From: Fabian Seoane <[EMAIL PROTECTED]>
Also fixes a docstring that caused test_doc to fail and some formatting typos
where corrected
---
sympy/solvers/solvers.py | 167 ++++++++++++++++++-----------------
sympy/solvers/tests/test_solvers.py | 27 +++---
2 files changed, 97 insertions(+), 97 deletions(-)
diff --git a/sympy/solvers/solvers.py b/sympy/solvers/solvers.py
index dfe7d1f..5f1d5aa 100644
--- a/sympy/solvers/solvers.py
+++ b/sympy/solvers/solvers.py
@@ -53,6 +53,8 @@ def guess_solve_strategy(expr, symbol):
Examples
========
+ >>> from sympy import Symbol, Rational
+ >>> x = Symbol('x')
>>> guess_solve_strategy(x**2 + 1, x)
0
>>> guess_solve_strategy(x**Rational(1,2) + 1, x)
@@ -160,89 +162,88 @@ def solve(f, *symbols, **flags):
if isinstance(f, Equality):
f = f.lhs - f.rhs
- if len(symbols) == 1:
- symbol = symbols[0]
-
- strategy = guess_solve_strategy(f, symbol)
-
- if strategy == GS_POLY:
- poly = f.as_poly( symbol )
- assert poly is not None
- result = roots(poly, cubics=True, quartics=True).keys()
-
- elif strategy == GS_RATIONAL:
- P, Q = f.as_numer_denom()
- #TODO: check for Q != 0
- return solve(P, symbol, **flags)
-
- elif strategy == GS_POLY_CV_1:
- # we must search for a suitable change of variable
- # collect exponents
- exponents_denom = list()
- args = list(f.args)
- if isinstance(f, Add):
- for arg in args:
- if isinstance(arg, Pow):
- exponents_denom.append(arg.exp.q)
- elif isinstance(arg, Mul):
- for mul_arg in arg.args:
- if isinstance(mul_arg, Pow):
- exponents_denom.append(mul_arg.exp.q)
- elif isinstance(f, Mul):
- for mul_arg in args:
- if isinstance(mul_arg, Pow):
- exponents_denom.append(mul_arg.exp.q)
-
- assert len(exponents_denom) > 0
- if len(exponents_denom) == 1:
- m = exponents_denom[0]
- else:
- # get the GCD of the denominators
- m = ilcm(*exponents_denom)
- # x -> y**m.
- # we assume positive for simplification purposes
- t = Symbol('t', positive=True, dummy=True)
- f_ = f.subs(symbol, t**m)
- if guess_solve_strategy(f_, t) != GS_POLY:
- raise TypeError("Could not convert to a polynomial
equation: %s" % f_)
- cv_sols = solve(f_, t)
- result = list()
- for sol in cv_sols:
- result.append(sol**(S.One/m))
-
- elif strategy == GS_POLY_CV_2:
- m = 0
- args = list(f.args)
- if isinstance(f, Add):
- for arg in args:
- if isinstance(arg, Pow):
- m = min(m, arg.exp)
- elif isinstance(arg, Mul):
- for mul_arg in arg.args:
- if isinstance(mul_arg, Pow):
- m = min(m, mul_arg.exp)
- elif isinstance(f, Mul):
- for mul_arg in args:
- if isinstance(mul_arg, Pow):
- m = min(m, mul_arg.exp)
- f1 = simplify(f*symbol**(-m))
- result = solve(f1, symbol)
- # TODO: we might have introduced unwanted solutions
- # when multiplied by x**-m
-
- elif strategy == GS_TRASCENDENTAL:
- #a, b = f.as_numer_denom()
- # Let's throw away the denominator for now. When we have robust
- # assumptions, it should be checked, that for the solution,
- # b!=0.
- result = tsolve(f, *symbols)
- elif strategy == -1:
- raise Exception('Could not parse expression %s' % f)
+ if len(symbols) != 1:
+ raise NotImplementedError('Support for multivariate equation is
not implemented')
+
+ symbol = symbols[0]
+
+ strategy = guess_solve_strategy(f, symbol)
+
+ if strategy == GS_POLY:
+ poly = f.as_poly( symbol )
+ assert poly is not None
+ result = roots(poly, cubics=True, quartics=True).keys()
+
+ elif strategy == GS_RATIONAL:
+ P, Q = f.as_numer_denom()
+ #TODO: check for Q != 0
+ return solve(P, symbol, **flags)
+
+ elif strategy == GS_POLY_CV_1:
+ # we must search for a suitable change of variable
+ # collect exponents
+ exponents_denom = list()
+ args = list(f.args)
+ if isinstance(f, Add):
+ for arg in args:
+ if isinstance(arg, Pow):
+ exponents_denom.append(arg.exp.q)
+ elif isinstance(arg, Mul):
+ for mul_arg in arg.args:
+ if isinstance(mul_arg, Pow):
+ exponents_denom.append(mul_arg.exp.q)
+ elif isinstance(f, Mul):
+ for mul_arg in args:
+ if isinstance(mul_arg, Pow):
+ exponents_denom.append(mul_arg.exp.q)
+
+ assert len(exponents_denom) > 0
+ if len(exponents_denom) == 1:
+ m = exponents_denom[0]
else:
- raise NotImplementedError("No algorithms where implemented to
solve equation %s" % f)
+ # get the GCD of the denominators
+ m = ilcm(*exponents_denom)
+ # x -> y**m.
+ # we assume positive for simplification purposes
+ t = Symbol('t', positive=True, dummy=True)
+ f_ = f.subs(symbol, t**m)
+ if guess_solve_strategy(f_, t) != GS_POLY:
+ raise TypeError("Could not convert to a polynomial equation:
%s" % f_)
+ cv_sols = solve(f_, t)
+ result = list()
+ for sol in cv_sols:
+ result.append(sol**(S.One/m))
+
+ elif strategy == GS_POLY_CV_2:
+ m = 0
+ args = list(f.args)
+ if isinstance(f, Add):
+ for arg in args:
+ if isinstance(arg, Pow):
+ m = min(m, arg.exp)
+ elif isinstance(arg, Mul):
+ for mul_arg in arg.args:
+ if isinstance(mul_arg, Pow):
+ m = min(m, mul_arg.exp)
+ elif isinstance(f, Mul):
+ for mul_arg in args:
+ if isinstance(mul_arg, Pow):
+ m = min(m, mul_arg.exp)
+ f1 = simplify(f*symbol**(-m))
+ result = solve(f1, symbol)
+ # TODO: we might have introduced unwanted solutions
+ # when multiplied by x**-m
+
+ elif strategy == GS_TRASCENDENTAL:
+ #a, b = f.as_numer_denom()
+ # Let's throw away the denominator for now. When we have robust
+ # assumptions, it should be checked, that for the solution,
+ # b!=0.
+ result = tsolve(f, *symbols)
+ elif strategy == -1:
+ raise Exception('Could not parse expression %s' % f)
else:
- #TODO: if we do it the other way round we can avoid one nesting
- raise NotImplementedError('multivariate equation')
+ raise NotImplementedError("No algorithms where implemented to
solve equation %s" % f)
if flags.get('simplified', True):
return map(simplify, result)
@@ -684,10 +685,10 @@ def tsolve(eq, sym):
>>> x = Symbol('x')
>>> tsolve(3**(2*x+5)-4, x)
- (-5*log(3) + log(4))/(2*log(3))
+ [(-5*log(3) + log(4))/(2*log(3))]
>>> tsolve(log(x) + 2*x, x)
- 1/2*LambertW(2)
+ [1/2*LambertW(2)]
"""
if patterns is None:
diff --git a/sympy/solvers/tests/test_solvers.py
b/sympy/solvers/tests/test_solvers.py
index a15dd21..b5c09e8 100644
--- a/sympy/solvers/tests/test_solvers.py
+++ b/sympy/solvers/tests/test_solvers.py
@@ -29,7 +29,7 @@ def test_guess_strategy():
# polynomial equations via a change of variable
assert guess_solve_strategy( x**Rational(1,2) + 1, x ) == GS_POLY_CV_1
assert guess_solve_strategy( x**Rational(1,3) + x**Rational(1,2) + 1, x )
== GS_POLY_CV_1
-
+
# polynomial equation multiplying both sides by x**n
assert guess_solve_strategy( x + 1/x + y, x )
@@ -58,8 +58,8 @@ def test_solve_polynomial():
assert solve( x - y**3, x) == [y**3]
assert solve( x - y**3, y) == [
- (-x**Rational(1,3))/2 + I*sqrt(3)*x**Rational(1,3)/2,
- x**Rational(1,3),
+ (-x**Rational(1,3))/2 + I*sqrt(3)*x**Rational(1,3)/2,
+ x**Rational(1,3),
(-x**Rational(1,3))/2 - I*sqrt(3)*x**Rational(1,3)/2
]
@@ -75,8 +75,8 @@ def test_solve_polynomial():
assert solve((x-y, x+y), (x, y)) == solution
assert solve((x-y, x+y), [x, y]) == solution
- assert solve( x**3 - 15*x - 4, x) == [-2 + 3**Rational(1,2),
- 4,
+ assert solve( x**3 - 15*x - 4, x) == [-2 + 3**Rational(1,2),
+ 4,
-2 - 3**Rational(1,2) ]
raises(TypeError, "solve(x**2-pi, pi)")
@@ -87,28 +87,27 @@ def test_solve_polynomial_cv_1():
Test for solving on equations that can be converted to a polynomial
equation
using the change of variable y -> x**Rational(p, q)
"""
-
+
x = Symbol('x')
assert solve( x**Rational(1,2) - 1, x) == [1]
assert solve( x**Rational(1,2) - 2, x) == [sqrt(2)]
-
+
def test_solve_polynomial_cv_2():
"""
Test for solving on equations that can be converted to a polynomial
equation
multiplying both sides of the equation by x**m
"""
-
+
x = Symbol('x')
-
+
assert solve( x + 1/x - 1, x) == [Rational(1,2) + I*sqrt(3)/2,
Rational(1,2) - I*sqrt(3)/2]
-
+
def test_solve_rational():
x = Symbol('x')
y = Symbol('y')
-
+
solve( ( x - y**3 )/( (y**2)*sqrt(1 - y**2) ), x) == [x**Rational(1,3)]
-
def test_linear_system():
x, y, z, t, n = map(Symbol, 'xyztn')
@@ -181,7 +180,7 @@ def test_tsolve():
assert solve(cos(x)-y, x) == [acos(y)]
assert solve(2*cos(x)-y,x)== [acos(y/2)]
# XXX in the following test, log(2*y + 2*...) should -> log(2) + log(y
+...)
- assert solve(exp(x)+exp(-x)-y,x) == [-log(4) + log(2*y + 2*(-4 +
y**2)**Rational(1,2)),
+ assert solve(exp(x)+exp(-x)-y,x) == [-log(4) + log(2*y + 2*(-4 +
y**2)**Rational(1,2)),
-log(4) + log(2*y - 2*(-4 +
y**2)**Rational(1,2))]
assert tsolve(exp(x)-3, x) == [log(3)]
assert tsolve(Eq(exp(x), 3), x) == [log(3)]
@@ -213,5 +212,5 @@ def test_tsolve():
assert tsolve(z*cos(x), x) == [acos(0)]
- assert tsolve(exp(x)+exp(-x)-y, x)== [log(y/2 + Rational(1,2)*(-4 +
y**2)**Rational(1,2)),
+ assert tsolve(exp(x)+exp(-x)-y, x)== [log(y/2 + Rational(1,2)*(-4 +
y**2)**Rational(1,2)),
log(y/2 - Rational(1,2)*(-4 +
y**2)**Rational(1,2))]
--
1.6.0.2
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