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sagemath
GitHub Repository: sagemath/sagelib
 Path: blob/master/sage/structure/gens_py.py
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"""

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Pure python code for abstract base class for objects with generators

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"""

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#*****************************************************************************

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#       Copyright (C) 2005 William Stein <[email protected]>

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#

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#  Distributed under the terms of the GNU General Public License (GPL)

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#

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#    This code is distributed in the hope that it will be useful,

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#    but WITHOUT ANY WARRANTY; without even the implied warranty of

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#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

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#    General Public License for more details.

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#

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#  The full text of the GPL is available at:

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#

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#                  http://www.gnu.org/licenses/

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#*****************************************************************************

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def multiplicative_iterator(M):

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    from sage.rings.all import infinity

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    G = M.gens()

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    if len(G) == 0:

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        yield M(1)        

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        return

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    stop = list(M.generator_orders())

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    for i in range(len(stop)):

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        if stop[i] is infinity:

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            raise ArithmeticError, "%s is not finite."%M

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        stop[i] = stop[i] - 1

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    n = 0

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    z = M(1)

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    yield z

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    cnt = [0] * len(G)        

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    while cnt != stop:

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        z = z * G[0]

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        cnt[0] = cnt[0] + 1

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        i = 0

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        while i < len(cnt)-1 and cnt[i] > stop[i]:

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            cnt[i] = 0

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            cnt[i+1] = cnt[i+1] + 1

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            z = z * G[i+1]

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            i = i + 1

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        yield z

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def abelian_iterator(M):

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    from sage.rings.all import infinity    

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    G = M.gens()

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    if len(G) == 0:

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        yield M(0)

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        return

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    stop = list(M.generator_orders())

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    for i in range(len(stop)):

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        if stop[i] is infinity:

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            raise ArithmeticError, "%s is not finite."%M

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        stop[i] = stop[i] - 1

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    n = 0

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    z = M(0)

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    yield z

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    cnt = [0] * len(G)

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    while cnt != stop:

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        cnt[0] = cnt[0] + 1

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        z = z + G[0]

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        i = 0

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        while i < len(cnt)-1 and cnt[i] > stop[i]:

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            cnt[i] = 0

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            cnt[i+1] = cnt[i+1] + 1

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            z = z + G[i+1]

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            i = i + 1

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        yield z

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