Re: [sympy] Conditional substitution

[David Bailey]

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

[Oscar Benjamin]

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] How to get started with contributions?

[Jason Moore]

David,

Here is our introductory information:
https://github.com/sympy/sympy/wiki/introduction-to-contributing

Jason
moorepants.info
+01 530-601-9791


On Thu, Jan 6, 2022 at 8:48 PM David Dai  wrote:

> Hi everyone,
> My name is Jingze Dai and I am a CS student from McMaster University,
> Canada. I want to be a developer in the sympy group. But I do not know
> after learning, where should I get started? Can anyone give me some
> suggestions?
> Thank you so much
>
> Sincerely
> 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.
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> https://groups.google.com/d/msgid/sympy/ec39468a-7d9c-4ea6-8d2c-fdc3be0ec1f2n%40googlegroups.com
> 
> .
>

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Re: [sympy] Conditional substitution

[David Bailey]

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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[sympy] How to get started with contributions?

[David Dai]

Hi everyone,
My name is Jingze Dai and I am a CS student from McMaster University, 
Canada. I want to be a developer in the sympy group. But I do not know 
after learning, where should I get started? Can anyone give me some 
suggestions?
Thank you so much

Sincerely
David

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Re: [sympy] Conditional substitution

[Oscar Benjamin]

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

[David Bailey]

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

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