From: Fabian Seoane <[EMAIL PROTECTED]>
---
sympy/solvers/solvers.py | 161 +++++++++++++++++++++++-----------------------
1 files changed, 80 insertions(+), 81 deletions(-)
diff --git a/sympy/solvers/solvers.py b/sympy/solvers/solvers.py
index 6a9daf4..0c2bff1 100644
--- a/sympy/solvers/solvers.py
+++ b/sympy/solvers/solvers.py
@@ -162,89 +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('multivariate equation')
+
+ 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)
--
1.6.0.2
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups
"sympy-patches" group.
To post to this group, send email to sympy-patches@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at
http://groups.google.com/group/sympy-patches?hl=en
-~----------~----~----~----~------~----~------~--~---
