from .factors import expand_double, expand_single
from .sort import move_constant
from .numerics import multiply_one, multiply_zero, reduce_fraction_constants, \
        raise_numerics, remove_zero, multiply_numerics, add_numerics
from .logarithmic import factor_in_exponent_multiplicant, \
        factor_out_exponent, raised_base, factor_out_exponent_important
from .derivatives import chain_rule
from .negation import double_negation, negated_factor, negated_nominator, \
        negated_denominator, negated_zero, negated_factor
from .fractions import multiply_with_fraction
from .integrals import factor_out_constant, integrate_variable_root
from .powers import remove_power_of_one
from .sqrt import quadrant_sqrt, extract_sqrt_mult_priority


# Functions to move to the beginning of the possibilities list. Pairs of within
# the list itself are compared by their position in the list: lower in the list
# means lower priority
HIGH = [
        raised_base,
        ]


# Functions to move to the end of the possibilities list. Pairs of within the
# list itself are compared by their position in the list: lower in the list
# means lower priority
LOW = [
        factor_in_exponent_multiplicant,
        reduce_fraction_constants,
        move_constant,
        ]


# Fucntion precedences relative to eachother. Tuple (A, B) means that A has a
# higer priority than B. This list ignores occurences in the HIGH or LOW lists
# above
RELATIVE = [
        # Precedences needed for 'power rule'
        (chain_rule, raised_base),
        (raised_base, factor_out_exponent),

        # Expand 'single' before 'double' to avoid unnessecary complexity
        (expand_single, expand_double),

        (factor_out_exponent_important, raise_numerics),

        (factor_out_constant, multiply_with_fraction),

        # int x dx  ->  int x ^ 1 dx  # do not remove power of one that has
        #                             # deliberately been inserted
        (integrate_variable_root, remove_power_of_one),

        # When simplifying square roots, bring numeric quadrants out of the
        # root first
        (extract_sqrt_mult_priority, multiply_numerics),

        # sqrt(2 ^ 2)  ->  2  # not sqrt 4
        (quadrant_sqrt, raise_numerics),
        ]


# Convert to dictionaries for efficient lookup
HIGH = dict([(h, i) for i, h in enumerate(HIGH)])
LOW = dict([(h, i) for i, h in enumerate(LOW)])


# List of implicit rules. Implicit rules are considered trivial and are
# therefore not printed in verbose rewrite_all mode
IMPLICIT_RULES = [
        negated_factor,
        double_negation,
        negated_nominator,
        negated_denominator,
        multiply_one,
        multiply_zero,
        negated_zero,
        remove_zero,
        remove_power_of_one,
        negated_factor,
        multiply_numerics,
        add_numerics,
        ]