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       """
       Actual functions to use in Sage
       ST 2012-11-13
       Command line syntax:
         use from Sage (via the "load" or the "attach" commands)
       pobyso functions come in five flavors:
       - the _so_so (arguments and returned objects are pointers to Sollya objects,
         includes the void function and the no arguments function that return a
         pointer to a Sollya object);
       - the _so_sa (argument are pointers to Sollya objects, returned objects are
         Sage/Python objects or, more generally, information is transfered from the
         Sollya world to Sage/Python world; e.g. functions without arguments that
         return a Sage/Python object);
       - the _sa_so (arguments are Sage/Python objects, returned objects are
         pointers to Sollya objects);
       - the sa_sa (arguments and returned objects are all Sage/Python objects);
       - a catch all flavor, without any suffix, (e. g. functions that have no argument
         nor return value).
       This classification is not always very strict. Conversion functions from Sollya
       to Sage/Python are sometimes decorated with Sage/Python arguments to set
       the precision. These functions remain in the so_sa category.
       NOTES:
       Reported errors in Eclipse come from the calls to
       the Sollya library
       ToDo (among other things):
        -memory management.
       """
       from ctypes import *
       import re
       from sage.symbolic.expression_conversions import polynomial
       from sage.symbolic.expression_conversions import PolynomialConverter
       """
       Create the equivalent to an enum for the Sollya function types.
       """
       (SOLLYA_BASE_FUNC_ABS,
       SOLLYA_BASE_FUNC_ACOS,
           SOLLYA_BASE_FUNC_ACOSH,
           SOLLYA_BASE_FUNC_ADD,
           SOLLYA_BASE_FUNC_ASIN,
           SOLLYA_BASE_FUNC_ASINH,
           SOLLYA_BASE_FUNC_ATAN,
           SOLLYA_BASE_FUNC_ATANH,
           SOLLYA_BASE_FUNC_CEIL,
           SOLLYA_BASE_FUNC_CONSTANT,
           SOLLYA_BASE_FUNC_COS,
           SOLLYA_BASE_FUNC_COSH,
           SOLLYA_BASE_FUNC_DIV,
           SOLLYA_BASE_FUNC_DOUBLE,
           SOLLYA_BASE_FUNC_DOUBLEDOUBLE,
           SOLLYA_BASE_FUNC_DOUBLEEXTENDED,
           SOLLYA_BASE_FUNC_ERF,
           SOLLYA_BASE_FUNC_ERFC,
           SOLLYA_BASE_FUNC_EXP,
           SOLLYA_BASE_FUNC_EXP_M1,
           SOLLYA_BASE_FUNC_FLOOR,
           SOLLYA_BASE_FUNC_FREE_VARIABLE,
           SOLLYA_BASE_FUNC_HALFPRECISION,
           SOLLYA_BASE_FUNC_LIBRARYCONSTANT,
           SOLLYA_BASE_FUNC_LIBRARYFUNCTION,
           SOLLYA_BASE_FUNC_LOG,
           SOLLYA_BASE_FUNC_LOG_10,
           SOLLYA_BASE_FUNC_LOG_1P,
           SOLLYA_BASE_FUNC_LOG_2,
           SOLLYA_BASE_FUNC_MUL,
           SOLLYA_BASE_FUNC_NEARESTINT,
           SOLLYA_BASE_FUNC_NEG,
           SOLLYA_BASE_FUNC_PI,
           SOLLYA_BASE_FUNC_POW,
           SOLLYA_BASE_FUNC_PROCEDUREFUNCTION,
           SOLLYA_BASE_FUNC_QUAD,
           SOLLYA_BASE_FUNC_SIN,
           SOLLYA_BASE_FUNC_SINGLE,
           SOLLYA_BASE_FUNC_SINH,
           SOLLYA_BASE_FUNC_SQRT,
           SOLLYA_BASE_FUNC_SUB,
           SOLLYA_BASE_FUNC_TAN,
           SOLLYA_BASE_FUNC_TANH,
       SOLLYA_BASE_FUNC_TRIPLEDOUBLE) = map(int,xrange(44))
       print "\nSuperficial pobyso check..."
       print "First constant - SOLLYA_BASE_FUNC_ABS: ", SOLLYA_BASE_FUNC_ABS
       print "Last constant  - SOLLYA_BASE_FUNC_TRIPLEDOUBLE: ", SOLLYA_BASE_FUNC_TRIPLEDOUBLE
       pobyso_max_arity = 9
       def pobyso_absolute_so_so():
           return(sollya_lib_absolute(None))
       def pobyso_autoprint(arg):
           sollya_lib_autoprint(arg,None)
       def pobyso_autoprint_so_so(arg):
           sollya_lib_autoprint(arg,None)
       def pobyso_bounds_to_range_sa_so(rnLowerBoundSa, rnUpperBoundSa, \
                                        precisionSa=None):
           """
           Return a Sollya range from to 2 RealField Sage elements.
           The Sollya range element has a sufficient precision to hold all
           the digits of the Sage bounds.
           """
           # Sanity check.
           if rnLowerBoundSa > rnUpperBoundSa:
               return None
           # Precision stuff.
           if precisionSa is None:
               # Check for the largest precision.
               lbPrecSa = rnLowerBoundSa.parent().precision()
               ubPrecSa = rnLowerBoundSa.parent().precision()
               maxPrecSa = max(lbPrecSa, ubPrecSa)
           else:
               maxPrecSa = precisionSa
           # From Sage to Sollya bounds.
           lowerBoundSo = sollya_lib_constant(get_rn_value(rnLowerBoundSa),
                                              maxPrecSa)
           upperBoundSo = sollya_lib_constant(get_rn_value(rnUpperBoundSa),
                                              maxPrecSa)
           # From Sollya bounds to range.
           rangeSo = sollya_lib_range(lowerBoundSo, upperBoundSo)
           # Back to original precision.
           # Clean up
           sollya_lib_clear_obj(lowerBoundSo)
           sollya_lib_clear_obj(upperBoundSo)
           return rangeSo
       # End pobyso_bounds_to_range_sa_so
       def pobyso_build_function_sub_so_so(exp1So, exp2So):
           return(sollya_lib_build_function_sub(exp1So, exp2So))
       def pobyso_change_var_in_function_so_so(funcSo, chvarExpSo):
           """
           Variable change in a function.
           """
           return(sollya_lib_evaluate(funcSo,chvarExpSo))
       # End pobyso_change_var_in_function_so_so
       def pobyso_chebyshevform_so_so(functionSo, degreeSo, intervalSo):
           resultSo = sollya_lib_chebyshevform(functionSo, degreeSo, intervalSo)
           return(resultSo)
       # End pobyso_chebyshevform_so_so.
       def pobyso_clear_taylorform_sa_so(taylorFormSaSo):
           """
           This method is necessary to correctly clean up the memory from Taylor forms.
           These are made of a Sollya object, a Sollya object list, a Sollya object.
           For no clearly understood reason, sollya_lib_clear_object_list crashed
           when applied to the object list.
           Here, we decompose it into Sage list of Sollya objects references and we
            clear them one by one.
           """
           sollya_lib_clear_obj(taylorFormSaSo[0])
           (coefficientsErrorsListSaSo, numElementsSa, isEndEllipticSa) = \
               pobyso_get_list_elements_so_so(taylorFormSaSo[1])
           for element in coefficientsErrorsListSaSo:
               sollya_lib_clear_obj(element)
           sollya_lib_clear_obj(taylorFormSaSo[1])
           sollya_lib_clear_obj(taylorFormSaSo[2])
       # End pobyso_clear_taylorform_sa_so
       def pobyso_cmp(rnArgSa, cteSo):
           """
           Compare the MPFR value a RealNumber with that of a Sollya constant.
           Get the value of the Sollya constant into a RealNumber and compare
           using MPFR. Could be optimized by working directly with a mpfr_t
           for the intermediate number.
           """
           # Get the precision of the Sollya constant to build a Sage RealNumber
           # with enough precision.to hold it.
           precisionOfCte = c_int(0)
           # From the Sollya constant, create a local Sage RealNumber.
           sollya_lib_get_prec_of_constant(precisionOfCte, cteSo)
           #print "Precision of constant: ", precisionOfCte
           RRRR = RealField(precisionOfCte.value)
           rnLocalSa = RRRR(0)
           sollya_lib_get_constant(get_rn_value(rnLocalSa), cteSo)
+          #
           ## Compare the Sage RealNumber version of the Sollya constant with rnArg.
           return(cmp_rn_value(rnArgSa, rnLocal))
       # End pobyso_smp
       def pobyso_compute_pos_function_abs_val_bounds_sa_sa(funcSa, lowerBoundSa, \
                                                            upperBoundSa):
           """
           TODO: completely rework and test.
           """
           pobyso = pobyso_name_free_variable_sa_so(funcSa.variables()[0])
           funcSo = pobyso_parse_string(funcSa._assume_str())
           rangeSo = pobyso_range_sa_so(lowerBoundSa, upperBoundSa)
           infnormSo = pobyso_infnorm_so_so(funcSo,rangeSo)
           # Sollya return the infnorm as an interval.
           fMaxSa = pobyso_get_interval_from_range_so_sa(infnormSo)
           # Get the top bound and compute the binade top limit.
           fMaxUpperBoundSa = fMaxSa.upper()
           binadeTopLimitSa = 2**ceil(fMaxUpperBoundSa.log2())
           # Put up together the function to use to compute the lower bound.
           funcAuxSo = pobyso_parse_string(str(binadeTopLimitSa) +  \
                                           '-(' + f._assume_str() + ')')
           pobyso_autoprint(funcAuxSo)
           # Clear the Sollya range before a new call to infnorm and issue the call.
           sollya_lib_clear_obj(infnormSo)
           infnormSo = pobyso_infnorm_so_so(funcAuxSo,rangeSo)
           fMinSa = pobyso_get_interval_from_range_so_sa(infnormSo)
           sollya_lib_clear_obj(infnormSo)
           fMinLowerBoundSa = binadeTopLimitSa - fMinSa.lower()
           # Compute the maximum of the precisions of the different bounds.
           maxPrecSa = max([fMinLowerBoundSa.parent().precision(), \
                            fMaxUpperBoundSa.parent().precision()])
           # Create a RealIntervalField and create an interval with the "good" bounds.
           RRRI = RealIntervalField(maxPrecSa)
           imageIntervalSa = RRRI(fMinLowerBoundSa, fMaxUpperBoundSa)
           # Free the unneeded Sollya objects
           sollya_lib_clear_obj(funcSo)
           sollya_lib_clear_obj(funcAuxSo)
           sollya_lib_clear_obj(rangeSo)
           return(imageIntervalSa)
       # End pobyso_compute_pos_function_abs_val_bounds_sa_sa
       def pobyso_constant(rnArg):
           """ Legacy function. See pobyso_constant_sa_so. """
           return(pobyso_constant_sa_so(rnArg))
       def pobyso_constant_sa_so(rnArgSa, precisionSa=None):
           """
           Create a Sollya constant from a Sage RealNumber.
           """
           # Precision stuff
           if precisionSa is None:
               precisionSa = rnArgSa.parent().precision()
           currentSollyaPrecisionSo = sollya_lib_get_prec()
           currentSollyaPrecisionSa = \
               pobyso_constant_from_int(currentSollyaPrecisionSo)
           # Sollya constant creation takes place here.
           if precisionSa > currentSollyaPrecisionSa:
               pobyso_set_prec_sa_so(precisionSa)
               constantSo = sollya_lib_constant(get_rn_value(rnArgSa))
               pobyso_set_prec_so_so(currentSollyaPrecisionSo)
           else:
               constantSo = sollya_lib_constant(get_rn_value(rnArgSa))
           sollya_lib_clear_obj(currentSollyaPrecisionSo)
           return constantSo
       # End pobyso_constant_sa_so
       def pobyso_constant_0_sa_so():
           """
           Obvious.
           """
           return(pobyso_constant_from_int_sa_so(0))
       def pobyso_constant_1():
           """
           Obvious.
           Legacy function. See pobyso_constant_so_so.
           """
           return(pobyso_constant_1_sa_so())
       def pobyso_constant_1_sa_so():
           """
           Obvious.
           """
           return(pobyso_constant_from_int_sa_so(1))
       def pobyso_constant_from_int(anInt):
           """ Legacy function. See pobyso_constant_from_int_sa_so. """
           return(pobyso_constant_from_int_sa_so(anInt))
       def pobyso_constant_from_int_sa_so(anInt):
           """
           Get a Sollya constant from a Sage int.
           """
           return(sollya_lib_constant_from_int(int(anInt)))
       def pobyso_constant_from_int_so_sa(constSo):
           """
           Get a Sage int from a Sollya int constant.
           Usefull for precision or powers in polynomials.
           """
           constSa = c_int(0)
           sollya_lib_get_constant_as_int(byref(constSa), constSo)
           return(constSa.value)
       # End pobyso_constant_from_int_so_sa
       def pobyso_error_so():
           return sollya_lib_error(None)
       # End pobyso_error().
       def pobyso_function_type_as_string(funcType):
           """ Legacy function. See pobyso_function_type_as_string_so_sa. """
           return(pobyso_function_type_as_string_so_sa(funcType))
       def pobyso_function_type_as_string_so_sa(funcType):
           """
           Numeric Sollya function codes -> Sage mathematical function names.
           Notice that pow -> ^ (a la Sage, not a la Python).
           """
           if funcType == SOLLYA_BASE_FUNC_ABS:
               return "abs"
           elif funcType == SOLLYA_BASE_FUNC_ACOS:
               return "arccos"
           elif funcType == SOLLYA_BASE_FUNC_ACOSH:
               return "arccosh"
           elif funcType == SOLLYA_BASE_FUNC_ADD:
               return "+"
           elif funcType == SOLLYA_BASE_FUNC_ASIN:
               return "arcsin"
           elif funcType == SOLLYA_BASE_FUNC_ASINH:
               return "arcsinh"
           elif funcType == SOLLYA_BASE_FUNC_ATAN:
               return "arctan"
           elif funcType == SOLLYA_BASE_FUNC_ATANH:
               return "arctanh"
           elif funcType == SOLLYA_BASE_FUNC_CEIL:
               return "ceil"
           elif funcType == SOLLYA_BASE_FUNC_CONSTANT:
               return "cte"
           elif funcType == SOLLYA_BASE_FUNC_COS:
               return "cos"
           elif funcType == SOLLYA_BASE_FUNC_COSH:
               return "cosh"
           elif funcType == SOLLYA_BASE_FUNC_DIV:
               return "/"
           elif funcType == SOLLYA_BASE_FUNC_DOUBLE:
               return "double"
           elif funcType == SOLLYA_BASE_FUNC_DOUBLEDOUBLE:
               return "doubleDouble"
           elif funcType == SOLLYA_BASE_FUNC_DOUBLEEXTENDED:
               return "doubleDxtended"
           elif funcType == SOLLYA_BASE_FUNC_ERF:
               return "erf"
           elif funcType == SOLLYA_BASE_FUNC_ERFC:
               return "erfc"
           elif funcType == SOLLYA_BASE_FUNC_EXP:
               return "exp"
           elif funcType == SOLLYA_BASE_FUNC_EXP_M1:
               return "expm1"
           elif funcType == SOLLYA_BASE_FUNC_FLOOR:
               return "floor"
           elif funcType == SOLLYA_BASE_FUNC_FREE_VARIABLE:
               return "freeVariable"
           elif funcType == SOLLYA_BASE_FUNC_HALFPRECISION:
               return "halfPrecision"
           elif funcType == SOLLYA_BASE_FUNC_LIBRARYCONSTANT:
               return "libraryConstant"
           elif funcType == SOLLYA_BASE_FUNC_LIBRARYFUNCTION:
               return "libraryFunction"
           elif funcType == SOLLYA_BASE_FUNC_LOG:
               return "log"
           elif funcType == SOLLYA_BASE_FUNC_LOG_10:
               return "log10"
           elif funcType == SOLLYA_BASE_FUNC_LOG_1P:
               return "log1p"
           elif funcType == SOLLYA_BASE_FUNC_LOG_2:
               return "log2"
           elif funcType == SOLLYA_BASE_FUNC_MUL:
               return "*"
           elif funcType == SOLLYA_BASE_FUNC_NEARESTINT:
               return "round"
           elif funcType == SOLLYA_BASE_FUNC_NEG:
               return "__neg__"
           elif funcType == SOLLYA_BASE_FUNC_PI:
               return "pi"
           elif funcType == SOLLYA_BASE_FUNC_POW:
               return "^"
           elif funcType == SOLLYA_BASE_FUNC_PROCEDUREFUNCTION:
               return "procedureFunction"
           elif funcType == SOLLYA_BASE_FUNC_QUAD:
               return "quad"
           elif funcType == SOLLYA_BASE_FUNC_SIN:
               return "sin"
           elif funcType == SOLLYA_BASE_FUNC_SINGLE:
               return "single"
           elif funcType == SOLLYA_BASE_FUNC_SINH:
               return "sinh"
           elif funcType == SOLLYA_BASE_FUNC_SQRT:
               return "sqrt"
           elif funcType == SOLLYA_BASE_FUNC_SUB:
               return "-"
           elif funcType == SOLLYA_BASE_FUNC_TAN:
               return "tan"
           elif funcType == SOLLYA_BASE_FUNC_TANH:
               return "tanh"
           elif funcType == SOLLYA_BASE_FUNC_TRIPLEDOUBLE:
               return "tripleDouble"
           else:
               return None
       def pobyso_get_constant(rnArgSa, constSo):
           """ Legacy function. See pobyso_get_constant_so_sa. """
           return(pobyso_get_constant_so_sa(rnArgSa, constSo))
       def pobyso_get_constant_so_sa(rnArgSa, constSo):
           """
           Set the value of rnArgSo to the value of constSo in MPFR_RNDN mode.
           rnArg must already exist and belong to some RealField.
           We assume that constSo points to a Sollya constant.
           """
           return(sollya_lib_get_constant(get_rn_value(rnArgSa), constSo))
       def pobyso_get_constant_as_rn(ctExpSo):
           """
           Legacy function. See pobyso_get_constant_as_rn_so_sa.
           """
           return(pobyso_get_constant_as_rn_so_sa(ctExpSo))
       def pobyso_get_constant_as_rn_so_sa(constExpSo):
           """
           Get a Sollya constant as a Sage "real number".
           The precision of the floating-point number returned is that of the Sollya
           constant.
           """
           precisionSa  = pobyso_get_prec_of_constant_so_sa(constExpSo)
           RRRR = RealField(precisionSa)
           rnSa = RRRR(0)
           sollya_lib_get_constant(get_rn_value(rnSa), constExpSo)
           return(rnSa)
       # End pobyso_get_constant_as_rn_so_sa
       def pobyso_get_constant_as_rn_with_rf(ctExp, realField):
           """
           Legacy function. See pobyso_get_constant_as_rn_with_rf_so_sa.
           """
           return(pobyso_get_constant_as_rn_with_rf_so_sa(ctExp, realField))
       def pobyso_get_constant_as_rn_with_rf_so_sa(ctExpSo, realFieldSa = None):
           """
           Get a Sollya constant as a Sage "real number".
           If no real field is specified, the precision of the floating-point number
           returned is that of the Sollya constant.
           Otherwise is is that of the real field. Hence rounding may happen.
           """
           if realFieldSa is None:
               sollyaPrecSa = pobyso_get_prec_of_constant_so_sa(ctExpSo)
               realFieldSa = RealField(sollyaPrecSa)
           rnSa = realFieldSa(0)
           sollya_lib_get_constant(get_rn_value(rnSa), ctExpSo)
           return(rnSa)
       # End pobyso_get_constant_as_rn_with_rf_so_sa
       def pobyso_get_free_variable_name():
           """
           Legacy function. See pobyso_get_free_variable_name_so_sa.
           """
           return(pobyso_get_free_variable_name_so_sa())
       def pobyso_get_free_variable_name_so_sa():
           return(sollya_lib_get_free_variable_name())
       def pobyso_get_function_arity(expressionSo):
           """
           Legacy function. See pobyso_get_function_arity_so_sa.
           """
           return(pobyso_get_function_arity_so_sa(expressionSo))
       def pobyso_get_function_arity_so_sa(expressionSo):
           arity = c_int(0)
           sollya_lib_get_function_arity(byref(arity),expressionSo)
           return(int(arity.value))
       def pobyso_get_head_function(expressionSo):
           """
           Legacy function. See pobyso_get_head_function_so_sa.
           """
           return(pobyso_get_head_function_so_sa(expressionSo))
       def pobyso_get_head_function_so_sa(expressionSo):
           functionType = c_int(0)
           sollya_lib_get_head_function(byref(functionType), expressionSo, None)
           return(int(functionType.value))
       def pobyso_get_interval_from_range_so_sa(soRange, realIntervalFieldSa = None ):
           """
           Return the Sage interval corresponding to the Sollya range argument.
           If no reaIntervalField is passed as an argument, the interval bounds are not
           rounded: they are elements of RealIntervalField of the "right" precision
           to hold all the digits.
           """
           prec = c_int(0)
           if realIntervalFieldSa is None:
               retval = sollya_lib_get_prec_of_range(byref(prec), soRange, None)
               if retval == 0:
                   return(None)
               realIntervalFieldSa = RealIntervalField(prec.value)
           intervalSa = realIntervalFieldSa(0,0)
           retval = \
               sollya_lib_get_interval_from_range(get_interval_value(intervalSa),\
                                                  soRange)
           if retval == 0:
               return(None)
           return(intervalSa)
       # End pobyso_get_interval_from_range_so_sa
       def pobyso_get_list_elements(soObj):
           """ Legacy function. See pobyso_get_list_elements_so_so. """
           return(pobyso_get_list_elements_so_so(soObj))
       def pobyso_get_list_elements_so_so(objectListSo):
           """
           Get the Sollya list elements as a Sage/Python array of Sollya objects.
           INPUT:
           - objectListSo: a Sollya list of Sollya objects.
           OUTPUT:
           - a Sage/Python tuple made of:
             - a Sage/Python list of Sollya objects,
             - a Sage/Python int holding the number of elements,
             - a Sage/Python int stating (!= 0) that the list is end-elliptic.
           NOTE::
               We recover the addresses of the Sollya object from the list of pointers
               returned by sollya_lib_get_list_elements. The list itself is freed.
           TODO::
               Figure out what to do with numElements since the number of elements
               can easily be recovered from the list itself.
               Ditto for isEndElliptic.
           """
           listAddress = POINTER(c_longlong)()
           numElements = c_int(0)
           isEndElliptic = c_int(0)
           listAsSageList = []
           result = sollya_lib_get_list_elements(byref(listAddress),\
                                                 byref(numElements),\
                                                 byref(isEndElliptic),\
                                                 objectListSo)
           if result == 0 :
               return None
           for i in xrange(0, numElements.value, 1):
              #listAsSageList.append(sollya_lib_copy_obj(listAddress[i]))
              listAsSageList.append(listAddress[i])
              # Clear each of the elements returned by Sollya.
              #sollya_lib_clear_obj(listAddress[i])
           # Free the list itself.
           sollya_lib_free(listAddress)
           return(listAsSageList, numElements.value, isEndElliptic.value)
       def pobyso_get_max_prec_of_exp(soExp):
           """ Legacy function. See pobyso_get_max_prec_of_exp_so_sa. """
           return(pobyso_get_max_prec_of_exp_so_sa(soExp))
       def pobyso_get_max_prec_of_exp_so_sa(expSo):
           """
           Get the maximum precision used for the numbers in a Sollya expression.
           Arguments:
           soExp -- a Sollya expression pointer
           Return value:
           A Python integer
           TODO:
           - error management;
           - correctly deal with numerical type such as DOUBLEEXTENDED.
           """
           maxPrecision = 0
           minConstPrec = 0
           currentConstPrec = 0
           operator = pobyso_get_head_function_so_sa(expSo)
           if (operator != SOLLYA_BASE_FUNC_CONSTANT) and \
           (operator != SOLLYA_BASE_FUNC_FREE_VARIABLE):
               (arity, subexpressions) = pobyso_get_subfunctions_so_sa(expSo)
               for i in xrange(arity):
                   maxPrecisionCandidate = \
                       pobyso_get_max_prec_of_exp_so_sa(subexpressions[i])
                   if maxPrecisionCandidate > maxPrecision:
                       maxPrecision = maxPrecisionCandidate
               return(maxPrecision)
           elif operator == SOLLYA_BASE_FUNC_CONSTANT:
               #minConstPrec = pobyso_get_min_prec_of_constant_so_sa(expSo)
               #currentConstPrec = pobyso_get_min_prec_of_constant_so_sa(soExp)
               #print minConstPrec, " - ", currentConstPrec
               return(pobyso_get_min_prec_of_constant_so_sa(expSo))
           elif operator == SOLLYA_BASE_FUNC_FREE_VARIABLE:
               return(0)
           else:
               print "pobyso_get_max_prec_of_exp_so_sa: unexepected operator."
               return(0)
       def pobyso_get_min_prec_of_constant_so_sa(constExpSo):
           """
           Get the minimum precision necessary to represent the value of a Sollya
           constant.
           MPFR_MIN_PREC and powers of 2 are taken into account.
           We assume that constExpSo is a point
           """
           constExpAsRnSa = pobyso_get_constant_as_rn_so_sa(constExpSo)
           return(min_mpfr_size(get_rn_value(constExpAsRnSa)))
       def pobyso_get_sage_exp_from_sollya_exp(sollyaExpSo, realField = RR):
           """ Legacy function. See pobyso_get_sage_exp_from_sollya_exp_so_sa. """
           return(pobyso_get_sage_exp_from_sollya_exp_so_sa(sollyaExpSo, \
                                                            realField = RR))
       def pobyso_get_sage_exp_from_sollya_exp_so_sa(sollyaExpSo, realFieldSa = RR):
           """
           Get a Sage expression from a Sollya expression.
           Currently only tested with polynomials with floating-point coefficients.
           Notice that, in the returned polynomial, the exponents are RealNumbers.
           """
           #pobyso_autoprint(sollyaExp)
           operatorSa = pobyso_get_head_function_so_sa(sollyaExpSo)
           sollyaLibFreeVariableName = sollya_lib_get_free_variable_name()
           # Constants and the free variable are special cases.
           # All other operator are dealt with in the same way.
           if (operatorSa != SOLLYA_BASE_FUNC_CONSTANT) and \
              (operatorSa != SOLLYA_BASE_FUNC_FREE_VARIABLE):
               (aritySa, subexpressionsSa) = pobyso_get_subfunctions_so_sa(sollyaExpSo)
               if aritySa == 1:
                   sageExpSa = eval(pobyso_function_type_as_string_so_sa(operatorSa) + \
                   "(" + pobyso_get_sage_exp_from_sollya_exp_so_sa(subexpressionsSa[0], \
                   realFieldSa) + ")")
               elif aritySa == 2:
                   # We do not get through the preprocessor.
                   # The "^" operator is then a special case.
                   if operatorSa == SOLLYA_BASE_FUNC_POW:
                       operatorAsStringSa = "**"
                   else:
                       operatorAsStringSa = \
                           pobyso_function_type_as_string_so_sa(operatorSa)
                   sageExpSa = \
                     eval("pobyso_get_sage_exp_from_sollya_exp_so_sa(subexpressionsSa[0], realFieldSa)"\
                     + " " + operatorAsStringSa + " " + \
                          "pobyso_get_sage_exp_from_sollya_exp_so_sa(subexpressionsSa[1], realFieldSa)")
               # We do not know yet how to deal with arity >= 3
               # (is there any in Sollya anyway?).
               else:
                   sageExpSa = eval('None')
               return(sageExpSa)
           elif operatorSa == SOLLYA_BASE_FUNC_CONSTANT:
               #print "This is a constant"
               return pobyso_get_constant_as_rn_with_rf_so_sa(sollyaExpSo, realFieldSa)
           elif operatorSa == SOLLYA_BASE_FUNC_FREE_VARIABLE:
               #print "This is free variable"
               return(eval(sollyaLibFreeVariableName))
           else:
               print "Unexpected"
               return eval('None')
       # End pobyso_get_sage_poly_from_sollya_poly
       def pobyso_get_poly_sa_so(polySo, realFieldSa=None):
           """
           Create a Sollya polynomial from a Sage polynomial.
           """
           pass
       # pobyso_get_poly_sa_so
       def pobyso_get_poly_so_sa(polySo, realFieldSa=None):
           """
           Convert a Sollya polynomial into a Sage polynomial.
           We assume that the polynomial is in canonical form.
           If no realField is given, a RealField corresponding to the maximum
           precision of the coefficients is internally computed.
           The real field is not returned but can be easily retrieved from
           the polynomial itself.
           ALGORITHM:
           - (optional) compute the RealField of the coefficients;
           - convert the Sollya expression into a Sage expression;
           - convert the Sage expression into a Sage polynomial
           TODO: the canonical thing for the polynomial.
           """
           if realFieldSa is None:
               expressionPrecSa = pobyso_get_max_prec_of_exp_so_sa(polySo)
               realFieldSa = RealField(expressionPrecSa)
           #print "Sollya expression before...",
           #pobyso_autoprint(polySo)
           expressionSa = pobyso_get_sage_exp_from_sollya_exp_so_sa(polySo, \
                                                                    realFieldSa)
           #print "...Sollya expression after.",
           #pobyso_autoprint(polySo)
           polyVariableSa = expressionSa.variables()[0]
           polyRingSa = realFieldSa[str(polyVariableSa)]
           #print polyRingSa
           # Do not use the polynomial(expressionSa, ring=polyRingSa) form!
           polynomialSa = polyRingSa(expressionSa)
           return(polynomialSa)
       # End pobyso_get_sage_poly_from_sollya_poly
       def pobyso_get_subfunctions(expressionSo):
           """ Legacy function. See pobyso_get_subfunctions_so_sa. """
           return(pobyso_get_subfunctions_so_sa(expressionSo))
       def pobyso_get_subfunctions_so_sa(expressionSo):
           """
           Get the subfunctions of an expression.
           Return the number of subfunctions and the list of subfunctions addresses.
           S.T.: Could not figure out another way than that ugly list of declarations
           to recover the addresses of the subfunctions.
           We limit ourselves to arity 8 functions.
           """
           subf0 = c_int(0)
           subf1 = c_int(0)
           subf2 = c_int(0)
           subf3 = c_int(0)
           subf4 = c_int(0)
           subf5 = c_int(0)
           subf6 = c_int(0)
           subf7 = c_int(0)
           subf8 = c_int(0)
           arity = c_int(0)
           nullPtr = POINTER(c_int)()
           sollya_lib_get_subfunctions(expressionSo, byref(arity), \
             byref(subf0), byref(subf1), byref(subf2), byref(subf3), \
             byref(subf4), byref(subf5),\
             byref(subf6), byref(subf7), byref(subf8), nullPtr, None)
       #    byref(cast(subfunctions[0], POINTER(c_int))), \
       #    byref(cast(subfunctions[0], POINTER(c_int))), \
       #    byref(cast(subfunctions[2], POINTER(c_int))), \
       #    byref(cast(subfunctions[3], POINTER(c_int))), \
       #    byref(cast(subfunctions[4], POINTER(c_int))), \
       #    byref(cast(subfunctions[5], POINTER(c_int))), \
       #    byref(cast(subfunctions[6], POINTER(c_int))), \
       #    byref(cast(subfunctions[7], POINTER(c_int))), \
       #    byref(cast(subfunctions[8], POINTER(c_int))), nullPtr)
           subfunctions = [subf0, subf1, subf2, subf3, subf4, subf5, subf6, subf7, \
                           subf8]
           subs = []
           if arity.value > pobyso_max_arity:
               return(0,[])
           for i in xrange(arity.value):
               subs.append(int(subfunctions[i].value))
               #print subs[i]
           return(int(arity.value), subs)
       def pobyso_get_prec():
           """ Legacy function. See pobyso_get_prec_so_sa(). """
           return(pobyso_get_prec_so_sa())
       def pobyso_get_prec_so():
           """
           Get the current default precision in Sollya.
           The return value is a Sollya object.
           Usefull when modifying the precision back and forth by avoiding
           extra conversions.
           """
           return(sollya_lib_get_prec(None))
       def pobyso_get_prec_so_sa():
           """
           Get the current default precision in Sollya.
           The return value is Sage/Python int.
           """
           precSo = sollya_lib_get_prec(None)
           precSa = c_int(0)
           sollya_lib_get_constant_as_int(byref(precSa), precSo)
           sollya_lib_clear_obj(precSo)
           return int(precSa.value)
       # End pobyso_get_prec_so_sa.
       def pobyso_get_prec_of_constant(ctExpSo):
           """ Legacy function. See pobyso_get_prec_of_constant_so_sa. """
           return(pobyso_get_prec_of_constant_so_sa(ctExpSo))
       def pobyso_get_prec_of_constant_so_sa(ctExpSo):
           prec = c_int(0)
           retc = sollya_lib_get_prec_of_constant(byref(prec), ctExpSo, None)
           if retc == 0:
               return(None)
           return(int(prec.value))
       def pobyso_get_prec_of_range_so_sa(rangeSo):
           prec = c_int(0)
           retc = sollya_lib_get_prec_of_range(byref(prec), rangeSo, None)
           if retc == 0:
               return(None)
           return(int(prec.value))
       # End pobyso_get_prec_of_range_so_sa()
       def pobyso_guess_degree_sa_sa(functionSa, intervalSa, approxErrorSa,
                                     weightSa=None, degreeBoundSa=None):
           """
           Sa_sa variant of the solly_guessdegree function.
           Return 0 if something goes wrong.
           """
           functionAsStringSa = functionSa._assume_str()
           functionSo = pobyso_parse_string_sa_so(functionAsStringSa)
           if pobyso_is_error_so_sa(functionSo):
               sollya_lib_clear_obj(functionSo)
               return 0
           rangeSo = pobyso_interval_to_range_sa_so(intervalSa)
           # The approximation error is expected to be a floating point number.
           if pobyso_is_floating_point_number_sa_sa(approxErrorSa):
               approxErrorSo = pobyso_constant_sa_so(approxErrorSa)
           else:
               approxErrorSo = pobyso_constant_sa_so(RR(approxErrorSa))
           if not weightSa is None:
               weightAsStringSa = weightSa._assume_str()
               weightSo = pobyso_parse_string_sa_so(weightAsStringSa)
               if pobyso_is_error(weightSo):
                   sollya_lib_clear_obj(functionSo)
                   sollya_lib_clear_obj(rangeSo)
                   sollya_lib_clear_obj(approxErrorSo)
                   sollya_lib_clear_obj(weightSo)
                   return 0
           else:
               weightSo = None
           if not degreeBoundSa is None:
               degreeBoundSo = pobyso_constant_from_int_sa_so(degreeBoundSa)
           else:
               degreeBoundSo = None
           guessedDegreeSa = pobyso_guess_degree_so_sa(functionSo,
                                                     rangeSo,
                                                     approxErrorSo,
                                                     weightSo,
                                                     degreeBoundSo)
           sollya_lib_clear_obj(functionSo)
           sollya_lib_clear_obj(rangeSo)
           sollya_lib_clear_obj(approxErrorSo)
           if not weightSo is None:
               sollya_lib_clear_obj(weightSo)
           if not degreeBoundSo is None:
               sollya_lib_clear_obj(degreeBoundSo)
           return guessedDegreeSa
       # End poyso_guess_degree_sa_sa
       def pobyso_guess_degree_so_sa(functionSo, rangeSo, errorSo, weightSo=None, \
                                     degreeBoundSo=None):
           """
           Thin wrapper around the guessdegree function.
           Nevertheless, some precision control stuff has been appended.
           """
           # Deal with Sollya internal precision issues: if it is too small,
           # compared with the error, increases it to about twice -log2(error).
           errorSa = pobyso_get_constant_as_rn_with_rf_so_sa(errorSo)
           log2ErrorSa = errorSa.log2()
           if log2ErrorSa < 0:
               neededPrecisionSa = int(2 * int(-log2ErrorSa) / 64) * 64
           else:
               neededPrecisionSa = int(2 * int(log2ErrorSa) / 64) * 64
           #print "Needed precision:", neededPrecisionSa
           currentPrecSa = pobyso_get_prec_so_sa()
           if neededPrecisionSa > currentPrecSa:
               currentPrecSo = pobyso_get_prec_so()
               pobyso_set_prec_sa_so(neededPrecisionSa)
           # weightSo and degreeBoundsSo are optional arguments.
           if weightSo is None:
               degreeRangeSo = sollya_lib_guessdegree(functionSo, rangeSo, errorSo, None)
           elif degreeBoundSo is None:
               degreeRangeSo =  sollya_lib_guessdegree(functionSo, rangeSo, \
                                                       errorSo, weightSo, None)
           else:
               degreeRangeSo =  sollya_lib_guessdegree(functionSo, rangeSo, errorSo, \
                                                       weightSo, degreeBoundSo, None)
           # Restore internal precision, if applicable.
           if neededPrecisionSa > currentPrecSa:
               pobyso_set_prec_so_so(currentPrecSo)
               sollya_lib_clear_obj(currentPrecSo)
           degreeIntervalSa = pobyso_range_to_interval_so_sa(degreeRangeSo)
           sollya_lib_clear_obj(degreeRangeSo)
           # When ok, both bounds match.
           # When the degree bound is too low, the upper bound is the degree
           # for which the error can be honored.
           # When it really goes wrong, the upper bound is infinity.
           if degreeIntervalSa.lower() == degreeIntervalSa.upper():
               return int(degreeIntervalSa.lower())
           else:
               if degreeIntervalSa.upper().is_infinity():
                   return None
               else:
                   return int(degreeIntervalSa.upper())
           # End pobyso_guess_degree_so_sa
       def pobyso_infnorm_so_so(func, interval, file = None, intervalList = None):
           print "Do not use this function. User pobyso_supnorm_so_so instead."
           return(None)
       def pobyso_interval_to_range_sa_so(intervalSa, precisionSa=None):
           if precisionSa is None:
               precisionSa = intervalSa.parent().precision()
           intervalSo = pobyso_bounds_to_range_sa_so(intervalSa.lower(),\
                                                     intervalSa.upper(),\
                                                     precisionSa)
           return(intervalSo)
       # End pobyso_interval_to_range_sa_so
       def pobyso_is_error_so_sa(objSo):
           """
           Thin wrapper around the sollya_lib_obj_is_error() function.
           """
           if sollya_lib_obj_is_error(objSo) != 0:
               return True
           else:
               return False
       # End pobyso_is_error-so_sa
       def pobyso_is_floating_point_number_sa_sa(numberSa):
           """
           Check whether a Sage number is floating point
           """
           return numberSa.parent().__class__ is RR.__class__
       def pobyso_lib_init():
           sollya_lib_init(None)
       def pobyso_lib_close():
           sollya_lib_close(None)
       def pobyso_name_free_variable(freeVariableNameSa):
           """ Legacy function. See pobyso_name_free_variable_sa_so. """
           pobyso_name_free_variable_sa_so(freeVariableNameSa)
       def pobyso_name_free_variable_sa_so(freeVariableNameSa):
           """
           Set the free variable name in Sollya from a Sage string.
           """
           sollya_lib_name_free_variable(freeVariableNameSa)
       def pobyso_parse_string(string):
           """ Legacy function. See pobyso_parse_string_sa_so. """
           return(pobyso_parse_string_sa_so(string))
       def pobyso_parse_string_sa_so(string):
           """
           Get the Sollya expression computed from a Sage string or
           a Sollya error object if parsing failed.
           """
           return(sollya_lib_parse_string(string))
       def pobyso_range(rnLowerBound, rnUpperBound):
           """ Legacy function. See pobyso_range_sa_so. """
           return(pobyso_range_sa_so(rnLowerBound, rnUpperBound))
       def pobyso_range_to_interval_so_sa(rangeSo, realIntervalFieldSa = None):
           """
           Get a Sage interval from a Sollya range.
           If no realIntervalField is given as a parameter, the Sage interval
           precision is that of the Sollya range.
           Otherwise, the precision is that of the realIntervalField. In this case
           rounding may happen.
           """
           if realIntervalFieldSa is None:
               precSa = pobyso_get_prec_of_range_so_sa(rangeSo)
               realIntervalFieldSa = RealIntervalField(precSa)
           intervalSa = \
               pobyso_get_interval_from_range_so_sa(rangeSo, realIntervalFieldSa)
           return(intervalSa)
       def pobyso_remez_canonical_sa_sa(func, \
                                        degree, \
                                        lowerBound, \
                                        upperBound, \
                                        weight = None, \
                                        quality = None):
           """
           All arguments are Sage/Python.
           The functions (func and weight) must be passed as expressions or strings.
           Otherwise the function fails.
           The return value is a Sage polynomial.
           """
           var('zorglub')    # Dummy variable name for type check only. Type of
           # zorglub is "symbolic expression".
           polySo = pobyso_remez_canonical_sa_so(func, \
                                        degree, \
                                        lowerBound, \
                                        upperBound, \
                                        weight, \
                                        quality)
           # String test
           if parent(func) == parent("string"):
               functionSa = eval(func)
           # Expression test.
           elif type(func) == type(zorglub):
               functionSa = func
           else:
               return None
+          #
           maxPrecision = 0
           if polySo is None:
               return(None)
           maxPrecision = pobyso_get_max_prec_of_exp_so_sa(polySo)
           RRRRSa = RealField(maxPrecision)
           polynomialRingSa = RRRRSa[functionSa.variables()[0]]
           expSa = pobyso_get_sage_exp_from_sollya_exp_so_sa(polySo, RRRRSa)
           polySa = polynomial(expSa, polynomialRingSa)
           sollya_lib_clear_obj(polySo)
           return(polySa)
       # End pobyso_remez_canonical_sa_sa
       def pobyso_remez_canonical(func, \
                                  degree, \
                                  lowerBound, \
                                  upperBound, \
                                  weight = "1", \
                                  quality = None):
           """ Legacy function. See pobyso_remez_canonical_sa_so. """
           return(pobyso_remez_canonical_sa_so(func, \
                                               degree, \
                                               lowerBound, \
                                               upperBound, \
                                               weight, \
                                               quality))
       def pobyso_remez_canonical_sa_so(func, \
                                        degree, \
                                        lowerBound, \
                                        upperBound, \
                                        weight = None, \
                                        quality = None):
           """
           All arguments are Sage/Python.
           The functions (func and weight) must be passed as expressions or strings.
           Otherwise the function fails.
           The return value is a pointer to a Sollya function.
           """
           var('zorglub')    # Dummy variable name for type check only. Type of
           # zorglub is "symbolic expression".
           currentVariableNameSa = None
           # The func argument can be of different types (string,
           # symbolic expression...)
           if parent(func) == parent("string"):
               localFuncSa = eval(func)
               if len(localFuncSa.variables()) > 0:
                   currentVariableNameSa = localFuncSa.variables()[0]
                   sollya_lib_name_free_variable(str(currentVariableNameSa))
                   functionSo = sollya_lib_parse_string(localFuncSa._assume_str())
           # Expression test.
           elif type(func) == type(zorglub):
               # Until we are able to translate Sage expressions into Sollya
               # expressions : parse the string version.
               if len(func.variables()) > 0:
                   currentVariableNameSa = func.variables()[0]
                   sollya_lib_name_free_variable(str(currentVariableNameSa))
                   functionSo = sollya_lib_parse_string(func._assume_str())
           else:
               return(None)
           if weight is None: # No weight given -> 1.
               weightSo = pobyso_constant_1_sa_so()
           elif parent(weight) == parent("string"): # Weight given as string: parse it.
               weightSo = sollya_lib_parse_string(func)
           elif type(weight) == type(zorglub): # Weight given as symbolice expression.
               functionSo = sollya_lib_parse_string_sa_so(weight._assume_str())
           else:
               return(None)
           degreeSo = pobyso_constant_from_int(degree)
           rangeSo = pobyso_bounds_to_range_sa_so(lowerBound, upperBound)
           if not quality is None:
               qualitySo= pobyso_constant_sa_so(quality)
           else:
               qualitySo = None
           remezPolySo = sollya_lib_remez(functionSo, \
                                          degreeSo, \
                                          rangeSo, \
                                          weightSo, \
                                          qualitySo, \
                                          None)
           sollya_lib_clear_obj(functionSo)
           sollya_lib_clear_obj(degreeSo)
           sollya_lib_clear_obj(rangeSo)
           sollya_lib_clear_obj(weightSo)
           if not qualitySo is None:
               sollya_lib_clear_obj(qualitySo)
           return(remezPolySo)
       # End pobyso_remez_canonical_sa_so
       def pobyso_remez_canonical_so_so(funcSo, \
                                        degreeSo, \
                                        rangeSo, \
                                        weightSo = pobyso_constant_1_sa_so(),\
                                        qualitySo = None):
           """
           All arguments are pointers to Sollya objects.
           The return value is a pointer to a Sollya function.
           """
           if not sollya_lib_obj_is_function(funcSo):
               return(None)
           return(sollya_lib_remez(funcSo, degreeSo, rangeSo, weightSo, qualitySo, None))
       def pobyso_set_canonical_off():
           sollya_lib_set_canonical(sollya_lib_off())
       def pobyso_set_canonical_on():
           sollya_lib_set_canonical(sollya_lib_on())
       def pobyso_set_prec(p):
           """ Legacy function. See pobyso_set_prec_sa_so. """
           pobyso_set_prec_sa_so(p)
       def pobyso_set_prec_sa_so(p):
           a = c_int(p)
           precSo = c_void_p(sollya_lib_constant_from_int(a))
           sollya_lib_set_prec(precSo, None)
       def pobyso_set_prec_so_so(newPrecSo):
           sollya_lib_set_prec(newPrecSo, None)
       def pobyso_supnorm_so_so(polySo, funcSo, intervalSo, errorTypeSo = None,\
                                accuracySo = None):
           """
           Computes the supnorm of the approximation error between the given
           polynomial and function.
           errorTypeSo defaults to "absolute".
           accuracySo defaults to 2^(-40).
           """
           if errorTypeSo is None:
               errorTypeSo = sollya_lib_absolute(None)
               errorTypeIsNone = True
           else:
               errorTypeIsNone = False
+          #
           if accuracySo is None:
               # Notice the **!
               accuracySo = pobyso_constant_sa_so(RR(2**(-40)))
               accuracyIsNone = True
           else:
               accuracyIsNone = False
           pobyso_autoprint(accuracySo)
           resultSo = \
               sollya_lib_supnorm(polySo, funcSo, intervalSo, errorTypeSo, \
                                     accuracySo)
           if errorTypeIsNone:
               sollya_lib_clear_obj(errorTypeSo)
           if accuracyIsNone:
               sollya_lib_clear_obj(accuracySo)
           return resultSo
       # End pobyso_supnorm_so_so
       def pobyso_taylor_expansion_with_change_var_so_so(functionSo, degreeSo, \
                                                         rangeSo, \
                                                         errorTypeSo=None, \
                                                         sollyaPrecSo=None):
           """
           Compute the Taylor expansion with the variable change
           x -> (x-intervalCenter) included.
           """
           # No global change of the working precision.
           if not sollyaPrecSo is None:
               initialPrecSo = sollya_lib_get_prec(None)
               sollya_lib_set_prec(sollyaPrecSo)
+          #
           # Error type stuff: default to absolute.
           if errorTypeSo is None:
               errorTypeIsNone = True
               errorTypeSo = sollya_lib_absolute(None)
           else:
               errorTypeIsNone = False
           intervalCenterSo = sollya_lib_mid(rangeSo)
           taylorFormSo = sollya_lib_taylorform(functionSo, degreeSo, \
                                                intervalCenterSo, \
                                                rangeSo, errorTypeSo, None)
           # taylorFormListSaSo is a Python list of Sollya objects references that
           # are copies of the elements of taylorFormSo.
           # pobyso_get_list_elements_so_so clears taylorFormSo.
           (taylorFormListSo, numElements, isEndElliptic) = \
               pobyso_get_list_elements_so_so(taylorFormSo)
           polySo = taylorFormListSo[0]
           errorRangeSo = taylorFormListSo[2]
           maxErrorSo = sollya_lib_sup(errorRangeSo)
           changeVarExpSo = sollya_lib_build_function_sub(\
                              sollya_lib_build_function_free_variable(),\
                              sollya_lib_copy_obj(intervalCenterSo))
           polyVarChangedSo = sollya_lib_evaluate(polySo, changeVarExpSo)
           sollya_lib_clear_obj(changeVarExpSo)
           # If changed, reset the Sollya working precision.
           if not sollyaPrecSo is None:
               sollya_lib_set_prec(initialPrecSo)
               sollya_lib_clear_obj(initialPrecSo)
           if errorTypeIsNone:
               sollya_lib_clear_obj(errorTypeSo)
           sollya_lib_clear_obj(taylorFormSo)
           # Do not clear maxErrorSo.
           return((polyVarChangedSo, intervalCenterSo, maxErrorSo))
       # end pobyso_taylor_expansion_with_change_var_so_so
       def pobyso_taylor_expansion_no_change_var_so_so(functionSo, degreeSo, rangeSo,
                                                       errorTypeSo=None,
                                                       sollyaPrecSo=None):
           """
           Compute the Taylor expansion without the variable change
           x -> x-intervalCenter.
           """
           # No global change of the working precision.
           if not sollyaPrecSo is None:
               initialPrecSo = sollya_lib_get_prec(None)
               sollya_lib_set_prec(sollyaPrecSo)
           # Error type stuff: default to absolute.
           if errorTypeSo is None:
               errorTypeIsNone = True
               errorTypeSo = sollya_lib_absolute(None)
           else:
               errorTypeIsNone = False
           intervalCenterSo = sollya_lib_mid(rangeSo, None)
           taylorFormSo = sollya_lib_taylorform(functionSo, degreeSo,
                                                intervalCenterSo,
                                                rangeSo, errorTypeSo, None)
           # taylorFormListSaSo is a Python list of Sollya objects references that
           # are copies of the elements of taylorFormSo.
           # pobyso_get_list_elements_so_so clears taylorFormSo.
           (taylorFormListSaSo, numElementsSa, isEndEllipticSa) = \
               pobyso_get_list_elements_so_so(taylorFormSo)
           polySo = sollya_lib_copy_obj(taylorFormListSaSo[0])
           #print "Num elements:", numElementsSa
           sollya_lib_clear_obj(taylorFormSo)
           #polySo = taylorFormListSaSo[0]
           #errorRangeSo = sollya_lib_copy_obj(taylorFormListSaSo[2])
           errorRangeSo = taylorFormListSaSo[2]
           # No copy_obj needed here: a new object is created.
           maxErrorSo = sollya_lib_sup(errorRangeSo)
           # If changed, reset the Sollya working precision.
           if not sollyaPrecSo is None:
               sollya_lib_set_prec(initialPrecSo)
               sollya_lib_clear_obj(initialPrecSo)
           if errorTypeIsNone:
               sollya_lib_clear_obj(errorTypeSo)
           pobyso_clear_taylorform_sa_so(taylorFormListSaSo)
           return((polySo, intervalCenterSo, maxErrorSo))
       # end pobyso_taylor_expansion_no_change_var_so_so
       def pobyso_taylor(function, degree, point):
           """ Legacy function. See pobysoTaylor_so_so. """
           return(pobyso_taylor_so_so(function, degree, point))
       def pobyso_taylor_so_so(functionSo, degreeSo, pointSo):
           return(sollya_lib_taylor(functionSo, degreeSo, pointSo))
       def pobyso_taylorform(function, degree, point = None,
                             interval = None, errorType=None):
           """ Legacy function. See pobyso_taylorform_sa_sa;"""
       def pobyso_taylorform_sa_sa(functionSa, \
                                   degreeSa, \
                                   pointSa, \
                                   intervalSa=None, \
                                   errorTypeSa=None, \
                                   precisionSa=None):
           """
           Compute the Taylor form of 'degreeSa' for 'functionSa' at 'pointSa'
           for 'intervalSa' with 'errorTypeSa' (a string) using 'precisionSa'.
           point: must be a Real or a Real interval.
           return the Taylor form as an array
           TODO: take care of the interval and of the point when it is an interval;
                 when errorType is not None;
                 take care of the other elements of the Taylor form (coefficients
                 errors and delta.
           """
           # Absolute as the default error.
           if errorTypeSa is None:
               errorTypeSo = sollya_lib_absolute()
           elif errorTypeSa == "relative":
               errorTypeSo = sollya_lib_relative()
           elif errortypeSa == "absolute":
               errorTypeSo = sollya_lib_absolute()
           else:
               # No clean up needed.
               return None
           # Global precision stuff
           precisionChangedSa = False
           currentSollyaPrecSo = pobyso_get_prec_so()
           currentSollyaPrecSa = pobyso_constant_from_int_so_sa(currentSollyaPrecSo)
           if not precisionSa is None:
               if precisionSa > currentSollyaPrecSa:
                   pobyso_set_prec_sa_so(precisionSa)
                   precisionChangedSa = True
           if len(functionSa.variables()) > 0:
               varSa = functionSa.variables()[0]
               pobyso_name_free_variable_sa_so(str(varSa))
           # In any case (point or interval) the parent of pointSa has a precision
           # method.
           pointPrecSa = pointSa.parent().precision()
           if precisionSa > pointPrecSa:
               pointPrecSa = precisionSa
           # In any case (point or interval) pointSa has a base_ring() method.
           pointBaseRingString = str(pointSa.base_ring())
           if re.search('Interval', pointBaseRingString) is None: # Point
               pointSo = pobyso_constant_sa_so(pointSa, pointPrecSa)
           else: # Interval.
               pointSo = pobyso_interval_to_range_sa_so(pointSa, pointPrecSa)
           # Sollyafy the function.
           functionSo = pobyso_parse_string_sa_so(functionSa._assume_str())
           if sollya_lib_obj_is_error(functionSo):
               print "pobyso_tailorform: function string can't be parsed!"
               return None
           # Sollyafy the degree
           degreeSo = sollya_lib_constant_from_int(int(degreeSa))
           # Sollyafy the point
           # Call Sollya
           taylorFormSo = \
               sollya_lib_taylorform(functionSo, degreeSo, pointSo, errorTypeSo,\
                                                None)
           sollya_lib_clear_obj(functionSo)
           sollya_lib_clear_obj(degreeSo)
           sollya_lib_clear_obj(pointSo)
           sollya_lib_clear_obj(errorTypeSo)
           (tfsAsList, numElements, isEndElliptic) = \
                   pobyso_get_list_elements_so_so(taylorFormSo)
           polySo = tfsAsList[0]
           maxPrecision = pobyso_get_max_prec_of_exp_so_sa(polySo)
           polyRealField = RealField(maxPrecision)
           expSa = pobyso_get_sage_exp_from_sollya_exp_so_sa(polySo, polyRealField)
           if precisionChangedSa:
               sollya_lib_set_prec(currentSollyaPrecSo)
               sollya_lib_clear_obj(currentSollyaPrecSo)
           polynomialRing = polyRealField[str(varSa)]
           polySa = polynomial(expSa, polynomialRing)
           taylorFormSa = [polySa]
           # Final clean-up.
           sollya_lib_clear_obj(taylorFormSo)
           return(taylorFormSa)
       # End pobyso_taylor_form_sa_sa
       def pobyso_taylorform_so_so(functionSo, degreeSo, pointSo, intervalSo=None, \
                                   errorTypeSo=None):
           createdErrorType = False
           if errorTypeSo is None:
               errorTypeSo = sollya_lib_absolute()
               createdErrorType = True
           else:
               #TODO: deal with the other case.
               pass
           if intervalSo is None:
               resultSo = sollya_lib_taylorform(functionSo, degreeSo, pointSo, \
                                                errorTypeSo, None)
           else:
               resultSo = sollya_lib_taylorform(functionSo, degreeSo, pointSo, \
                                                intervalSo, errorTypeSo, None)
           if createdErrorType:
               sollya_lib_clear_obj(errorTypeSo)
           return(resultSo)
       def pobyso_univar_polynomial_print_reverse(polySa):
           """ Legacy function. See pobyso_univar_polynomial_print_reverse_sa_sa. """
           return(pobyso_univar_polynomial_print_reverse_sa_sa(polySa))
       def pobyso_univar_polynomial_print_reverse_sa_sa(polySa):
           """
           Return the string representation of a univariate polynomial with
           monomials ordered in the x^0..x^n order of the monomials.
           Remember: Sage
           """
           polynomialRing = polySa.base_ring()
           # A very expensive solution:
           # -create a fake multivariate polynomial field with only one variable,
           #   specifying a negative lexicographical order;
           mpolynomialRing = PolynomialRing(polynomialRing.base(), \
                                            polynomialRing.variable_name(), \
 , order='neglex')
           # - convert the univariate argument polynomial into a multivariate
           #   version;
           p = mpolynomialRing(polySa)
           # - return the string representation of the converted form.
           # There is no simple str() method defined for p's class.
           return(p.__str__())
+      #
       print pobyso_get_prec()
       pobyso_set_prec(165)
       print pobyso_get_prec()
       a=100
       print type(a)
       id(a)
       print "Max arity: ", pobyso_max_arity
       print "Function tripleDouble (43) as a string: ", pobyso_function_type_as_string(43)
       print "Function None (44) as a string: ", pobyso_function_type_as_string(44)
       print "...Pobyso check done"

Laboratoire de l'Informatique et du Parallélisme » Pobyso

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