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Merge branch 'u/vbraun/buggy_to_poly_solve' of ssh://trac.sagemath.or…
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…g/sage into ticket/16908-maxima-5.34.1

Conflicts:
	src/sage/symbolic/expression.pyx
	src/sage/symbolic/relation.py
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@pjbruin
pjbruin committed Sep 11, 2014
2 parents 2785ccc + 1fa0110 commit b8babff
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3 changes: 1 addition & 2 deletions src/sage/rings/number_field/number_field_element.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -2145,8 +2145,7 @@ cdef class NumberFieldElement(FieldElement):
sage: K.<a> = NumberField(x^3 + x - 1, embedding=0.68)
sage: b = SR(a); b # indirect doctest
1/3*(3*(1/18*sqrt(31)*sqrt(3) + 1/2)^(2/3) - 1)/(1/18*sqrt(31)*sqrt(3) + 1/2)^(1/3)
(1/18*sqrt(31)*sqrt(3) + 1/2)^(1/3) - 1/3/(1/18*sqrt(31)*sqrt(3) + 1/2)^(1/3)
sage: (b^3 + b - 1).simplify_radical()
0
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114 changes: 59 additions & 55 deletions src/sage/symbolic/expression.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -9225,7 +9225,7 @@ cdef class Expression(CommutativeRingElement):

def solve(self, x, multiplicities=False, solution_dict=False, explicit_solutions=False, to_poly_solve=False):
r"""
Analytically solve the equation ``self == 0`` or an univarite
Analytically solve the equation ``self == 0`` or a univariate
inequality for the variable `x`.
.. warning::
Expand Down Expand Up @@ -9255,8 +9255,8 @@ cdef class Expression(CommutativeRingElement):
solutions, but possibly encounter approximate solutions.
This keyword is incompatible with ``multiplicities=True``
and is not used when solving an inequality. Setting ``to_poly_solve``
to 'force' (string) omits Maxima's solve command (usefull when
some solution of trigonometric equations are lost).
to ``'force'`` omits Maxima's solve command (useful when
some solutions of trigonometric equations are lost).
EXAMPLES::
Expand All @@ -9267,7 +9267,7 @@ cdef class Expression(CommutativeRingElement):
sage: solve((z^3-1)^3, z, multiplicities=True)
([z == 1/2*I*sqrt(3) - 1/2, z == -1/2*I*sqrt(3) - 1/2, z == 1], [3, 3, 3])
A simple example to show use of the keyword
A simple example to show the use of the keyword
``multiplicities``::
sage: ((x^2-1)^2).solve(x)
Expand All @@ -9290,7 +9290,7 @@ cdef class Expression(CommutativeRingElement):
sage: solve(x*sin(x)==x^2,x,explicit_solutions=True)
[x == 0]
The following examples show use of the keyword ``to_poly_solve``::
The following examples show the use of the keyword ``to_poly_solve``::
sage: solve(abs(1-abs(1-x)) == 10, x)
[abs(abs(x - 1) - 1) == 10]
Expand Down Expand Up @@ -9339,34 +9339,32 @@ cdef class Expression(CommutativeRingElement):
sage: forget()
In some cases it may be worthwhile to directly use to_poly_solve,
In some cases it may be worthwhile to directly use ``to_poly_solve``
if one suspects some answers are being missed::
sage: solve(cos(x)==0,x)
sage: solve(cos(x)==0, x)
[x == 1/2*pi]
sage: solve(cos(x)==0,x,to_poly_solve=True)
sage: solve(cos(x)==0, x, to_poly_solve=True)
[x == 1/2*pi]
sage: from sage.calculus.calculus import maxima
sage: sol = maxima(cos(x)==0).to_poly_solve(x)
sage: sol.sage()
[[x == 1/2*pi + pi*z90]]
sage: solve(cos(x)==0, x, to_poly_solve='force')
[x == 1/2*pi + pi*z85]
If a returned unsolved expression has a denominator, but the
original one did not, this may also be true::
The same may also apply if a returned unsolved expression has a
denominator, but the original one did not::
sage: solve(cos(x) * sin(x) == 1/2, x, to_poly_solve=True)
[sin(x) == 1/2/cos(x)]
sage: from sage.calculus.calculus import maxima
sage: sol = maxima(cos(x) * sin(x) == 1/2).to_poly_solve(x)
sage: sol.sage()
[[x == 1/4*pi + pi*z...]]
sage: solve(cos(x) * sin(x) == 1/2, x, to_poly_solve=True, explicit_solutions=True)
[x == 1/4*pi + pi*z...]
sage: solve(cos(x) * sin(x) == 1/2, x, to_poly_solve='force')
[x == 1/4*pi + pi*z...]
We can also solve for several variables::
sage: var('b, c')
(b, c)
sage: solve((b-1)*(c-1), [b,c])
[[b == 1, c == r3], [b == r4, c == 1]]
[[b == 1, c == r4], [b == r5, c == 1]]
Some basic inequalities can be also solved::
Expand Down Expand Up @@ -9422,8 +9420,8 @@ cdef class Expression(CommutativeRingElement):
::
sage: solve(sin(x)==1/2,x,to_poly_solve='force')
[x == 5/6*pi + 2*pi*z..., x == 1/6*pi + 2*pi*z...]
sage: solve(sin(x)==1/2, x, to_poly_solve='force')
[x == 1/6*pi + 2*pi*z..., x == 5/6*pi + 2*pi*z...]
:trac:`11618` fixed::
Expand All @@ -9442,6 +9440,17 @@ cdef class Expression(CommutativeRingElement):
Traceback (most recent call last):
...
TypeError: (1, 2) are not valid variables.
:trac:`16651` fixed::
sage: (x^7-x-1).solve(x, to_poly_solve=True) # abs tol 1e-6
[x == 1.11277569705,
x == (-0.363623519329 - 0.952561195261*I),
x == (0.617093477784 - 0.900864951949*I),
x == (-0.809857800594 - 0.262869645851*I),
x == (-0.809857800594 + 0.262869645851*I),
x == (0.617093477784 + 0.900864951949*I),
x == (-0.363623519329 + 0.952561195261*I)]
"""
import operator
cdef Expression ex
Expand All @@ -9463,7 +9472,6 @@ cdef class Expression(CommutativeRingElement):
if multiplicities and to_poly_solve:
raise NotImplementedError("to_poly_solve does not return multiplicities")


if isinstance(x, (list, tuple)):
if not all([isinstance(i, Expression) for i in x]):
raise TypeError("%s are not valid variables." % repr(x))
Expand Down Expand Up @@ -9525,36 +9533,34 @@ cdef class Expression(CommutativeRingElement):
# but also allows for the possibility of approximate #
# solutions being returned. #
########################################################
if to_poly_solve and not multiplicities:
if len(X)==0: # if Maxima's solve gave no solutions, only try it
if to_poly_solve:
if len(X) == 0:
# Maxima's solve gave no solutions
solutions_so_far = [ex]
ignore_exceptions = True
else:
solutions_so_far = X
ignore_exceptions = False
X = []
for eq in solutions_so_far:
if eq.lhs().is_symbol() and (eq.lhs() == x) and (x not in eq.rhs().variables()):
X.append(eq)
continue
try:
s = m.to_poly_solve(x)
m = eq._maxima_()
s = m.to_poly_solve(x, options='algexact:true')
T = string_to_list_of_solutions(repr(s))
X = [t[0] for t in T]
except Exception: # if that gives an error, stick with no solutions
X = []

for eq in X:
# If the RHS of one solution also has the variable, or if
# the LHS is not the variable, try another way to get solutions
if repr(x) in map(repr, eq.rhs().variables()) or \
repr(x) in repr(eq.lhs()):
try:
# try to solve it using to_poly_solve
Y = eq._maxima_().to_poly_solve(x).sage()
X.remove(eq)
# replace with the new solutions
X.extend([y[0] for y in Y])
except TypeError as mess:
if "Error executing code in Maxima" in str(mess) or \
"unable to make sense of Maxima expression" in\
str(mess):
if explicit_solutions:
X.remove(eq) # this removes an implicit solution
else:
pass # we keep this implicit solution
else:
raise
X.extend([t[0] for t in T])
except TypeError as mess:
if ignore_exceptions:
continue
elif "Error executing code in Maxima" in str(mess) or \
"unable to make sense of Maxima expression" in \
str(mess):
if not explicit_solutions:
X.append(eq) # we keep this implicit solution
else:
raise

# make sure all the assumptions are satisfied
from sage.symbolic.assumptions import assumptions
Expand All @@ -9568,11 +9574,8 @@ cdef class Expression(CommutativeRingElement):
del ret_multiplicities[ix]
continue

# if solution_dict is True:
# Relaxed form suggested by Mike Hansen (#8553):
if solution_dict:
X=[dict([[sol.left(),sol.right()]]) for sol in X]

X = [dict([[sol.left(), sol.right()]]) for sol in X]
if multiplicities:
return X, ret_multiplicities
else:
Expand Down Expand Up @@ -9667,7 +9670,8 @@ cdef class Expression(CommutativeRingElement):
sage: b.solve(t)
[]
sage: b.solve(t, to_poly_solve=True)
[t == 1/450*I*pi*z... + 1/900*log(3/4*sqrt(41) + 25/4), t == 1/450*I*pi*z... + 1/900*log(-3/4*sqrt(41) + 25/4)]
[t == 1/450*I*pi*z... + 1/900*log(-3/4*sqrt(41) + 25/4),
t == 1/450*I*pi*z... + 1/900*log(3/4*sqrt(41) + 25/4)]
sage: n(1/900*log(-3/4*sqrt(41) + 25/4))
0.000411051404934985
Expand Down
2 changes: 1 addition & 1 deletion src/sage/symbolic/relation.py
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Original file line number Diff line number Diff line change
Expand Up @@ -615,7 +615,7 @@ def solve(f, *args, **kwds):
be implicitly an integer (hence the ``z``)::
sage: solve([cos(x)*sin(x) == 1/2, x+y == 0],x,y)
[[x == 1/4*pi + pi*z88, y == -1/4*pi - pi*z88]]
[[x == 1/4*pi + pi*z87, y == -1/4*pi - pi*z87]]
Expressions which are not equations are assumed to be set equal
to zero, as with `x` in the following example::
Expand Down

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