from calculus import maxima as maxima_calculus
from calculus import (laplace, inverse_laplace,
limit, lim)
from functional import (diff, derivative,
expand,
taylor, simplify)
from functions import (wronskian,jacobian)
from desolvers import (desolve, desolve_laplace, desolve_system,
eulers_method, eulers_method_2x2,
eulers_method_2x2_plot, desolve_rk4, desolve_system_rk4,
desolve_odeint)
from var import (var, function, clear_vars)
# 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)
import desolvers