correcting series reversion doc

[maciejskorski]

Fixing some mistakes in the documentation.

References to other Issues or PRs

Fixes #24244.

Brief description of what is fixed or changed

Correcting typos and the algorithm logic.

Other comments

Draft a connection to Newton iterations? Would fix the missing reference.

Release Notes

• polys
  • correcting docs in ring_series module

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• polys
  • correcting docs in ring_series module (#24245 by @maciejskorski)

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<!-- Your title above should be a short description of what
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Fixing some mistakes in the documentation.

#### References to other Issues or PRs
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Fixes #24244.

#### Brief description of what is fixed or changed

Correcting typos and the algorithm logic.

#### Other comments

Draft a connection to Newton iterations? Would fix the missing reference.

#### Release Notes

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* solvers
  * Added a new solver for logarithmic equations.

* functions
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* polys
  * correcting docs in ring_series module

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[maciejskorski]

Note: it would be good to add a reference too.

[oscarbenjamin]

This docstring is generally not very well written. The point about "depending polynomially on other variables" is confusing. We can have arbitrary expressions as the coefficients:

In [4]: R, xr, yr = ring('x, y', EX)

In [5]: rs = EX(S.One)*xr + EX(tan(t)+sqrt(pi))*xr**2 + EX(1/sqrt(f(t)))*xr**3

In [6]: rs.as_expr()
Out[6]: 
    3                          
   x        2                  
──────── + x ⋅(tan(t) + √π) + x
  ______                       
╲╱ f(t)                        

In [8]: from sympy.polys.ring_series import rs_series_reversion

In [9]: result = rs_series_reversion(rs, xr, 3, yr)

In [10]: result.as_expr()
Out[10]: 
 2                   
y ⋅(-tan(t) - √π) + y

In [11]: result = rs_series_reversion(rs, xr, 4, yr)

In [12]: result.as_expr()
Out[12]: 
 3 ⎛     2                             1    ⎞    2                   
y ⋅⎜2⋅tan (t) + 4⋅√π⋅tan(t) + 2⋅π - ────────⎟ + y ⋅(-tan(t) - √π) + y
   ⎜                                  ______⎟                        
   ⎝                                ╲╱ f(t) ⎠  

[maciejskorski]

This docstring is generally not very well written. The point about "depending polynomially on other variables" is confusing. We can have arbitrary expressions as the coefficients:

Thanks, could you share a minimal working example - with valid imports etc?

[oscarbenjamin]

Thanks, could you share a minimal working example - with valid imports etc?

Those examples come from isympy which does this when you run it:

These commands were executed:
>>> from sympy import *
>>> x, y, z, t = symbols('x y z t')
>>> k, m, n = symbols('k m n', integer=True)
>>> f, g, h = symbols('f g h', cls=Function)
>>> init_printing()

The easiest way to run those imports is just to run isympy from the terminal.