Mrvasympt #7529

avichaldayal · 2014-05-28T19:00:16Z

MrvAsympt algorithm to find asymptotic expansion.

skirpichev · 2014-05-29T11:12:42Z

sympy/core/expr.py

@@ -2468,6 +2468,9 @@ def series(self, x=None, x0=0, n=6, dir="+", logx=None):
                if (s1 + o).removeO() == s1:
                    o = S.Zero

+            # Try asymptotic expansion
+            if s1.removeO() == 0:
+                return self.subs(x, 1/x).aseries(x, n, logx, False).subs(x, 1/x)


It looks for me, this line wasn't covered by your test suite. Perhaps, you should add a test when coeff.series(x, S.Infinity, n, logx=logx) call aseries?

Earlier as soon as coefficient had an infinite series expansion we terminated. Now other terms are also added as long as they don't have an infinite series expansion

skirpichev · 2014-06-02T17:35:38Z

sympy/core/expr.py

@@ -2646,6 +2649,101 @@ def _eval_nseries(self, x, n, logx):
                     nseries calls it.""" % self.func)
                     )

+    def aseries(self, x, n=6, logx=None, bound=0, hir=False):
+        """
+        This algorithm is directly induced from the limit computational algorithm


No, that's not a good docstring. See this.

Docstring shouldn't be about the algorithm in first place.

skirpichev · 2014-06-02T17:38:30Z

@Krastanov

akshayah3 · 2014-06-03T08:53:35Z

sympy/core/expr.py

+        Use the ``hir`` parameter to produce hierarchical series. It stops the recursion
+        at an early level and may provide nicer and more useful results.
+
+        If the most rapidly varrying subexpression of a given expression f is f itself,


typo *varying

avichaldayal · 2014-06-05T16:19:53Z

better name?

In the thesis, it mentions the parameter as growth-bound

skirpichev · 2014-06-06T08:47:05Z

sympy/core/expr.py

@@ -2646,6 +2649,107 @@ def _eval_nseries(self, x, n, logx):
                     nseries calls it.""" % self.func)
                     )

+    def aseries(self, x, n=6, logx=None, bound=0, hir=False):
+        """
+        Returns the asymptotic expansion of self.


you can add a reference here.

avichaldayal · 2014-06-08T17:00:51Z

hey, we have n and logx parameters too...

Yes, but the user can call the series method directly. Using aseries provides him the option to mention hir and bound parameters

you can add a reference here.

I added the wikipedia reference in the references section. I'll mention that there.

skirpichev · 2014-06-08T19:39:13Z

Again. Please keep context of the discussion. Use "Add a line note" buttons or reply to email notifications.

I added the wikipedia reference in the references section.

I'm not sure if you do this right. Please take look to other docstrings and please actually build the documentation.

Yes, but the user can call the series method directly.

I mean that you should document all parameters.

avichaldayal · 2014-09-14T17:47:45Z

The following line : O(x**3).subs(x, exp(-x**2)) works in SymPy live and older commmits.

I tried using git bisect and it points to the following commit:
012a919
But this commit doesn't change anything in order.py. Anyways I compared order.py from this commit to the latest version and created a patch.

When I applied the patch, the substitution works.
I'm unable to find which lines in order.py cause the error though.

asmeurer · 2014-09-15T02:30:05Z

The pull request #7636 removed denesting of certain powers x**y**z -> x**(y*z). So something implicitly relies on that working.

skirpichev · 2014-09-15T19:01:15Z

So something implicitly relies on that working.

No. Someone just don't get familar with git bisect. For commit above the one from #7636:

$ git log --oneline
..
0700b30 watch for improper separation of base and exp in powsimp
8fc5951 Merge pull request #7634 from sushant-hiray/coth-fix
..
$ git checkout 8fc5951
$ cat a.py
from sympy import *
x = Symbol('x')
print(O(x**3).subs(x, exp(-x**2)))
$ python a.py
...
ValueError: expecting a Symbol but got nan

asmeurer · 2014-09-21T21:15:14Z

I haven't seen any work on this, so I'm going to bump the milestone. Please let me know if it should be put back on.

skirpichev · 2014-12-01T15:47:29Z

closed in favor of #8542

mihir-w · 2015-02-09T13:09:43Z

Hi! I have read the algorithm and would like to work upon the XFAIL'ed test.
I am still new to git. How do I pick these commits in my local repo ( cherry-pick shows bad revision ) ? Should I clone this repo ? In that case, where do I send the PR ( or commit ) ?
Thanks.

certik · 2015-02-09T23:26:03Z

Do something like this:

git checkout -b avichaldayal-mrvasympt master
git pull https://github.com/avichaldayal/sympy.git mrvasympt

Then commit more changes and push into your own fork at github and create a new PR.

Note that you also have to resolve conflicts with master (git merge master).

skirpichev · 2015-02-09T23:38:30Z

On Mon, Feb 09, 2015 at 03:26:10PM -0800, Ondřej Čertík wrote:

Note that you also have to resolve conflicts with master (git merge
master).

Conflicts are resolved in the linked pr #8542.

(BTW, a little example how you, Ondrej, read pr content first ;))

Unsubscribed.

mihir-w · 2015-02-14T10:22:22Z

There seems to be 2 issues:

First:
Substitution of the type O(x**3).subs(exp(-x**2)) fails. This was attempted in #8568 but is yet to be resolved.

Second:
Even if the above error is somehow circumvented the error still remains. Consider the expected output of the XFAIL'ed test:

>>> (exp(2*a*x + 1/x)/2 + exp(2*b*x + 1/x)/2 - exp(a*x + b*x + 1/x))*exp(-2*x**2) + (exp(a*x + 1/x) - exp(b*x + 1/x))*exp(-x**2) + O(exp(-3*x**2), (x, oo))

Just entering the expression in the console raise the error that the answer is dependent on the sign of a and b. The expression is attempted to be simplified but since it does not know about a and b, it raises error. So even if the first error is solved, problem in subs in hierarchical series will remain.

The hierarchical series expansion should not be attempted to be simplified, rather it should be printed as it is. It is just an intermediate expansion.( Explained at Page 95). However when we substitute the final variable:

if hir
    return s.subs(d,exp(logw))

it automatically tries to simplify and fails.

Any help to how to proceed ? Is there a way to just substitute and not try to evaluate it ? Or should I return as a string ?

asmeurer · 2015-02-15T03:26:27Z

Don't return strings.

What kind of simplification are you trying to avoid?

mihir-w · 2015-02-15T20:39:42Z

Consider the XFAIL'ed test:

>>> e = exp(1/x + exp(-x**2)*(exp(a*x) - exp(b*x))) - exp(1/x)
>>> e.aseries( x, n=3, hir=True)

Following is the expected output:

(exp(2*a*x + 1/x)/2 + exp(2*b*x + 1/x)/2 - exp(a*x + b*x + 1/x))*exp(-2*x**2) + (exp(a*x + 1/x) - exp(b*x + 1/x))*exp(-x**2) + O(exp(-3*x**2), (x, oo))

In the function, one step before the final answer is returned, following is the intermediate output:

_d*(exp(x*a + 1/x) - exp(x*b + 1/x)) + _d**2*(exp(2*x*a + 1/x)/2 + exp(2*x*b + 1/x)/2 - exp(x*a + x*b + 1/x)) + O(_d**3)

with d = exp(-x**2)

Clearly the answer achieved here is correct. Only substitution of d is left and we have the answer.
Currently the substitution fails which is a different issue. However even if the substitution works, let's say d = exp(-x). Then on substituting:

Traceback (most recent call last):
  File "test_aseries.py", line 66, in <module>
    test_issue_7872()
  File "test_aseries.py", line 58, in test_issue_7872
    print (e.aseries(x, n=3, hir=True) )
  File "/home/nightwing/sympy_final/sympy/sympy/core/expr.py", line 2734, in aseries
    return self.subs(x, xpos).aseries(xpos, n, bound, hir).subs(xpos, x)
  File "/home/nightwing/sympy_final/sympy/sympy/core/expr.py", line 2779, in aseries
    return s.subs(d,exp(logw))
  File "/home/nightwing/sympy_final/sympy/sympy/core/basic.py", line 892, in subs
    rv = rv._subs(old, new, **kwargs)
  File "/home/nightwing/sympy_final/sympy/sympy/core/basic.py", line 1006, in _subs
    rv = fallback(self, old, new)
  File "/home/nightwing/sympy_final/sympy/sympy/core/basic.py", line 983, in fallback
    rv = self.func(*args)
  File "/home/nightwing/sympy_final/sympy/sympy/core/operations.py", line 41, in __new__
    c_part, nc_part, order_symbols = cls.flatten(args)
  File "/home/nightwing/sympy_final/sympy/sympy/core/add.py", line 240, in flatten
    if o.contains(t):
  File "/home/nightwing/sympy_final/sympy/sympy/series/order.py", line 383, in contains
    obj = self.func(expr, *self.args[1:])
  File "/home/nightwing/sympy_final/sympy/sympy/series/order.py", line 216, in __new__
    expr = expr.as_leading_term(*args)
  File "/home/nightwing/sympy_final/sympy/sympy/core/expr.py", line 2857, in as_leading_term
    obj = self._eval_as_leading_term(x)
  File "/home/nightwing/sympy_final/sympy/sympy/core/mul.py", line 1455, in _eval_as_leading_term
    return self.func(*[t.as_leading_term(x) for t in self.args])
  File "/home/nightwing/sympy_final/sympy/sympy/core/expr.py", line 2857, in as_leading_term
    obj = self._eval_as_leading_term(x)
  File "/home/nightwing/sympy_final/sympy/sympy/core/add.py", line 703, in _eval_as_leading_term
    plain = expr.func(*[s for s, _ in expr.extract_leading_order(x)])
  File "/home/nightwing/sympy_final/sympy/sympy/core/add.py", line 646, in extract_leading_order
    if o.contains(of) and o != of:
  File "/home/nightwing/sympy_final/sympy/sympy/series/order.py", line 372, in contains
    l = ratio.limit(s, point)
  File "/home/nightwing/sympy_final/sympy/sympy/core/expr.py", line 2806, in limit
    return limit(self, x, xlim, dir)
  File "/home/nightwing/sympy_final/sympy/sympy/series/limits.py", line 42, in limit
    return Limit(e, z, z0, dir).doit(deep=False)
  File "/home/nightwing/sympy_final/sympy/sympy/series/limits.py", line 157, in doit
    r = gruntz(e, z, z0, dir)
  File "/home/nightwing/sympy_final/sympy/sympy/series/gruntz.py", line 651, in gruntz
    r = limitinf(e0, z)
  File "/home/nightwing/sympy_final/sympy/sympy/series/gruntz.py", line 424, in limitinf
    c0, e0 = mrv_leadterm(e, x)
  File "/home/nightwing/sympy_final/sympy/sympy/series/gruntz.py", line 505, in mrv_leadterm
    f, logw = rewrite(exps, Omega, x, w)
  File "/home/nightwing/sympy_final/sympy/sympy/series/gruntz.py", line 577, in rewrite
    raise NotImplementedError('Result depends on the sign of %s' % sig)
NotImplementedError: Result depends on the sign of sign(2*a - 2*b)

Basically when the value gets substituted, the expression becomes univariate in x. subs by it's nature tries to simplify the expression. While simplifying it encounters a and b whose signs are unknown and hence it raises NotImplementedError. If 'aandb` are some defined integers, everything works out fine.

Other tests did not have any symbols apart from x in them and hence I guess it went unnoticed.

So what is needed that d gets substituted in the given expression without further simplification. I have tried xreplace and replace but for them the substituted part should be a symbol which is not the case here.

avichaldayal · 2015-02-18T16:52:44Z

When finding series expansion of a function, x is substituted with a positive x dummy variable.
Can we do the same for other variables in the expression too?

In this case a and b can be replaced by positive a and positive b which might fix the issue.

skirpichev · 2015-02-22T19:03:50Z

In this case a and b can be replaced by positive a and positive b which might fix the issue.

Great idea! Lets assume something arbitrary about parameters to get random output in turn

asmeurer · 2015-02-22T19:43:58Z

The issue here is that Add shouldn't ever raise NotImplementedError. It should catch the error and return an unevaluated expression. The way O() works, the expression isn't going to be wrong if terms aren't absorbed into it. So I would add a try, except NotImplementedError in Add.flatten where it calls o.contains(t).

I also don't think it should call gruntz (that is, no O() simplification should happen automatically), but that's a different issue.

skirpichev · 2015-02-22T20:20:09Z

The issue here is that Add shouldn't ever raise NotImplementedError.

Yes.

It should catch the error and return an unevaluated expression.

If you have one broken place (contains method) - lets fix one in another, completely unrelated. Sympy way

So I would add a try, except NotImplementedError in Add.flatten where it calls o.contains(t).

No. The correct way is enforce the contract "foo.contains(t) should return either boolean or None".

Something like this:

diff --git a/sympy/series/order.py b/sympy/series/order.py
index 33049a0..6208798 100644
--- a/sympy/series/order.py
+++ b/sympy/series/order.py
@@ -369,7 +369,10 @@ def contains(self, expr):
             ratio = self.expr/expr.expr
             ratio = powsimp(ratio, deep=True, combine='exp')
             for s in common_symbols:
-                l = ratio.limit(s, point)
+                try:
+                    l = ratio.limit(s, point)
+                except NotImplementedError:
+                    l = None
                 if not isinstance(l, C.Limit):
                     l = l != 0
                 else:

asmeurer · 2015-02-22T20:29:18Z

Yes, returning None does sound better, although that would strictly speaking change the API.

skirpichev · 2015-02-22T20:37:24Z

Mentioned above "contract" is a part of the API. Raising a not implemented error - is not, in any case.

czgdp1807 · 2020-04-24T08:17:32Z

sympy/series/tests/test_aseries.py

+    # 6.6
+    e = sin(1/x + exp(-x)) - sin(1/x)
+    assert e.aseries(x) == (1/(24*x**4) - 1/(2*x**2) + 1 + O(x**(-6), (x, oo)))*exp(-x)
+    assert e.series(x, oo) == (1/(24*x**4) - 1/(2*x**2) + 1 + O(x**(-6), (x, oo)))*exp(-x)


This fails on master.

czgdp1807 · 2020-04-24T08:17:52Z

sympy/series/tests/test_aseries.py

+    # 6.15
+    e3 = lambda x: exp(exp(exp(x)))
+    e = e3(x)/e3(x-1/e3(x))
+    assert e.aseries(x, n=3) == 1 + exp(x + exp(x))*exp(-exp(exp(x))) + ((-exp(x)/2 - S.Half)*exp(x + exp(x)) + \


czgdp1807 · 2020-04-24T08:18:21Z

sympy/series/tests/test_aseries.py

+def test_issue_7872():
+    a, b = symbols('a b', integer=True)
+    e = exp(1/x + exp(-x**2) * (exp(a*x) - exp(b*x))) - exp(1/x)
+    assert e.aseries(x, n=3, hir=True) == (exp(2*a*x + 1/x)/2 + exp(2*b*x + 1/x)/2 - \


0sidharth · 2021-09-29T08:46:15Z

Closing this as all the code apart from example 6.15 is already there in master. I will open a separate PR with that example

avichaldayal added 2 commits May 27, 2014 15:54

Implemented MrvAsympt algorithm to compute asymptotic expansion

188b9f8

Added test cases for asymptotic series

0ba0587

skirpichev added Series labels May 29, 2014

skirpichev reviewed May 29, 2014
View reviewed changes

avichaldayal added 2 commits May 30, 2014 18:25

Added part to find normalised representation of the function

bb387a7

Keep on adding terms unless we get another infinite series

8b66508

Earlier as soon as coefficient had an infinite series expansion we terminated. Now other terms are also added as long as they don't have an infinite series expansion

skirpichev reviewed Jun 2, 2014
View reviewed changes

akshayah3 reviewed Jun 3, 2014
View reviewed changes

Update docstring and minor fixes

c5b25a6

skirpichev reviewed Jun 6, 2014
View reviewed changes

Minor fixes

54b2252

asmeurer removed this from the 0.7.6 milestone Sep 21, 2014

asmeurer mentioned this pull request Sep 22, 2014

limit(4**(acos(1/(1+x**2))**2)/log(1+x, 4), x, 0) raises NotImplementedError: Don't know how to calculate the mrv of 'O(1/_w, (_w, oo))' #8061

Closed

skirpichev closed this Dec 1, 2014

asmeurer reopened this Jan 19, 2015

jcrist mentioned this pull request Apr 21, 2015

Asymptotic expansion #3112

Closed

czgdp1807 added the Please take over label Feb 12, 2020

czgdp1807 reviewed Apr 24, 2020

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0sidharth mentioned this pull request Jun 8, 2021

[GSoC] A few leading term methods changed #21589

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0sidharth closed this Sep 29, 2021

0sidharth mentioned this pull request Sep 29, 2021

Added example 6.15 of Gruntz thesis for aseries #22179

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Mrvasympt #7529

Mrvasympt #7529

avichaldayal commented May 28, 2014

skirpichev May 29, 2014

skirpichev Jun 2, 2014

skirpichev commented Jun 2, 2014

akshayah3 Jun 3, 2014

avichaldayal commented Jun 5, 2014

skirpichev Jun 6, 2014

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skirpichev commented Dec 1, 2014

mihir-w commented Feb 9, 2015

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asmeurer commented Feb 15, 2015

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avichaldayal commented Feb 18, 2015

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skirpichev commented Feb 22, 2015

czgdp1807 Apr 24, 2020

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czgdp1807 Apr 24, 2020

0sidharth commented Sep 29, 2021

Mrvasympt #7529

Mrvasympt #7529

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avichaldayal commented May 28, 2014

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