A one-dimensional polynomial class.
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_r : array_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
System Message: WARNING/2 (x^2 + 2x + 3)
latex exited with error
[stdout]
This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/TeX Live for SUSE Linux)
restricted \write18 enabled.
entering extended mode
(./math.tex
LaTeX2e <2011/06/27>
Babel <3.9f> and hyphenation patterns for 78 languages loaded.
(/usr/share/texmf/tex/latex/base/article.cls
Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
(/usr/share/texmf/tex/latex/base/size12.clo))
(/usr/share/texmf/tex/latex/base/inputenc.sty
! LaTeX Error: File `utf8x.def’ not found.
Type X to quit or <RETURN> to proceed,
or enter new name. (Default extension: def)
Enter file name:
! Emergency stop.
<read *>
l.131 \endinput
^^M
No pages of output.
Transcript written on math.log.
, whereas poly1d([1, 2, 3], True) returns
one that represents
System Message: WARNING/2 ((x-1)(x-2)(x-3) = x^3 - 6x^2 + 11x -6)
latex exited with error
[stdout]
This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/TeX Live for SUSE Linux)
restricted \write18 enabled.
entering extended mode
(./math.tex
LaTeX2e <2011/06/27>
Babel <3.9f> and hyphenation patterns for 78 languages loaded.
(/usr/share/texmf/tex/latex/base/article.cls
Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
(/usr/share/texmf/tex/latex/base/size12.clo))
(/usr/share/texmf/tex/latex/base/inputenc.sty
! LaTeX Error: File `utf8x.def’ not found.
Type X to quit or <RETURN> to proceed,
or enter new name. (Default extension: def)
Enter file name:
! Emergency stop.
<read *>
l.131 \endinput
^^M
No pages of output.
Transcript written on math.log.
.
r : bool, optional
If True, c_or_r specifies the polynomial’s roots; the default
is False.
variable : str, optional
Changes the variable used when printing p from x to variable
(see Examples).
|
Examples
Construct the polynomial
System Message: WARNING/2 (x^2 + 2x + 3)
latex exited with error
[stdout]
This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/TeX Live for SUSE Linux)
restricted \write18 enabled.
entering extended mode
(./math.tex
LaTeX2e <2011/06/27>
Babel <3.9f> and hyphenation patterns for 78 languages loaded.
(/usr/share/texmf/tex/latex/base/article.cls
Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
(/usr/share/texmf/tex/latex/base/size12.clo))
(/usr/share/texmf/tex/latex/base/inputenc.sty
! LaTeX Error: File `utf8x.def’ not found.
Type X to quit or <RETURN> to proceed,
or enter new name. (Default extension: def)
Enter file name:
! Emergency stop.
<read *>
l.131 \endinput
^^M
No pages of output.
Transcript written on math.log.
:
>>> p = np.poly1d([1, 2, 3])
>>> print np.poly1d(p)
2
1 x + 2 x + 3
Evaluate the polynomial at
System Message: WARNING/2 (x = 0.5)
latex exited with error
[stdout]
This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/TeX Live for SUSE Linux)
restricted \write18 enabled.
entering extended mode
(./math.tex
LaTeX2e <2011/06/27>
Babel <3.9f> and hyphenation patterns for 78 languages loaded.
(/usr/share/texmf/tex/latex/base/article.cls
Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
(/usr/share/texmf/tex/latex/base/size12.clo))
(/usr/share/texmf/tex/latex/base/inputenc.sty
! LaTeX Error: File `utf8x.def’ not found.
Type X to quit or <RETURN> to proceed,
or enter new name. (Default extension: def)
Enter file name:
! Emergency stop.
<read *>
l.131 \endinput
^^M
No pages of output.
Transcript written on math.log.
:
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])
These numbers in the previous line represent (0, 0) to machine precision
Show the coefficients:
Display the order (the leading zero-coefficients are removed):
Show the coefficient of the k-th power in the polynomial
(which is equivalent to p.c[-(i+1)]):
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
Methods
deriv([m]) |
Return a derivative of this polynomial. |
integ([m, k]) |
Return an antiderivative (indefinite integral) of this polynomial. |