2010/2/21 Øyvind Jensen <jensen.oyv...@gmail.com>:
> The keyword pretty_indices used to be boolean, but is now a dict of lists
> containing letters to label the new dummy indices. This allows the user much
> better control over the resulting expression.
>
> Docstring and doctests updated accordingly.
> ---
> sympy/physics/secondquant.py | 104
> +++++++++++++++++++++++++++---------------
> 1 files changed, 67 insertions(+), 37 deletions(-)
>
> diff --git a/sympy/physics/secondquant.py b/sympy/physics/secondquant.py
> index 6a5fa60..9285f83 100644
> --- a/sympy/physics/secondquant.py
> +++ b/sympy/physics/secondquant.py
> @@ -2541,7 +2541,7 @@ def _substitute(expr, ordered_dummies, arg_iterator,
> **require):
> return result
>
>
> -def substitute_dummies(expr, new_indices=False, reverse_order=True,
> pretty_indices=True):
> +def substitute_dummies(expr, new_indices=False, reverse_order=True,
> pretty_indices={}):
> """
> Collect terms by substitution of dummy variables.
>
> @@ -2551,19 +2551,22 @@ def substitute_dummies(expr, new_indices=False,
> reverse_order=True, pretty_indic
> The idea is to substitute all dummy variables consistently depending on
> position in the term. For each term, we collect a sequence of all dummy
> variables, where the order is determined by index position. These indices
> - are then substituted consistently in each term. E.g.
> + are then substituted consistently in each term.
> +
> + Examples
> + ========
>
> >>> from sympy import symbols, Function
> >>> from sympy.physics.secondquant import substitute_dummies
> - >>> a,b = symbols('ab',dummy=True)
> - >>> c,d = symbols('cd',dummy=True)
> + >>> a,b,c,d = symbols('abcd',dummy=True, above_fermi=True)
> + >>> i,j = symbols('ij',dummy=True, below_fermi=True)
> >>> f = Function('f')
>
> >>> expr = f(a,b) + f(c,d); expr
> f(_a, _b) + f(_c, _d)
>
> - Since a, b, c and d are summation indices, this can be simplified to a
> - single summation term with a factor 2
> + Since a, b, c and d are equivalent summation indices, the expression can
> be
> + simplified to a single term (for which the dummy indices are still
> summed over)
>
> >>> substitute_dummies(expr, reverse_order=False)
> 2*f(_a, _b)
> @@ -2577,37 +2580,67 @@ def substitute_dummies(expr, new_indices=False,
> reverse_order=True, pretty_indic
> >>> substitute_dummies(expr, reverse_order=True)
> 2*f(_b, _a)
>
> - """
> + Controlling output
> + ==================
>
> - # pretty_indices = True # Prettier
> - # pretty_indices = False # Easier to debug
> + By default the dummy symbols that are already present in the expression
> + will be reused. However, if new_indices=True, new dummies will be
> + generated and inserted.
>
> + The keyword 'pretty_indices' can be used to control this generation of
> new
> + symbols.
>
> - if not pretty_indices:
> - def _i(number):
> - return 'i_'+str(number)
> - def _a(number):
> - return 'a_'+str(number)
> - def _p(number):
> - return 'p_'+str(number)
> + By default the new dummies will be generated on the form i_1, i_2, a_1,
> + etc. If you supply a dictionary with key:value pairs in the form:
>
> + { index_group: string_of_letters }
> +
> + The letters will be used as labels for the new dummy symbols. The
> + index_groups must be one of 'above', 'below' or 'general'.
> +
> + >>> expr = f(a,b,i,j)
> + >>> my_dummies = { 'above':'st','below':'uv' }
> + >>> substitute_dummies(expr, new_indices=True, pretty_indices=my_dummies)
> + f(_t, _s, _v, _u)
> +
> + If we run out of letters, or if there is no keyword for some index_group
> + the default dummy generator will be used as a fallback:
> +
> + >>> p,q = symbols('pq',dummy=True) # general indices
> + >>> expr = f(p,q)
> + >>> substitute_dummies(expr, new_indices=True, pretty_indices=my_dummies)
> + f(_p_1, _p_0)
> +
> + """
> +
> + # setup the replacing dummies
> + if new_indices:
> + letters_above = pretty_indices.get('above',"")
> + letters_below = pretty_indices.get('below',"")
> + letters_general= pretty_indices.get('general',"")
> + len_above = len(letters_above)
> + len_below = len(letters_below)
> + len_general= len(letters_general)
>
> - else:
> def _i(number):
> - if number<5:
> - return "klmno"[number]
> - else:
> - return 'o_'+str(number-5)
> + try:
> + return letters_below[number]
> + except IndexError:
> + return 'i_'+str(number-len_below)
> +
> def _a(number):
> - if number<6:
> - return "cdefgh"[number]
> - else:
> - return 'h_'+str(number-6)
> + try:
> + return letters_above[number]
> + except IndexError:
> + return 'a_'+str(number-len_above)
> +
> def _p(number):
> - if number<7:
> - return "tuvwxyz"[number]
> - else:
> - return 'z_'+str(number-7)
> + try:
> + return letters_general[number]
> + except IndexError:
> + return 'p_'+str(number-len_general)
> +
> +
>
> # reverse iterator for use in _get_dummies()
> if reverse_order:
> @@ -2632,21 +2665,20 @@ def arg_iterator(seq):
> dummies = [ d for d in expr.atoms() if isinstance(d,Dummy) ]
> dummies.sort()
>
> + # generate lists with the dummies we will insert
> a = i = p = 0
> for d in dummies:
> assum = d.assumptions0
> assum["dummy"]=True
> +
> if assum.get("above_fermi"):
> - sym = _a(a)
> - a +=1
> + if new_indices: sym = _a(a); a +=1
> l1 = aboves
> elif assum.get("below_fermi"):
> - sym = _i(i)
> - i +=1
> + if new_indices: sym = _i(i); i +=1
> l1 = belows
> else:
> - sym = _p(p)
> - p +=1
> + if new_indices: sym = _p(p); p +=1
> l1 = generals
>
> if new_indices:
> @@ -2655,8 +2687,6 @@ def arg_iterator(seq):
> l1.append(d)
>
>
> -
> -
> cases = (
> ({'above_fermi':True}, aboves),
> ({'below_fermi':True}, belows),
> --
> 1.6.5
>
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I would prefer if this would use the new assumptions system. Or should
'above_fermi' etc. be tied to symbols? The rest of the patches looks
fine to me, assuming all tests pass.
Vinzent
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