Re: [sympy] Conditional substitution
On 06/01/2022 22:19, Oscar Benjamin wrote:
On Thu, 6 Jan 2022 at 21:23, David Bailey wrote:
On 06/01/2022 16:41, Oscar Benjamin wrote:
You can use replace to make arbitrary conditions on substitution.
There are different syntaxes so here's how you do it using wild
pattern-matching:
In [15]: expr = (a*x**14 + b*x + c)
In [16]: expr
Out[16]:
14
a⋅x + b⋅x + c
In [17]: w = Wild('w')
In [18]: expr.replace(x**w, lambda w: y**(w/2) if w.is_even else x**w)
Out[18]:
7
a⋅y + b⋅x + c
Here's how you do it with just functions:
In [19]: query = lambda e: e.is_Pow and e.base == x and e.exp.is_even
In [20]: replacer = lambda e: y**(e.exp/2)
In [21]: expr.replace(query, replacer)
Out[21]:
7
a⋅y + b⋅x + c
Since query and replacer can be completely arbitrary functions any
kind of replacement rule can be implemented in this way.
Thanks very much for that Oscar, your solution looks extremely useful
and general. Somehow I hadn't realised the power of Wild(), although I
knew Wild existed. The Wild/replace method looks most useful to me - I
get easily lost in multiple lambda's!.
The lambdas can get confusing. The point to note though is that a
lambda function is just a shorthand for creating a Python function
e.g.
f = lambda e: e.is_Pow
is equivalent to
def f(e):
return e.is_Pow
What that means is that in the functional form of replace you can pass
completely arbitrary functions for the query and the replacer. The
query function is given a subexpression as query(e) and returns True
or False to determine if a replacement should be made. If query(e)
returns True then replacer(e) generates the replacement expression so
if f and g are functions then
expr.replace(f, g)
looks at all subexpressions e in expr and if f(e) is True then e is
replaced by g(e). That's about as general as you can get for
replacements. In the Wild form the query function is replaced by a
pattern so it looks more like pattern-matching. The pattern is easier
to read but pattern matching is strictly less powerful than being able
to use a completely arbitrary query function.
The pattern form is especially nice if you use a pattern for both
query and replacement e.g.:
In [1]: w = Wild('w')
In [2]: (sin(x)**2 + tan(x)).replace(sin(w), exp(w))
Out[2]:
2⋅x
ℯ+ tan(x)
--
Oscar
Thanks again, Oscar for that second helping of insight into how to use Wild!
If only you could be cloned about 6 times, a couple of your copies could
create some SymPy documentation that would sparkle with gems like this.
David
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Re: [sympy] Conditional substitution
On Thu, 6 Jan 2022 at 21:23, David Bailey wrote:
>
> On 06/01/2022 16:41, Oscar Benjamin wrote:
> > You can use replace to make arbitrary conditions on substitution.
> > There are different syntaxes so here's how you do it using wild
> > pattern-matching:
> >
> > In [15]: expr = (a*x**14 + b*x + c)
> >
> > In [16]: expr
> > Out[16]:
> > 14
> > a⋅x + b⋅x + c
> >
> > In [17]: w = Wild('w')
> >
> > In [18]: expr.replace(x**w, lambda w: y**(w/2) if w.is_even else x**w)
> > Out[18]:
> > 7
> > a⋅y + b⋅x + c
> >
> > Here's how you do it with just functions:
> >
> > In [19]: query = lambda e: e.is_Pow and e.base == x and e.exp.is_even
> >
> > In [20]: replacer = lambda e: y**(e.exp/2)
> >
> > In [21]: expr.replace(query, replacer)
> > Out[21]:
> > 7
> > a⋅y + b⋅x + c
> >
> > Since query and replacer can be completely arbitrary functions any
> > kind of replacement rule can be implemented in this way.
> >
> Thanks very much for that Oscar, your solution looks extremely useful
> and general. Somehow I hadn't realised the power of Wild(), although I
> knew Wild existed. The Wild/replace method looks most useful to me - I
> get easily lost in multiple lambda's!.
The lambdas can get confusing. The point to note though is that a
lambda function is just a shorthand for creating a Python function
e.g.
f = lambda e: e.is_Pow
is equivalent to
def f(e):
return e.is_Pow
What that means is that in the functional form of replace you can pass
completely arbitrary functions for the query and the replacer. The
query function is given a subexpression as query(e) and returns True
or False to determine if a replacement should be made. If query(e)
returns True then replacer(e) generates the replacement expression so
if f and g are functions then
expr.replace(f, g)
looks at all subexpressions e in expr and if f(e) is True then e is
replaced by g(e). That's about as general as you can get for
replacements. In the Wild form the query function is replaced by a
pattern so it looks more like pattern-matching. The pattern is easier
to read but pattern matching is strictly less powerful than being able
to use a completely arbitrary query function.
The pattern form is especially nice if you use a pattern for both
query and replacement e.g.:
In [1]: w = Wild('w')
In [2]: (sin(x)**2 + tan(x)).replace(sin(w), exp(w))
Out[2]:
2⋅x
ℯ+ tan(x)
--
Oscar
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Re: [sympy] Conditional substitution
On 06/01/2022 16:41, Oscar Benjamin wrote:
You can use replace to make arbitrary conditions on substitution.
There are different syntaxes so here's how you do it using wild
pattern-matching:
In [15]: expr = (a*x**14 + b*x + c)
In [16]: expr
Out[16]:
14
a⋅x + b⋅x + c
In [17]: w = Wild('w')
In [18]: expr.replace(x**w, lambda w: y**(w/2) if w.is_even else x**w)
Out[18]:
7
a⋅y + b⋅x + c
Here's how you do it with just functions:
In [19]: query = lambda e: e.is_Pow and e.base == x and e.exp.is_even
In [20]: replacer = lambda e: y**(e.exp/2)
In [21]: expr.replace(query, replacer)
Out[21]:
7
a⋅y + b⋅x + c
Since query and replacer can be completely arbitrary functions any
kind of replacement rule can be implemented in this way.
--
Oscar
Thanks very much for that Oscar, your solution looks extremely useful
and general. Somehow I hadn't realised the power of Wild(), although I
knew Wild existed. The Wild/replace method looks most useful to me - I
get easily lost in multiple lambda's!.
David
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Re: [sympy] Conditional substitution
On Thu, 6 Jan 2022 at 14:41, David Bailey wrote:
>
> Dear group,
>
> A substitution like this is easy to make with SymPy:
>
> (a*x**2+b*x+c).subs(x,y)
>
> However, how can I make a conditional substitution, such as:
>
> a) One that would replace even powers of x only.
>
> b) One which would replace even powers of x by y**(n/2) resulting in
> a*y**7+b*x+c? I.e. one where parts of the object being replaced would be
> available to form part of the result - thus x**14 would contribute '7'
> to the resultant expression.
You can use replace to make arbitrary conditions on substitution.
There are different syntaxes so here's how you do it using wild
pattern-matching:
In [15]: expr = (a*x**14 + b*x + c)
In [16]: expr
Out[16]:
14
a⋅x + b⋅x + c
In [17]: w = Wild('w')
In [18]: expr.replace(x**w, lambda w: y**(w/2) if w.is_even else x**w)
Out[18]:
7
a⋅y + b⋅x + c
Here's how you do it with just functions:
In [19]: query = lambda e: e.is_Pow and e.base == x and e.exp.is_even
In [20]: replacer = lambda e: y**(e.exp/2)
In [21]: expr.replace(query, replacer)
Out[21]:
7
a⋅y + b⋅x + c
Since query and replacer can be completely arbitrary functions any
kind of replacement rule can be implemented in this way.
--
Oscar
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[sympy] Conditional substitution
Dear group, A substitution like this is easy to make with SymPy: (a*x**2+b*x+c).subs(x,y) However, how can I make a conditional substitution, such as: a) One that would replace even powers of x only. b) One which would replace even powers of x by y**(n/2) resulting in a*y**7+b*x+c? I.e. one where parts of the object being replaced would be available to form part of the result - thus x**14 would contribute '7' to the resultant expression. Thanks in anticipation! David -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/f4c4ab4c-d84f-cd9b-1e6d-0e0260804c1d%40dbailey.co.uk.
Re: [sympy] Conditional substitution and on the fly dictionary creation
It should work with a custom dictionary. At the very least, it will
work with any iterator or (old, new) pairs.
You could also make f symbolic and unevaluated by default, then call
doit after the substitution. It won't be 100% efficient if the same f
will appear more than once, though.
Aaron Meurer
On Apr 27, 2013, at 10:51 AM, Alan Bromborsky wrote:
> On 04/27/2013 12:40 PM, Alan Bromborsky wrote:
>> consider the sympy expressions -
>>
>> a = a_1*e_1+...+a_n*e_n
>>
>> b = b_1*e_1+...+b_n*e_n
>>
>> where the a_i's and the b_i's are commutative sympy expressions and the
>> e_i's are non-commutative symbols and you have a dictionary
>>
>> mul_dict = {e_i*e_j: f(e_i,e_j)}
>>
>> if mul_dict is fully populated then
>>
>> a*b = (a*b).subs(mul_dict)
>>
>> However many of the entries in the dictionary will never be used since most
>> of
>> the a_i's and b_i's will be zero, but you don't know which ones ahead of the
>> multiplication.
>>
>> Likewise the function f(e_i,e_j) is know but time consuming to evaluate.
>>
>> Is there a way to do a subsitution in a sympy expression where if e_i*e_j is
>> a key subs will use
>> the dictionary, but is e_i*e_j is not a key f(e_i,e_j) will be evaluated,
>> added to the dictionary, and
>> the substitution performed?
> I guess the real question is is there a way of use a custom dictionary class
> Mydict(dict) with the sympy
> subs operation?
>
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Re: [sympy] Conditional substitution and on the fly dictionary creation
On 04/27/2013 12:40 PM, Alan Bromborsky wrote:
consider the sympy expressions -
a = a_1*e_1+...+a_n*e_n
b = b_1*e_1+...+b_n*e_n
where the a_i's and the b_i's are commutative sympy expressions and the
e_i's are non-commutative symbols and you have a dictionary
mul_dict = {e_i*e_j: f(e_i,e_j)}
if mul_dict is fully populated then
a*b = (a*b).subs(mul_dict)
However many of the entries in the dictionary will never be used since
most of
the a_i's and b_i's will be zero, but you don't know which ones ahead
of the multiplication.
Likewise the function f(e_i,e_j) is know but time consuming to evaluate.
Is there a way to do a subsitution in a sympy expression where if
e_i*e_j is a key subs will use
the dictionary, but is e_i*e_j is not a key f(e_i,e_j) will be
evaluated, added to the dictionary, and
the substitution performed?
I guess the real question is is there a way of use a custom dictionary
class Mydict(dict) with the sympy
subs operation?
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[sympy] Conditional substitution and on the fly dictionary creation
consider the sympy expressions -
a = a_1*e_1+...+a_n*e_n
b = b_1*e_1+...+b_n*e_n
where the a_i's and the b_i's are commutative sympy expressions and the
e_i's are non-commutative symbols and you have a dictionary
mul_dict = {e_i*e_j: f(e_i,e_j)}
if mul_dict is fully populated then
a*b = (a*b).subs(mul_dict)
However many of the entries in the dictionary will never be used since
most of
the a_i's and b_i's will be zero, but you don't know which ones ahead of
the multiplication.
Likewise the function f(e_i,e_j) is know but time consuming to evaluate.
Is there a way to do a subsitution in a sympy expression where if
e_i*e_j is a key subs will use
the dictionary, but is e_i*e_j is not a key f(e_i,e_j) will be
evaluated, added to the dictionary, and
the substitution performed?
--
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