Coverage for local/lib/python2.7/site-packages/sage/calculus/all.py : 33%

from __future__ import absolute_import 

from .calculus import maxima as maxima_calculus 

from .calculus import (laplace, inverse_laplace, 

limit, lim) 

from .integration import numerical_integral 

integral_numerical = numerical_integral 

from .interpolation import spline, Spline 

from .functional import (diff, derivative, 

expand, 

taylor, simplify) 

from .functions import (wronskian,jacobian) 

from .ode import ode_solver, ode_system 

from .desolvers import (desolve, desolve_laplace, desolve_system, 

eulers_method, eulers_method_2x2, 

eulers_method_2x2_plot, desolve_rk4, desolve_system_rk4, 

desolve_odeint, desolve_mintides, desolve_tides_mpfr) 

from .var import (var, function, clear_vars) 

from .transforms.all import * 

# We lazy_import the following modules since they import numpy which slows down sage startup 

from sage.misc.lazy_import import lazy_import 

lazy_import("sage.calculus.riemann",["Riemann_Map"]) 

lazy_import("sage.calculus.interpolators",["polygon_spline","complex_cubic_spline"]) 

from sage.modules.all import vector 

def symbolic_expression(x): 

""" 

Create a symbolic expression or vector of symbolic expressions from x. 

INPUT: 

- ``x`` - an object 

OUTPUT: 

- a symbolic expression. 

EXAMPLES:: 

sage: a = symbolic_expression(3/2); a 

3/2 

sage: type(a) 

<type 'sage.symbolic.expression.Expression'> 

sage: R.<x> = QQ[]; type(x) 

<type 'sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint'> 

sage: a = symbolic_expression(2*x^2 + 3); a 

2*x^2 + 3 

sage: type(a) 

<type 'sage.symbolic.expression.Expression'> 

sage: from sage.symbolic.expression import is_Expression 

sage: is_Expression(a) 

True 

sage: a in SR 

True 

sage: a.parent() 

Symbolic Ring 

Note that equations exist in the symbolic ring:: 

sage: E = EllipticCurve('15a'); E 

Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 10*x - 10 over Rational Field 

sage: symbolic_expression(E) 

x*y + y^2 + y == x^3 + x^2 - 10*x - 10 

sage: symbolic_expression(E) in SR 

True 

If x is a list or tuple, create a vector of symbolic expressions:: 

sage: v=symbolic_expression([x,1]); v 

(x, 1) 

sage: v.base_ring() 

Symbolic Ring 

sage: v=symbolic_expression((x,1)); v 

(x, 1) 

sage: v.base_ring() 

Symbolic Ring 

sage: v=symbolic_expression((3,1)); v 

(3, 1) 

sage: v.base_ring() 

Symbolic Ring 

sage: E = EllipticCurve('15a'); E 

Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 10*x - 10 over Rational Field 

sage: v=symbolic_expression([E,E]); v 

(x*y + y^2 + y == x^3 + x^2 - 10*x - 10, x*y + y^2 + y == x^3 + x^2 - 10*x - 10) 

sage: v.base_ring() 

Symbolic Ring 

""" 

from sage.symbolic.expression import Expression 

from sage.symbolic.ring import SR 

if isinstance(x, Expression): 

return x 

elif hasattr(x, '_symbolic_'): 

return x._symbolic_(SR) 

elif isinstance(x, (tuple,list)): 

return vector(SR,x) 

else: 

return SR(x) 

from . import desolvers