From: Priit Laes <[EMAIL PROTECTED]>
---
sympy/integrals/__init__.py | 2 +-
sympy/integrals/integrals.py | 45 +++++++++++++++++++++++++++
sympy/integrals/tests/test_lineintegrals.py | 9 +++++
3 files changed, 55 insertions(+), 1 deletions(-)
create mode 100644 sympy/integrals/tests/test_lineintegrals.py
diff --git a/sympy/integrals/__init__.py b/sympy/integrals/__init__.py
index 6027264..7abce35 100644
--- a/sympy/integrals/__init__.py
+++ b/sympy/integrals/__init__.py
@@ -5,4 +5,4 @@ Out[3]: log(x)
In [4]: integrate(sin(x),x)
Out[4]: -cos(x)
"""
-from integrals import integrate, Integral
+from integrals import integrate, Integral, line_integrate
diff --git a/sympy/integrals/integrals.py b/sympy/integrals/integrals.py
index 8094919..d541569 100644
--- a/sympy/integrals/integrals.py
+++ b/sympy/integrals/integrals.py
@@ -10,6 +10,7 @@ from sympy.series import limit
from sympy.polys import Poly
from sympy.solvers import solve
from sympy.functions import DiracDelta, Heaviside, Piecewise
+from sympy.geometry import Curve
class Integral(Basic):
"""Represents unevaluated integral."""
@@ -377,3 +378,47 @@ def integrate(*args, **kwargs):
return integral.doit()
else:
return integral
+
+
[EMAIL PROTECTED](use_add=False)
+def line_integrate(field, curve, vars):
+ """line_integrate(field, Curve, variables)
+
+ Compute the line integral.
+
+ Examples
+ --------
+ >>> from sympy import *
+ >>> x, y, t = symbols('xyt')
+ >>> C = Curve([E**t + 1, E**t - 1], (t, 0, ln(2)))
+ >>> line_integrate(x + y, C, [x, y])
+ 3*sqrt(2)
+
+ """
+ F = sympify(field)
+ if not F:
+ raise ValueError("Expecting function specifying field as first
argument.")
+ if not isinstance(curve, Curve):
+ raise ValueError("Expecting Curve entity as second argument.")
+ if not isinstance(vars, (list, tuple)):
+ raise ValueError("Expecting list/tuple for variables.")
+ if len(curve.functions) != len(vars):
+ raise ValueError("Field variable size does not match curve dimension.")
+
+ if curve.parameter in vars:
+ raise ValueError("Curve parameter clashes with field parameters.")
+
+ # Calculate derivatives for line parameter functions
+ # F(r) -> F(r(t)) and finally F(r(t)*r'(t))
+ Ft = F
+ dldt = 0
+ for i, var in enumerate(vars):
+ _f = curve.functions[i]
+ _dn = diff(_f, curve.parameter)
+ # ...arc length
+ dldt = dldt + (_dn * _dn)
+ Ft = Ft.subs(var, _f)
+ Ft = Ft * dldt**(S(1)/2)
+
+ integral = Integral(Ft, curve.limits).doit()
+ return integral
diff --git a/sympy/integrals/tests/test_lineintegrals.py
b/sympy/integrals/tests/test_lineintegrals.py
new file mode 100644
index 0000000..1cb8a8c
--- /dev/null
+++ b/sympy/integrals/tests/test_lineintegrals.py
@@ -0,0 +1,9 @@
+from sympy import (symbols, integrate, Integral, diff, sin, cos, pi, E, ln,
+ sympify, Curve, line_integrate, sqrt)
+
+s, t, x, y, z = symbols('stxyz')
+
+def test_lineintegral():
+ c = Curve([E**t + 1, E**t - 1], (t, 0, ln(2)))
+ assert line_integrate(x + y, c, [x, y]) == 3*sqrt(2)
+
--
1.6.0.4
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