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[GSoC] Core: Fixes _eval_nseries() of Mul #19369

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merged 8 commits into from May 24, 2020
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sachin-4099
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@sachin-4099 sachin-4099 commented May 19, 2020

Fixes: #14068

Brief description of what is fixed or changed

The series expansion of a product is computed as the product of expansions of the factors.

def _eval_nseries(self, x, n, logx):
    from sympy import Order, powsimp
    terms = [t.nseries(x, n=n, logx=logx) for t in self.args]
    res = powsimp(self.func(*terms).expand(), combine='exp', deep=True)
    if res.has(Order):
        res += Order(x**n, x)
    return res

This is correct if the leading term of each series is constant but not in general.

For example, to compute the expansion of f(x)/x**10 at x = 0 to order O(x**10) it is necessary to compute the series of f(x) to order O(x**20), the order O(x**10) does not suffice.

A working strategy could be the following:

  • Compute the order n0 of the leading term of the product as the sum of the orders of the leading terms of the factors.

  • For each factor, compute n - n0 terms of its series expansion (starting from its leading term of order n1 and ending at order n - n0 + n1).

  • Multiply the expansions (truncating at terms of order n).

Release Notes

  • core
    • Fixes _eval_nseries() function of mul.py

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Fixes: #14068

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

The series expansion of a product is computed as the product of expansions of the factors.

```
def _eval_nseries(self, x, n, logx):
    from sympy import Order, powsimp
    terms = [t.nseries(x, n=n, logx=logx) for t in self.args]
    res = powsimp(self.func(*terms).expand(), combine='exp', deep=True)
    if res.has(Order):
        res += Order(x**n, x)
    return res
```
This is correct if the leading term of each series is constant but not in general.

For example, to compute the expansion of `f(x)/x**10` at `x = 0` to order `O(x**10)` it is necessary to compute the series of `f(x)` to order `O(x**20)`, the order `O(x**10)` does not suffice.

A working strategy could be the following:

* Compute the order `n0` of the leading term of the product as the sum of the orders of the leading terms of the factors.

* For each factor, compute `n - n0` terms of its series expansion (starting from its leading term of order `n1` and ending at order `n - n0 + n1`).

* Multiply the expansions (truncating at terms of order `n`).

#### Release Notes


<!-- BEGIN RELEASE NOTES -->
* core
  * Fixes `_eval_nseries()` function of `mul.py`
<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

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codecov bot commented May 21, 2020

Codecov Report

Merging #19369 into master will increase coverage by 0.062%.
The diff coverage is 100.000%.

@@              Coverage Diff              @@
##            master    #19369       +/-   ##
=============================================
+ Coverage   75.576%   75.638%   +0.062%     
=============================================
  Files          651       652        +1     
  Lines       169536    169685      +149     
  Branches     40015     40049       +34     
=============================================
+ Hits        128130    128348      +218     
+ Misses       35786     35725       -61     
+ Partials      5620      5612        -8     

@sachin-4099
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sachin-4099 commented May 22, 2020

Are any additional regression tests required? @jksuom

@jksuom jksuom merged commit 31ddf98 into sympy:master May 24, 2020
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@oscarbenjamin
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oscarbenjamin commented Jun 11, 2020

There is a significant slowdown in

sympy/core/tests/test_power.py::test_issue_6068

I've bisected that to commit 8a06c07 in this #19369 (this PR).

The content of the test is

from sympy import *

x = Symbol('x')
assert sqrt(sin(x)).series(x, 0, 7) == \
    sqrt(x) - x**Rational(5, 2)/12 + x**Rational(9, 2)/1440 - \
    x**Rational(13, 2)/24192 + O(x**7)
assert sqrt(sin(x)).series(x, 0, 9) == \
    sqrt(x) - x**Rational(5, 2)/12 + x**Rational(9, 2)/1440 - \
    x**Rational(13, 2)/24192 - 67*x**Rational(17, 2)/29030400 + O(x**9)
assert sqrt(sin(x**3)).series(x, 0, 19) == \
    x**Rational(3, 2) - x**Rational(15, 2)/12 + x**Rational(27, 2)/1440 + O(x**19)
assert sqrt(sin(x**3)).series(x, 0, 20) == \
    x**Rational(3, 2) - x**Rational(15, 2)/12 + x**Rational(27, 2)/1440 - \
    x**Rational(39, 2)/24192 + O(x**20)

In sympy 1.6 that takes 5 seconds whereas on master it takes 45 seconds.

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4 participants