.roots() is inconsistent between polynomials and symbolic polynomials #4728
Description
The lack of multiplicities= keyword and the failure to try to convert to a polynomial first irritates me. Actually, the default symbolic 'x' irritates me most of all, but I don't intend to open a ticket for that.
sage: (var('x') - 1).roots()
[(1, 1)]
sage: (var('x') - 1).roots(QQbar)
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (2816, 0))
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (2790, 0))
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/Users/ncalexan/.sage/temp/pv139196.reshsg.uci.edu/96844/_Users_ncalexan__sage_init_sage_0.py in <module>()
----> 1
2
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/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-packages/sage/calculus/calculus.pyc in roots(self, x, explicit_solutions)
3077 if x is None:
3078 x = self.default_variable()
-> 3079 S, mul = self.solve(x, multiplicities=True, explicit_solutions=explicit_solutions)
3080 if len(mul) == 0 and explicit_solutions:
3081 raise RuntimeError, "no explicit roots found"
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-packages/sage/calculus/calculus.pyc in solve(self, x, multiplicities, explicit_solutions)
3103 """
3104 x = var(x)
-> 3105 return (self == 0).solve(x, multiplicities=multiplicities, explicit_solutions=explicit_solutions)
3106
3107 def find_root(self, a, b, var=None, xtol=10e-13, rtol=4.5e-16, maxiter=100, full_output=False):
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-packages/sage/calculus/equations.pyc in solve(self, x, multiplicities, solution_dict, explicit_solutions)
1021 from sage.calculus.calculus import SymbolicVariable, SymbolicFunction, SymbolicFunctionEvaluation
1022 if not isinstance(x,(SymbolicVariable,SymbolicFunction,SymbolicFunctionEvaluation)):
-> 1023 raise TypeError, "%s is not a valid variable."%x
1024
1025 m = self._maxima_()
TypeError: not all arguments converted during string formatting
sage: (var('x')^2 - 1).roots(CC)
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (2816, 0))
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (2791, 0))
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (592, 0))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
/Users/ncalexan/.sage/temp/pv139196.reshsg.uci.edu/96844/_Users_ncalexan__sage_init_sage_0.py in <module>()
----> 1
2
3
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/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-packages/sage/calculus/calculus.pyc in roots(self, x, explicit_solutions)
3077 if x is None:
3078 x = self.default_variable()
-> 3079 S, mul = self.solve(x, multiplicities=True, explicit_solutions=explicit_solutions)
3080 if len(mul) == 0 and explicit_solutions:
3081 raise RuntimeError, "no explicit roots found"
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-packages/sage/calculus/calculus.pyc in solve(self, x, multiplicities, explicit_solutions)
3102 [z == e^(2*I*pi/5), z == e^(4*I*pi/5), z == e^(-(4*I*pi/5)), z == e^(-(2*I*pi/5)), z == 1]
3103 """
-> 3104 x = var(x)
3105 return (self == 0).solve(x, multiplicities=multiplicities, explicit_solutions=explicit_solutions)
3106
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-packages/sage/calculus/calculus.pyc in var(s, create)
5467 return tuple([var(x.strip()) for x in s.split(',')])
5468 elif ' ' in s:
-> 5469 return tuple([var(x.strip()) for x in s.split()])
5470 try:
5471 v = _vars[s]
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-packages/sage/calculus/calculus.pyc in var(s, create)
5476 raise ValueError, "the variable '%s' has not been defined"%var
5477 pass
-> 5478 v = SymbolicVariable(s)
5479 _vars[s] = v
5480 _syms[s] = v
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-packages/sage/calculus/calculus.pyc in __init__(self, name)
5301 raise ValueError, "variable name must be nonempty"
5302 elif not is_python_identifier.match(name):
-> 5303 raise ValueError, "variable name is not a valid Python identifier"
5304
5305 def __hash__(self):
ValueError: variable name is not a valid Python identifier
sage: (var('x')^2 - 1).roots(CC, multiplicities=False)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/Users/ncalexan/.sage/temp/pv139196.reshsg.uci.edu/96844/_Users_ncalexan__sage_init_sage_0.py in <module>()
----> 1
2
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5
TypeError: roots() got an unexpected keyword argument 'multiplicities'
sage: (QQ['x'].0^2 - 1).roots(CC, multiplicities=False)
[-1.00000000000000, 1.00000000000000]
Component: commutative algebra
Keywords: roots symbolic polynomial
Issue created by migration from https://trac.sagemath.org/ticket/4728