window, see domain for its use. The default value is [-1, 1].  New in version 1.6.0.      Methods  
__call__(arg) Call self as a function.  
basis(deg[, domain, window]) Series basis polynomial of degree deg.  
cast(series[, domain, window]) Convert series to series of this class.  
convert([domain, kind, window]) Convert series to a different kind and/or domain and/or window.  
copy() Return a copy.  
cutdeg(deg) Truncate series to the given degree.  
degree() The degree of the series.  
deriv([m]) Differentiate.  
fit(x, y, deg[, domain, rcond, full, w, window]) Least squares fit to data.  
fromroots(roots[, domain, window]) Return series instance that has the specified roots.  
has_samecoef(other) Check if coefficients match.  
has_samedomain(other) Check if domains match.  
has_sametype(other) Check if types match.  
has_samewindow(other) Check if windows match.  
identity([domain, window]) Identity function.  
integ([m, k, lbnd]) Integrate.  
linspace([n, domain]) Return x, y values at equally spaced points in domain.  
mapparms() Return the mapping parameters.  
roots() Return the roots of the series polynomial.  
trim([tol]) Remove trailing coefficients  
truncate(size) Truncate series to length size.
numpy.polynomial.polynomial.Polynomial   class numpy.polynomial.polynomial.Polynomial(coef, domain=None, window=None)[source]
 
A power series class. The Polynomial class provides the standard Python numerical methods ‘+’, ‘-’, ‘*’, ‘//’, ‘%’, ‘divmod’, ‘**’, and ‘()’ as well as the attributes and methods listed in the ABCPolyBase documentation.  Parameters 
 
coefarray_like


Polynomial coefficients in order of increasing degree, i.e., (1, 2, 3) give 1 + 2*x + 3*x**2.  
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 [-1, 1].  
window(2,) array_like, optional


Window, see domain for its use. The default value is [-1, 1].  New in version 1.6.0.     Attributes 
 basis_name
   Methods  
__call__(arg) Call self as a function.  
basis(deg[, domain, window]) Series basis polynomial of degree deg.  
cast(series[, domain, window]) Convert series to series of this class.  
convert([domain, kind, window]) Convert series to a different kind and/or domain and/or window.  
copy() Return a copy.  
cutdeg(deg) Truncate series to the given degree.  
degree() The degree of the series.  
deriv([m]) Differentiate.  
fit(x, y, deg[, domain, rcond, full, w, window]) Least squares fit to data.  
fromroots(roots[, domain, window]) Return series instance that has the specified roots.  
has_samecoef(other) Check if coefficients match.  
has_samedomain(other) Check if domains match.  
has_sametype(other) Check if types match.  
has_samewindow(other) Check if windows match.  
identity([domain, window]) Identity function.  
integ([m, k, lbnd]) Integrate.  
linspace([n, domain]) Return x, y values at equally spaced points in domain.  
mapparms() Return the mapping parameters.  
roots() Return the roots of the series polynomial.  
trim([tol]) Remove trailing coefficients  
truncate(size) Truncate series to length size.