Python Mul._from_args方法代码示例

# 需要导入模块: from sympy.core.mul import Mul [as 别名]
# 或者: from sympy.core.mul.Mul import _from_args [as 别名]
def factor_terms(expr, radical=False):
    """Remove common factors from terms in all arguments without
    changing the underlying structure of the expr. No expansion or
    simplification (and no processing of non-commutatives) is performed.

    If radical=True then a radical common to all terms will be factored
    out of any Add sub-expressions of the expr.

    Examples
    ========

    >>> from sympy import factor_terms, Symbol
    >>> from sympy.abc import x, y
    >>> factor_terms(x + x*(2 + 4*y)**3)
    x*(8*(2*y + 1)**3 + 1)
    >>> A = Symbol('A', commutative=False)
    >>> factor_terms(x*A + x*A + x*y*A)
    x*(y*A + 2*A)

    """

    expr = sympify(expr)
    is_iterable = iterable(expr)

    if not isinstance(expr, Basic) or expr.is_Atom:
        if is_iterable:
            return type(expr)([factor_terms(i, radical=radical) for i in expr])
        return expr

    if expr.is_Function or is_iterable or not hasattr(expr, 'args_cnc'):
        args = expr.args
        newargs = tuple([factor_terms(i, radical=radical) for i in args])
        if newargs == args:
            return expr
        return expr.func(*newargs)

    cont, p = expr.as_content_primitive(radical=radical)
    list_args, nc = zip(*[ai.args_cnc() for ai in Add.make_args(p)])
    list_args = list(list_args)
    nc = [((Dummy(), Mul._from_args(i)) if i else None) for i in nc]
    ncreps = dict([i for i in nc if i is not None])
    for i, a in enumerate(list_args):
        if nc[i] is not None:
            a.append(nc[i][0])
        a = Mul._from_args(a) # gcd_terms will fix up ordering
        list_args[i] = gcd_terms(a, isprimitive=True)
        # cancel terms that may not have cancelled
    p = Add._from_args(list_args) # gcd_terms will fix up ordering
    p = gcd_terms(p, isprimitive=True).xreplace(ncreps)
    return _keep_coeff(cont, p)

# 需要导入模块: from sympy.core.mul import Mul [as 别名]
# 或者: from sympy.core.mul.Mul import _from_args [as 别名]
 def mask(terms):
     """replace nc portions of each term with a unique Dummy symbols
     and return the replacements to restore them"""
     args = [(a, []) if a.is_commutative else a.args_cnc() for a in terms]
     reps = []
     for i, (c, nc) in enumerate(args):
         if nc:
             nc = Mul._from_args(nc)
             d = Dummy()
             reps.append((d, nc))
             c.append(d)
             args[i] = Mul._from_args(c)
         else:
             args[i] = c
     return args, dict(reps)

# 需要导入模块: from sympy.core.mul import Mul [as 别名]
# 或者: from sympy.core.mul.Mul import _from_args [as 别名]
def factor_terms(expr):
    """Remove common factors from terms in all arguments without
    changing the underlying structure of the expr. No expansion or
    simplification (and no processing of non-commutative) is performed.

    **Examples**

    >>> from sympy import factor_terms, Symbol
    >>> from sympy.abc import x, y
    >>> factor_terms(x + x*(2 + 4*y)**3)
    x*(8*(2*y + 1)**3 + 1)
    >>> A = Symbol('A', commutative=False)
    >>> factor_terms(x*A + x*A + x*y*A)
    x*(y*A + 2*A)

    """

    expr = sympify(expr)

    if iterable(expr):
        return type(expr)([factor_terms(i) for i in expr])

    if not isinstance(expr, Basic) or expr.is_Atom:
        return expr

    if expr.is_Function:
        return expr.func(*[factor_terms(i) for i in expr.args])

    cont, p = expr.as_content_primitive()
    list_args, nc = zip(*[ai.args_cnc(clist=True) for ai in Add.make_args(p)])
    list_args = list(list_args)
    nc = [((Dummy(), Mul._from_args(i)) if i else None) for i in nc]
    ncreps = dict([i for i in nc if i is not None])
    for i, a in enumerate(list_args):
        if nc[i] is not None:
           a.append(nc[i][0])
        a = Mul._from_args(a) # gcd_terms will fix up ordering
        list_args[i] = gcd_terms(a, isprimitive=True)
        # cancel terms that may not have cancelled
    p = Add._from_args(list_args) # gcd_terms will fix up ordering
    p = gcd_terms(p, isprimitive=True).subs(ncreps) # exact subs could be used here
    return _keep_coeff(cont, p)

# 需要导入模块: from sympy.core.mul import Mul [as 别名]
# 或者: from sympy.core.mul.Mul import _from_args [as 别名]
def factor_nc(expr):
    """Return the factored form of ``expr`` while handling non-commutative
    expressions.

    **examples**
    >>> from sympy.core.exprtools import factor_nc
    >>> from sympy import Symbol
    >>> from sympy.abc import x
    >>> A = Symbol('A', commutative=False)
    >>> B = Symbol('B', commutative=False)
    >>> factor_nc((x**2 + 2*A*x + A**2).expand())
    (x + A)**2
    >>> factor_nc(((x + A)*(x + B)).expand())
    (x + A)*(x + B)
    """
    from sympy.simplify.simplify import _mexpand
    from sympy.polys import gcd, factor

    expr = sympify(expr)
    if not isinstance(expr, Expr) or not expr.args:
        return expr
    if not expr.is_Add:
        return expr.func(*[factor_nc(a) for a in expr.args])

    expr, rep, nc_symbols = _mask_nc(expr)
    if rep:
        return factor(expr).subs(rep)
    else:
        args = [a.args_cnc() for a in Add.make_args(expr)]
        c = g = l = r = S.One
        hit = False
        # find any commutative gcd term
        for i, a in enumerate(args):
            if i == 0:
                c = Mul._from_args(a[0])
            elif a[0]:
                c = gcd(c, Mul._from_args(a[0]))
            else:
                c = S.One
        if c is not S.One:
            hit = True
            c, g = c.as_coeff_Mul()
            if g is not S.One:
                for i, (cc, _) in enumerate(args):
                    cc = list(Mul.make_args(Mul._from_args(list(cc))/g))
                    args[i][0] = cc
            else:
                for i, (cc, _) in enumerate(args):
                    cc[0] = cc[0]/c
                    args[i][0] = cc
        # find any noncommutative common prefix
        for i, a in enumerate(args):
            if i == 0:
                n = a[1][:]
            else:
                n = common_prefix(n, a[1])
            if not n:
                # is there a power that can be extracted?
                if not args[0][1]:
                    break
                b, e = args[0][1][0].as_base_exp()
                ok = False
                if e.is_Integer:
                    for t in args:
                        if not t[1]:
                            break
                        bt, et = t[1][0].as_base_exp()
                        if et.is_Integer and bt == b:
                            e = min(e, et)
                        else:
                            break
                    else:
                        ok = hit = True
                        l = b**e
                        il = b**-e
                        for i, a in enumerate(args):
                            args[i][1][0] = il*args[i][1][0]
                        break
                if not ok:
                    break
        else:
            hit = True
            lenn = len(n)
            l = Mul(*n)
            for i, a in enumerate(args):
                args[i][1] = args[i][1][lenn:]
        # find any noncommutative common suffix
        for i, a in enumerate(args):
            if i == 0:
                n = a[1][:]
            else:
                n = common_suffix(n, a[1])
            if not n:
                # is there a power that can be extracted?
                if not args[0][1]:
                    break
                b, e = args[0][1][-1].as_base_exp()
                ok = False
                if e.is_Integer:
                    for t in args:
#.........这里部分代码省略.........

# 需要导入模块: from sympy.core.mul import Mul [as 别名]
# 或者: from sympy.core.mul.Mul import _from_args [as 别名]
    def __init__(self, factors=None):  # Factors
        """Initialize Factors from dict or expr.

        Examples
        ========

        >>> from sympy.core.exprtools import Factors
        >>> from sympy.abc import x
        >>> from sympy import I
        >>> e = 2*x**3
        >>> Factors(e)
        Factors({2: 1, x: 3})
        >>> Factors(e.as_powers_dict())
        Factors({2: 1, x: 3})
        >>> f = _
        >>> f.factors  # underlying dictionary
        {2: 1, x: 3}
        >>> f.gens  # base of each factor
        frozenset([2, x])
        >>> Factors(0)
        Factors({0: 1})
        >>> Factors(I)
        Factors({I: 1})

        Notes
        =====

        Although a dictionary can be passed, only minimal checking is
        performed: powers of -1 and I are made canonical.

        """
        if isinstance(factors, (SYMPY_INTS, float)):
            factors = S(factors)

        if isinstance(factors, Factors):
            factors = factors.factors.copy()
        elif factors is None or factors is S.One:
            factors = {}
        elif factors is S.Zero or factors == 0:
            factors = {S.Zero: S.One}
        elif isinstance(factors, Number):
            n = factors
            factors = {}
            if n < 0:
                factors[S.NegativeOne] = S.One
                n = -n
            if n is not S.One:
                if n.is_Float or n.is_Integer or n is S.Infinity:
                    factors[n] = S.One
                elif n.is_Rational:
                    # since we're processing Numbers, the denominator is
                    # stored with a negative exponent; all other factors
                    # are left .
                    if n.p != 1:
                        factors[Integer(n.p)] = S.One
                    factors[Integer(n.q)] = S.NegativeOne
                else:
                    raise ValueError('Expected Float|Rational|Integer, not %s' % n)
        elif isinstance(factors, Basic) and not factors.args:
            factors = {factors: S.One}
        elif isinstance(factors, Expr):
            c, nc = factors.args_cnc()
            i = c.count(I)
            for _ in range(i):
                c.remove(I)
            factors = dict(Mul._from_args(c).as_powers_dict())
            if i:
                factors[I] = S.One*i
            if nc:
                factors[Mul(*nc, evaluate=False)] = S.One
        else:
            factors = factors.copy()  # /!\ should be dict-like

            # tidy up -/+1 and I exponents if Rational

            handle = []
            for k in factors:
                if k is I or k in (-1, 1):
                    handle.append(k)
            if handle:
                i1 = S.One
                for k in handle:
                    if not _isnumber(factors[k]):
                        continue
                    i1 *= k**factors.pop(k)
                if i1 is not S.One:
                    for a in i1.args if i1.is_Mul else [i1]:  # at worst, -1.0*I*(-1)**e
                        if a is S.NegativeOne:
                            factors[a] = S.One
                        elif a is I:
                            factors[I] = S.One
                        elif a.is_Pow:
                            if S.NegativeOne not in factors:
                                factors[S.NegativeOne] = S.Zero
                            factors[S.NegativeOne] += a.exp
                        elif a == 1:
                            factors[a] = S.One
                        elif a == -1:
                            factors[-a] = S.One
                            factors[S.NegativeOne] = S.One
#.........这里部分代码省略.........

# 需要导入模块: from sympy.core.mul import Mul [as 别名]
# 或者: from sympy.core.mul.Mul import _from_args [as 别名]

#.........这里部分代码省略.........
        from sympy.polys.polytools import gcd

        def doit(p, q):
            """Try to return p % q if both are numbers or +/-p is known
            to be less than q.
            """

            if p == q or p == -q or p.is_Pow and p.exp.is_Integer and p.base == q:
                return S.Zero

            if p.is_Number and q.is_Number:
                return (p % q)

            # by ratio
            r = p/q
            try:
                d = int(r)
            except TypeError:
                pass
            else:
                if type(d) is int:
                    rv = p - d*q
                    if (rv*q < 0) is True:
                        rv += q
                    return rv

            # by differencec
            d = p - q
            if d.is_negative:
                if q.is_negative:
                    return d
                elif q.is_positive:
                    return p

        rv = doit(p, q)
        if rv is not None:
            return rv

        # denest
        if p.func is cls:
            # easy
            qinner = p.args[1]
            if qinner == q:
                return p
            # XXX other possibilities?

        # extract gcd; any further simplification should be done by the user
        G = gcd(p, q)
        if G is not S.One:
            p, q = [
                gcd_terms(i/G, clear=False, fraction=False) for i in (p, q)]
        pwas, qwas = p, q

        # simplify terms
        # (x + y + 2) % x -> Mod(y + 2, x)
        if p.is_Add:
            args = []
            for i in p.args:
                a = cls(i, q)
                if a.count(cls) > i.count(cls):
                    args.append(i)
                else:
                    args.append(a)
            if args != list(p.args):
                p = Add(*args)

        else:
            # handle coefficients if they are not Rational
            # since those are not handled by factor_terms
            # e.g. Mod(.6*x, .3*y) -> 0.3*Mod(2*x, y)
            cp, p = p.as_coeff_Mul()
            cq, q = q.as_coeff_Mul()
            ok = False
            if not cp.is_Rational or not cq.is_Rational:
                r = cp % cq
                if r == 0:
                    G *= cq
                    p *= int(cp/cq)
                    ok = True
            if not ok:
                p = cp*p
                q = cq*q

        # simple -1 extraction
        if p.could_extract_minus_sign() and q.could_extract_minus_sign():
            G, p, q = [-i for i in (G, p, q)]

        # check again to see if p and q can now be handled as numbers
        rv = doit(p, q)
        if rv is not None:
            return rv*G

        # put 1.0 from G on inside
        if G.is_Float and G == 1:
            p *= G
            return cls(p, q, evaluate=False)
        elif G.is_Mul and G.args[0].is_Float and G.args[0] == 1:
            p = G.args[0]*p
            G = Mul._from_args(G.args[1:])
        return G*cls(p, q, evaluate=(p, q) != (pwas, qwas))

# 需要导入模块: from sympy.core.mul import Mul [as 别名]
# 或者: from sympy.core.mul.Mul import _from_args [as 别名]

#.........这里部分代码省略.........
                return p
        elif isinstance(p, Add):
            # separating into modulus and non modulus
            both_l = non_mod_l, mod_l = [], []
            for arg in p.args:
                both_l[isinstance(arg, cls)].append(arg)
            # if q same for all
            if mod_l and all(inner.args[1] == q for inner in mod_l):
                net = Add(*non_mod_l) + Add(*[i.args[0] for i in mod_l])
                return cls(net, q)

        elif isinstance(p, Mul):
            # separating into modulus and non modulus
            both_l = non_mod_l, mod_l = [], []
            for arg in p.args:
                both_l[isinstance(arg, cls)].append(arg)

            if mod_l and all(inner.args[1] == q for inner in mod_l):
                # finding distributive term
                non_mod_l = [cls(x, q) for x in non_mod_l]
                mod = []
                non_mod = []
                for j in non_mod_l:
                    if isinstance(j, cls):
                        mod.append(j.args[0])
                    else:
                        non_mod.append(j)
                prod_mod = Mul(*mod)
                prod_non_mod = Mul(*non_mod)
                prod_mod1 = Mul(*[i.args[0] for i in mod_l])
                net = prod_mod1*prod_mod
                return prod_non_mod*cls(net, q)

            if q.is_Integer and q is not S.One:
                _ = []
                for i in non_mod_l:
                    if i.is_Integer and (i % q is not S.Zero):
                        _.append(i%q)
                    else:
                        _.append(i)
                non_mod_l = _

            p = Mul(*(non_mod_l + mod_l))

        # XXX other possibilities?

        # extract gcd; any further simplification should be done by the user
        G = gcd(p, q)
        if G != 1:
            p, q = [
                gcd_terms(i/G, clear=False, fraction=False) for i in (p, q)]
        pwas, qwas = p, q

        # simplify terms
        # (x + y + 2) % x -> Mod(y + 2, x)
        if p.is_Add:
            args = []
            for i in p.args:
                a = cls(i, q)
                if a.count(cls) > i.count(cls):
                    args.append(i)
                else:
                    args.append(a)
            if args != list(p.args):
                p = Add(*args)

        else:
            # handle coefficients if they are not Rational
            # since those are not handled by factor_terms
            # e.g. Mod(.6*x, .3*y) -> 0.3*Mod(2*x, y)
            cp, p = p.as_coeff_Mul()
            cq, q = q.as_coeff_Mul()
            ok = False
            if not cp.is_Rational or not cq.is_Rational:
                r = cp % cq
                if r == 0:
                    G *= cq
                    p *= int(cp/cq)
                    ok = True
            if not ok:
                p = cp*p
                q = cq*q

        # simple -1 extraction
        if p.could_extract_minus_sign() and q.could_extract_minus_sign():
            G, p, q = [-i for i in (G, p, q)]

        # check again to see if p and q can now be handled as numbers
        rv = doit(p, q)
        if rv is not None:
            return rv*G

        # put 1.0 from G on inside
        if G.is_Float and G == 1:
            p *= G
            return cls(p, q, evaluate=False)
        elif G.is_Mul and G.args[0].is_Float and G.args[0] == 1:
            p = G.args[0]*p
            G = Mul._from_args(G.args[1:])
        return G*cls(p, q, evaluate=(p, q) != (pwas, qwas))

# 需要导入模块: from sympy.core.mul import Mul [as 别名]
# 或者: from sympy.core.mul.Mul import _from_args [as 别名]
def factor_terms(expr, radical=False, clear=False):
    """Remove common factors from terms in all arguments without
    changing the underlying structure of the expr. No expansion or
    simplification (and no processing of non-commutatives) is performed.

    If radical=True then a radical common to all terms will be factored
    out of any Add sub-expressions of the expr.

    If clear=False (default) then coefficients will not be separated
    from a single Add if they can be distributed to leave one or more
    terms with integer coefficients.

    Examples
    ========

    >>> from sympy import factor_terms, Symbol, Mul, primitive
    >>> from sympy.abc import x, y
    >>> factor_terms(x + x*(2 + 4*y)**3)
    x*(8*(2*y + 1)**3 + 1)
    >>> A = Symbol('A', commutative=False)
    >>> factor_terms(x*A + x*A + x*y*A)
    x*(y*A + 2*A)

    When clear is False, a fraction will only appear factored out of an
    Add expression if all terms of the Add have coefficients that are
    fractions:

    >>> factor_terms(x/2 + 1, clear=False)
    x/2 + 1
    >>> factor_terms(x/2 + 1, clear=True)
    (x + 2)/2

    This only applies when there is a single Add that the coefficient
    multiplies:

    >>> factor_terms(x*y/2 + y, clear=True)
    y*(x + 2)/2
    >>> factor_terms(x*y/2 + y, clear=False) == _
    True

    """

    expr = sympify(expr)
    is_iterable = iterable(expr)

    if not isinstance(expr, Basic) or expr.is_Atom:
        if is_iterable:
            return type(expr)([factor_terms(i, radical=radical, clear=clear) for i in expr])
        return expr

    if expr.is_Pow or expr.is_Function or is_iterable or not hasattr(expr, 'args_cnc'):
        args = expr.args
        newargs = tuple([factor_terms(i, radical=radical, clear=clear) for i in args])
        if newargs == args:
            return expr
        return expr.func(*newargs)

    cont, p = expr.as_content_primitive(radical=radical)
    list_args, nc = zip(*[ai.args_cnc() for ai in Add.make_args(p)])
    list_args = list(list_args)
    nc = [((Dummy(), Mul._from_args(i)) if i else None) for i in nc]
    ncreps = dict([i for i in nc if i is not None])
    for i, a in enumerate(list_args):
        if nc[i] is not None:
            a.append(nc[i][0])
        a = Mul._from_args(a) # gcd_terms will fix up ordering
        list_args[i] = gcd_terms(a, isprimitive=True, clear=clear)
        # cancel terms that may not have cancelled
    p = Add._from_args(list_args) # gcd_terms will fix up ordering
    p = gcd_terms(p, isprimitive=True, clear=clear).xreplace(ncreps)
    return _keep_coeff(cont, p, clear=clear)