Issue 626 is fixed by these two patches. Also, solve can now Symbol,
Function, and Derivative types.
I implemented tests and everything passes on my machine.
Thanks,
~Luke
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From c0a8c3f80c494b703a7b2a1c80ebaab691f0aaeb Mon Sep 17 00:00:00 2001
From: Luke Peterson <hazelnu...@gmail.com>
Date: Thu, 21 May 2009 18:42:24 -0700
Subject: [PATCH] Implemented code to allow for solving for Function and Derivative instances.
---
sympy/solvers/solvers.py | 56 +++++++++++++++++++++++++++++++---
sympy/solvers/tests/test_solvers.py | 20 ++++++++++++-
2 files changed, 70 insertions(+), 6 deletions(-)
diff --git a/sympy/solvers/solvers.py b/sympy/solvers/solvers.py
index ae42d4b..50ad7a4 100644
--- a/sympy/solvers/solvers.py
+++ b/sympy/solvers/solvers.py
@@ -19,7 +19,7 @@ from sympy.core.basic import Basic, S, C, Mul, Add
from sympy.core.power import Pow
from sympy.core.symbol import Symbol, Wild
from sympy.core.relational import Equality
-from sympy.core.function import Derivative, diff
+from sympy.core.function import Derivative, diff, Function
from sympy.core.numbers import ilcm
from sympy.functions import sqrt, log, exp, LambertW
@@ -148,12 +148,40 @@ def solve(f, *symbols, **flags):
symbols = map(sympify, symbols)
result = list()
- if any(not s.is_Symbol for s in symbols):
- raise TypeError('not a Symbol')
+ symbols_new = []
+ SYMBOL_SWAPPED = False
+
+ if isinstance(symbols, (list, tuple)):
+ symbols_passed = symbols[:]
+ elif isinstance(symbols, set):
+ symbols_passed = symbols.copy()
+
+ i = 0
+ for s in symbols:
+ if s.is_Symbol:
+ s_new = s
+ elif s.is_Function:
+ SYMBOL_SWAPPED = True
+ s_new = Symbol('F%d' % i, dummy=True)
+ elif s.is_Derivative:
+ SYMBOL_SWAPPED = True
+ s_new = Symbol('D%d' % i, dummy=True)
+ else:
+ raise TypeError('not a Symbol or a Function')
+ symbols_new.append(s_new)
+ i += 1
+
+ if SYMBOL_SWAPPED:
+ swap_back_dict = dict(zip(symbols_new, symbols))
if not isinstance(f, (tuple, list, set)):
f = sympify(f)
+ if SYMBOL_SWAPPED:
+ swap_dict = zip(symbols, symbols_new)
+ f = f.subs(swap_dict)
+ symbols = symbols_new
+
if isinstance(f, Equality):
f = f.lhs - f.rhs
@@ -246,6 +274,11 @@ def solve(f, *symbols, **flags):
if not f:
return {}
else:
+ if SYMBOL_SWAPPED:
+ swap_dict = zip(symbols, symbols_new)
+ f = [fi.subs(swap_dict) for fi in f]
+ symbols = symbols_new
+
polys = []
for g in f:
@@ -273,9 +306,21 @@ def solve(f, *symbols, **flags):
except ValueError:
matrix[i, m] = -coeff
- return solve_linear_system(matrix, *symbols, **flags)
+ soln = solve_linear_system(matrix, *symbols, **flags)
else:
- return solve_poly_system(polys)
+ soln = solve_poly_system(polys)
+
+ if SYMBOL_SWAPPED:
+ if isinstance(soln, dict):
+ res = {}
+ for k in soln.keys():
+ res.update({swap_back_dict[k]: soln[k]})
+ return res
+ else:
+ return soln
+ else:
+ return soln
+
def solve_linear_system(system, *symbols, **flags):
"""Solve system of N linear equations with M variables, which means
@@ -883,3 +928,4 @@ def nsolve(*args, **kwargs):
# solve the system numerically
x = findroot(f, x0, J=J, **kwargs)
return x
+
diff --git a/sympy/solvers/tests/test_solvers.py b/sympy/solvers/tests/test_solvers.py
index c5ea403..de6359e 100644
--- a/sympy/solvers/tests/test_solvers.py
+++ b/sympy/solvers/tests/test_solvers.py
@@ -113,7 +113,6 @@ def test_solve_polynomial_cv_1a():
def test_solve_polynomial_cv_1b():
x, a = symbols('x a')
-
assert set(solve(4*x*(1 - a*x**(S(1)/2)), x)) == set([S(0), 1/a**2])
assert set(solve(x * (x**(S(1)/3) - 3), x)) == set([S(0), S(27)])
@@ -261,3 +260,22 @@ def test_tsolve_1():
def test_tsolve_2():
x, y, a, b = symbols('xyab')
assert solve(y-a*x**b, x) == [y**(1/b)*(1/a)**(1/b)]
+
+
+def test_solveForFunctionsDerivatives():
+ t = Symbol('t')
+ x = Function('x')(t)
+ y = Function('y')(t)
+ a11,a12,a21,a22,b1,b2 = symbols('a11','a12','a21','a22','b1','b2')
+ soln = solve([a11*x + a12*y - b1, a21*x + a22*y - b2], x, y)
+ assert soln == { y : (a11*b2 - a21*b1)/(a11*a22 - a12*a21),
+ x : (a22*b1 - a12*b2)/(a11*a22 - a12*a21) }
+ assert solve(x-1, x) == [1]
+ assert solve(3*x-2, x) == [Rational(2,3)]
+ soln = solve([a11*x.diff(t) + a12*y.diff(t) - b1, a21*x.diff(t) +
+ a22*y.diff(t) - b2], x.diff(t), y.diff(t))
+ assert soln == { y.diff(t) : (a11*b2 - a21*b1)/(a11*a22 - a12*a21),
+ x.diff(t) : (a22*b1 - a12*b2)/(a11*a22 - a12*a21) }
+ assert solve(x.diff(t)-1, x.diff(t)) == [1]
+ assert solve(3*x.diff(t)-2, x.diff(t)) == [Rational(2,3)]
+
--
1.6.0.4
From aeef51e6907af4062909c101e2c1b7164ae1813e Mon Sep 17 00:00:00 2001
From: Luke Peterson <hazelnu...@gmail.com>
Date: Fri, 22 May 2009 10:33:07 -0700
Subject: [PATCH] More functionality to allow solve to work with sets and Derivative objects.
---
sympy/core/basic.py | 1 +
sympy/solvers/solvers.py | 2 +-
sympy/solvers/tests/test_solvers.py | 8 ++++++++
3 files changed, 10 insertions(+), 1 deletions(-)
diff --git a/sympy/core/basic.py b/sympy/core/basic.py
index b48e633..f5a7556 100644
--- a/sympy/core/basic.py
+++ b/sympy/core/basic.py
@@ -70,6 +70,7 @@ ordering_of_classes = [
'Lambda',
# operators
'FDerivative','FApply',
+
# composition of functions
'FPow', 'Composition',
# Landau O symbol
diff --git a/sympy/solvers/solvers.py b/sympy/solvers/solvers.py
index 50ad7a4..e9d1445 100644
--- a/sympy/solvers/solvers.py
+++ b/sympy/solvers/solvers.py
@@ -154,7 +154,7 @@ def solve(f, *symbols, **flags):
if isinstance(symbols, (list, tuple)):
symbols_passed = symbols[:]
elif isinstance(symbols, set):
- symbols_passed = symbols.copy()
+ symbols_passed = list(symbols)
i = 0
for s in symbols:
diff --git a/sympy/solvers/tests/test_solvers.py b/sympy/solvers/tests/test_solvers.py
index de6359e..6a191f4 100644
--- a/sympy/solvers/tests/test_solvers.py
+++ b/sympy/solvers/tests/test_solvers.py
@@ -278,4 +278,12 @@ def test_solveForFunctionsDerivatives():
x.diff(t) : (a22*b1 - a12*b2)/(a11*a22 - a12*a21) }
assert solve(x.diff(t)-1, x.diff(t)) == [1]
assert solve(3*x.diff(t)-2, x.diff(t)) == [Rational(2,3)]
+ eqns = set((3*x - 1, 2*y-4))
+ assert solve(eqns, set((x,y))) == { x : Rational(1, 3), y: 2 }
+
+ x = Symbol('x')
+ f = Function('f')
+ F = x**2 + f(x)**2 - 4*x - 1
+ assert solve(F.diff(x), diff(f(x), x)) == [(2 - x)/f(x)]
+
--
1.6.0.4
