logic.py

        if u == ZERO: return -v
        if u == v: return ZERO
        if u == -v or v == -u: return ZERO
    elif op == '*': 
        if u == ZERO or v == ZERO: return ZERO
        if u == ONE: return v
        if v == ONE: return u
        if u == v: return u ** 2
    elif op == '/': 
        if u == ZERO: return ZERO
        if v == ZERO: return Expr('Undefined')
        if u == v: return ONE
        if u == -v or v == -u: return ZERO
    elif op == '**': 
        if u == ZERO: return ZERO
        if v == ZERO: return ONE
        if u == ONE: return ONE
        if v == ONE: return u
    elif op == 'log': 
        if u == ONE: return ZERO
    else: raise ValueError("Unknown op: " + op)
    ## If we fall through to here, we can not simplify further
    return Expr(op, *args)

def d(y, x):
    "Differentiate and then simplify."
    return simp(diff(y, x))    

#_______________________________________________________________________________

# Utilities for doctest cases
# These functions print their arguments in a standard order
# to compensate for the random order in the standard representation

def ppsubst(s):
    """Print substitution s"""
    ppdict(s)

def ppdict(d):
    """Print the dictionary d.
    
    Prints a string representation of the dictionary
    with keys in sorted order according to their string
    representation: {a: A, d: D, ...}.
    >>> ppdict({'m': 'M', 'a': 'A', 'r': 'R', 'k': 'K'})
    {'a': 'A', 'k': 'K', 'm': 'M', 'r': 'R'}
    >>> ppdict({z: C, y: B, x: A})
    {x: A, y: B, z: C}
    """

    def format(k, v):
        return "%s: %s" % (repr(k), repr(v))

    ditems = d.items()
    ditems.sort(key=str)
    k, v = ditems[0]
    dpairs = format(k, v)
    for (k, v) in ditems[1:]:
        dpairs += (', ' + format(k, v))
    print '{%s}' % dpairs

def ppset(s):
    """Print the set s.

    >>> ppset(set(['A', 'Q', 'F', 'K', 'Y', 'B']))
    set(['A', 'B', 'F', 'K', 'Q', 'Y'])
    >>> ppset(set([z, y, x]))
    set([x, y, z])
    """

    slist = list(s)
    slist.sort(key=str)
    print 'set(%s)' % slist