diff options
| -rw-r--r-- | doc/source/reference/routines.polynomials.classes.rst | 34 | ||||
| -rw-r--r-- | doc/source/reference/routines.polynomials.hermite.rst | 4 | ||||
| -rw-r--r-- | doc/source/reference/routines.polynomials.hermite_e.rst | 4 |
3 files changed, 26 insertions, 16 deletions
diff --git a/doc/source/reference/routines.polynomials.classes.rst b/doc/source/reference/routines.polynomials.classes.rst index 0651c8596..2cfbec5d9 100644 --- a/doc/source/reference/routines.polynomials.classes.rst +++ b/doc/source/reference/routines.polynomials.classes.rst @@ -56,7 +56,7 @@ the conventional Polynomial class because of its familiarity.:: Note that there are three parts to the long version of the printout. The first is the coefficients, the second is the domain, and the third is the -window.:: +window:: >>> p.coef array([ 1., 2., 3.]) @@ -66,7 +66,7 @@ window.:: array([-1., 1.]) Printing a polynomial yields a shorter form without the domain -and window.:: +and window:: >>> print p poly([ 1. 2. 3.]) @@ -91,7 +91,13 @@ Powers:: >>> p**2 Polynomial([ 1., 4., 10., 12., 9.], [-1., 1.], [-1., 1.]) -Division:: +Division: + +Floor_division, '//', is the division operator for the polynomial classes, +polynomials are treated like integers in this regard. For Python versions < +3.x the '/' operator maps to '//', as it does for Python, for later +versions the '/' will only work for division by scalars. At some point it +will be deprecated:: >>> p // P([-1, 1]) Polynomial([ 5., 3.], [-1., 1.], [-1., 1.]) @@ -120,7 +126,12 @@ Evaluation:: [ 17., 34.], [ 57., 86.]]) -Substitution:: +Substitution: + +Substitute a polynomial for x and expand the result. Here we substitute +p in itself leading to a new polynomial of degree 4 after expansion. If +the polynomials are regarded as functions this is composition of +functions:: >>> p(p) Polynomial([ 6., 16., 36., 36., 27.], [-1., 1.], [-1., 1.]) @@ -130,15 +141,11 @@ Roots:: >>> p.roots() array([-0.33333333-0.47140452j, -0.33333333+0.47140452j]) -Floor_division, '//', is the division operator for the polynomial classes, -polynomials are treated like integers in this regard. For Python versions < -3.x the '/' operator maps to '//', as it does for Python, for later -versions the '/' will only work for division by scalars. At some point it -will be deprecated. + It isn't always convenient to explicitly use Polynomial instances, so tuples, lists, arrays, and scalars are automatically cast in the arithmetic -operations.:: +operations:: >>> p + [1, 2, 3] Polynomial([ 2., 4., 6.], [-1., 1.], [-1., 1.]) @@ -170,12 +177,15 @@ arithmetic:: But different types can be used for substitution. In fact, this is how conversion of Polynomial classes among themselves is done for type, domain, -and window casting.:: +and window casting:: >>> p(T([0, 1])) Chebyshev([ 2.5, 2. , 1.5], [-1., 1.], [-1., 1.]) -The result is the polynomial 'p' cast to a Chebyshev series. +Which gives the polynomial 'p' in Chebyshev form. This works because +:math:`T_1(x) = x` and substituting :math:`x` for :math:`x` doesn't change +the original polynomial. However, all the multiplications and divisions +will be done using Chebyshev series, hence the type of the result. Calculus -------- diff --git a/doc/source/reference/routines.polynomials.hermite.rst b/doc/source/reference/routines.polynomials.hermite.rst index e8e2e1450..8ee72e97c 100644 --- a/doc/source/reference/routines.polynomials.hermite.rst +++ b/doc/source/reference/routines.polynomials.hermite.rst @@ -1,5 +1,5 @@ -Hermite Module (:mod:`numpy.polynomial.hermite`) -================================================ +Hermite Module, "Physicists'" (:mod:`numpy.polynomial.hermite`) +=============================================================== .. versionadded:: 1.6.0 diff --git a/doc/source/reference/routines.polynomials.hermite_e.rst b/doc/source/reference/routines.polynomials.hermite_e.rst index 5c84998f2..33a15bb44 100644 --- a/doc/source/reference/routines.polynomials.hermite_e.rst +++ b/doc/source/reference/routines.polynomials.hermite_e.rst @@ -1,5 +1,5 @@ -HermiteE Module (:mod:`numpy.polynomial.hermite_e`) -=================================================== +HermiteE Module, "Probabilists'" (:mod:`numpy.polynomial.hermite_e`) +==================================================================== .. versionadded:: 1.6.0 |