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Diffstat (limited to 'doc/source/reference/routines.polynomials.classes.rst')
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1 files changed, 24 insertions, 24 deletions
diff --git a/doc/source/reference/routines.polynomials.classes.rst b/doc/source/reference/routines.polynomials.classes.rst index 0db77eb7c..f44ddd46c 100644 --- a/doc/source/reference/routines.polynomials.classes.rst +++ b/doc/source/reference/routines.polynomials.classes.rst @@ -52,7 +52,7 @@ the conventional Polynomial class because of its familiarity:: >>> from numpy.polynomial import Polynomial as P >>> p = P([1,2,3]) >>> p - Polynomial([ 1., 2., 3.], [-1., 1.], [-1., 1.]) + Polynomial([ 1., 2., 3.], domain=[-1, 1], window=[-1, 1]) 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 @@ -77,19 +77,19 @@ we ignore them and run through the basic algebraic and arithmetic operations. Addition and Subtraction:: >>> p + p - Polynomial([ 2., 4., 6.], [-1., 1.], [-1., 1.]) + Polynomial([ 2., 4., 6.], domain=[-1, 1], window=[-1, 1]) >>> p - p - Polynomial([ 0.], [-1., 1.], [-1., 1.]) + Polynomial([ 0.], domain=[-1, 1], window=[-1, 1]) Multiplication:: >>> p * p - Polynomial([ 1., 4., 10., 12., 9.], [-1., 1.], [-1., 1.]) + Polynomial([ 1., 4., 10., 12., 9.], domain=[-1, 1], window=[-1, 1]) Powers:: >>> p**2 - Polynomial([ 1., 4., 10., 12., 9.], [-1., 1.], [-1., 1.]) + Polynomial([ 1., 4., 10., 12., 9.], domain=[-1, 1], window=[-1, 1]) Division: @@ -100,20 +100,20 @@ 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.]) + Polynomial([ 5., 3.], domain=[-1, 1], window=[-1, 1]) Remainder:: >>> p % P([-1, 1]) - Polynomial([ 6.], [-1., 1.], [-1., 1.]) + Polynomial([ 6.], domain=[-1, 1], window=[-1, 1]) Divmod:: >>> quo, rem = divmod(p, P([-1, 1])) >>> quo - Polynomial([ 5., 3.], [-1., 1.], [-1., 1.]) + Polynomial([ 5., 3.], domain=[-1, 1], window=[-1, 1]) >>> rem - Polynomial([ 6.], [-1., 1.], [-1., 1.]) + Polynomial([ 6.], domain=[-1, 1], window=[-1, 1]) Evaluation:: @@ -134,7 +134,7 @@ the polynomials are regarded as functions this is composition of functions:: >>> p(p) - Polynomial([ 6., 16., 36., 36., 27.], [-1., 1.], [-1., 1.]) + Polynomial([ 6., 16., 36., 36., 27.], domain=[-1, 1], window=[-1, 1]) Roots:: @@ -148,11 +148,11 @@ tuples, lists, arrays, and scalars are automatically cast in the arithmetic operations:: >>> p + [1, 2, 3] - Polynomial([ 2., 4., 6.], [-1., 1.], [-1., 1.]) + Polynomial([ 2., 4., 6.], domain=[-1, 1], window=[-1, 1]) >>> [1, 2, 3] * p - Polynomial([ 1., 4., 10., 12., 9.], [-1., 1.], [-1., 1.]) + Polynomial([ 1., 4., 10., 12., 9.], domain=[-1, 1], window=[-1, 1]) >>> p / 2 - Polynomial([ 0.5, 1. , 1.5], [-1., 1.], [-1., 1.]) + Polynomial([ 0.5, 1. , 1.5], domain=[-1, 1], window=[-1, 1]) Polynomials that differ in domain, window, or class can't be mixed in arithmetic:: @@ -180,7 +180,7 @@ conversion of Polynomial classes among themselves is done for type, domain, and window casting:: >>> p(T([0, 1])) - Chebyshev([ 2.5, 2. , 1.5], [-1., 1.], [-1., 1.]) + Chebyshev([ 2.5, 2. , 1.5], domain=[-1, 1], window=[-1, 1]) 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 @@ -195,18 +195,18 @@ Polynomial instances can be integrated and differentiated.:: >>> from numpy.polynomial import Polynomial as P >>> p = P([2, 6]) >>> p.integ() - Polynomial([ 0., 2., 3.], [-1., 1.], [-1., 1.]) + Polynomial([ 0., 2., 3.], domain=[-1, 1], window=[-1, 1]) >>> p.integ(2) - Polynomial([ 0., 0., 1., 1.], [-1., 1.], [-1., 1.]) + Polynomial([ 0., 0., 1., 1.], domain=[-1, 1], window=[-1, 1]) The first example integrates `p` once, the second example integrates it twice. By default, the lower bound of the integration and the integration constant are 0, but both can be specified.:: >>> p.integ(lbnd=-1) - Polynomial([-1., 2., 3.], [-1., 1.], [-1., 1.]) + Polynomial([-1., 2., 3.], domain=[-1, 1], window=[-1, 1]) >>> p.integ(lbnd=-1, k=1) - Polynomial([ 0., 2., 3.], [-1., 1.], [-1., 1.]) + Polynomial([ 0., 2., 3.], domain=[-1, 1], window=[-1, 1]) In the first case the lower bound of the integration is set to -1 and the integration constant is 0. In the second the constant of integration is set @@ -215,9 +215,9 @@ number of times the polynomial is differentiated:: >>> p = P([1, 2, 3]) >>> p.deriv(1) - Polynomial([ 2., 6.], [-1., 1.], [-1., 1.]) + Polynomial([ 2., 6.], domain=[-1, 1], window=[-1, 1]) >>> p.deriv(2) - Polynomial([ 6.], [-1., 1.], [-1., 1.]) + Polynomial([ 6.], domain=[-1, 1], window=[-1, 1]) Other Polynomial Constructors @@ -233,9 +233,9 @@ are demonstrated below:: >>> from numpy.polynomial import Chebyshev as T >>> p = P.fromroots([1, 2, 3]) >>> p - Polynomial([ -6., 11., -6., 1.], [-1., 1.], [-1., 1.]) + Polynomial([ -6., 11., -6., 1.], domain=[-1, 1], window=[-1, 1]) >>> p.convert(kind=T) - Chebyshev([ -9. , 11.75, -3. , 0.25], [-1., 1.], [-1., 1.]) + Chebyshev([ -9. , 11.75, -3. , 0.25], domain=[-1, 1], window=[-1, 1]) The convert method can also convert domain and window:: @@ -249,9 +249,9 @@ available. The cast method works like the convert method while the basis method returns the basis polynomial of given degree:: >>> P.basis(3) - Polynomial([ 0., 0., 0., 1.], [-1., 1.], [-1., 1.]) + Polynomial([ 0., 0., 0., 1.], domain=[-1, 1], window=[-1, 1]) >>> T.cast(p) - Chebyshev([ -9. , 11.75, -3. , 0.25], [-1., 1.], [-1., 1.]) + Chebyshev([ -9. , 11.75, -3. , 0.25], domain=[-1, 1], window=[-1, 1]) Conversions between types can be useful, but it is *not* recommended for routine use. The loss of numerical precision in passing from a |