2302 Canonical powers and fix to perfect_power #267

smichr · 2011-04-28T02:56:14Z

2302: gcd of multiplied integer bases are extracted

    When a sequence of integer-based powers is multiplied,
    a canonical representation can be obtained by attempting
    to separate all relatively prime bases with different powers.
    So for 2**(1/3)*3**(1/4)*6**(1/5) the 2 (and 3) are extracted
    from the 6 and the powers combined to give 2**(8/15)*3**(9, 20)

2302: canonical integer-base powers

    When a power of a prime factor of a power's base shares a gcd with
    the denominator of the base's exponent, e.g. in (2**4*3)**(1/6) the
    4 shares a gcd of 2 with 6, then that prime will be factored out of
    the base: e.g. to give 2**(2/3)*3**(1/6).

2321: Fix perfect_factor

    A number like 2**5*3**3 was coming back incorrectly as being a perfect power with exponent of 1. It should have returned None.

See issue 2302 and issue 2321.

smichr · 2011-04-28T06:38:22Z

TODO: wait for review

certik · 2011-04-28T10:29:18Z

Test results: http://pastebin.com/1tMs9kV3

Automatic review by sympy-bot.

smichr · 2011-04-29T09:07:53Z

@asmeurer, can you give this a review?

asmeurer · 2011-04-29T21:39:57Z

By the way, the commit from issue 415 was 7b87b62.

ness01 · 2011-04-29T21:57:53Z

sympy/core/mul.py

+                num_rat.extend(grow)
+                num_exp.append((bi, num_rat[i][1]))
+            i += 1
+


For this code to be correct it is important that igcd always returns a positive number. (This seems to be the case but I don't see where that guarantee on igcd is documented).

For this code to be correct it is important that igcd always returns
a positive number. (This seems to be the case but I don't see
where that guarantee on igcd is documented).

This is part of the igcd tests in test_numbers. But I added it to the docstring, too.

/c

ness01 · 2011-04-29T22:04:11Z

This looks good to me. Perhaps some tests with negative bases might be a good idea.

smichr · 2011-05-02T03:29:16Z

o perfect_power now returns False rather than None
o the gcd extraction has been reformulated as an addition commit
o a test has been added for issues 1095 so that issue can be closed
o the failing doctest of the deprecated block_diag has been gutted so the doctest no longer tests the deprecated function;
the diag method provides the documentation and comprable tests
o flatten treated 1.0 different than all other reals and this should not be done. 1 and 1.0 are no more similar than 2.0 and 2.
o a SKIP directive was removed form a matrix test with no adverse reaction under W32
o code from Mul.flatten that handled combination of bases was copied to powsimp so it, too, will follow power rules
o a force option was given to powsimp to allow ignoring of base-combination rules
o some dubious code (issue 2333) was refactored and a general tidyup of powsimp was done.

ness01 · 2011-05-04T16:59:06Z

Test results html report: http://pastehtml.com/view/1ed2zqy.html

Automatic review by sympy-bot.

ness01 · 2011-05-04T17:00:33Z

There seems to be a test failure in concrete/summations.

smichr · 2011-05-04T17:32:38Z

What can be wrong? Nothing fails here.

============================= test process starts ==============================

executable:   C:\Python26\python.exe  (2.6.4-final-0)
ground types: python

sympy\mpmath\tests\test_summation.py[5] .....                               [OK]


================== tests finished: 5 passed, in 0.61 seconds ===================


============================= test process starts ==============================

executable:   C:\Python26\python.exe  (2.6.4-final-0)
ground types: python

sympy\core\evalf.py[2] ..                                                   [OK]


================== tests finished: 2 passed, in 0.57 seconds ===================

============================== txt doctests start ==============================


doc\src\modules\evalf.txt [74]                                              [OK]

============================= test process starts ==============================

executable:   C:\Python26\python.exe  (2.6.4-final-0)
ground types: python

sympy\matrices\matrices.py[40] ........................................     [OK]


================== tests finished: 40 passed, in 1.52 seconds ==================

============================== txt doctests start ==============================


doc\src\modules\matrices.txt [98]                                           [OK]

C:\Documents and Settings\chris\sympy>\s\doc wester

C:\Documents and Settings\chris\sympy>\Python26\python.exe "C:\documents and set
tings\chris\sympy\bin\doctest"  wester
============================== txt doctests start ==============================


doc\src\modules\polys\wester.txt [60]                                       [OK]

Can anybody else confirm these failures? Is something strange going on?

ness01 · 2011-05-05T08:21:02Z

Well the failure in summation is actually a doctest, but I cannot reproduce it independently either. It only happens when I run setup.py test... I suppose it's some weird caching issue. Not that I know what to do about it ^^

certik · 2011-05-05T08:30:26Z

Test results html report: http://pastehtml.com/view/1edeyx6.html

Automatic review by sympy-bot.

certik · 2011-05-05T08:31:46Z

I get a few failures too in doctests. There seem to be some problem (e.g. wrong numbers returned), e.g. it's not just some hashing issue.

A number like 2**5*3**3 was coming back as being a perfect power with exponent of 1, i.e. (2**5*3**3, 1). It should be False to indicate that it is not a perfect power.

When a power of a prime factor of a power's base shares a gcd with the denominator of the base's exponent, e.g. in (2**4*3)**(1/6) the 4 shares a gcd of 2 with 6, then that prime will be factored out of the base: e.g. to give 2**(2/3)*3**(1/6).

When a sequence of integer-based powers is multiplied, a canonical representation can be obtained by attempting to separate all relatively prime bases with different powers. So for 2**(1/3)*3**(1/4)*6**(1/5) the 2 (and 3) are extracted from the 6 and the powers combined to give 2**(8/15)*3**(9, 20)

Now the gcd work is done after doing all the base and exponent combining. This leads to fewer terms to process. In addition, -1 is pulled out of every Number-based power with a Rational exponent and either stands alone or is re-inserted into a power with a matching exponent.

Some Rationals are protected from making changes to p and q. Others are not. When you change the p and q values you are modifying that object in place and if that is a cached object then that object will no longer have the same value when it is recalled later.

Real(1.0) was being changed to S.One by flatten. This was removed since no other Real was being treated that way, e.g. -1.0 is retained. A couple of test were changed.

Bases having a common exponent should not combine unless the bases are positive or the exponents are integers. The exception being that a negative base or a base with an unknown sign can join non-negative bases.

Some condensation of code was done and the portion where c_exp was traversed while being deleted and reconstructed was re-written.

smichr · 2011-05-05T18:22:07Z

I think I found the problem and left the commit (don't modify .p and .q) next to the offending commit so as not to forget this nasty little error. Can you guys confirm that there are now no failures?

ness01 · 2011-05-05T18:56:06Z

Test results html report: http://pastehtml.com/view/1edn0kz.html

Automatic review by sympy-bot.

ness01 · 2011-05-05T19:20:35Z

So the tests look good now [wester is not your fault].

smichr · 2011-05-05T20:39:09Z

OK, if there are no other objections this will be pushed in about 8 hours.

smichr · 2011-05-06T15:46:27Z

it's in.

ness01 reviewed Apr 29, 2011
View reviewed changes

smichr added 12 commits May 5, 2011 23:55

2321: Fix perfect_power

869432d

A number like 2**5*3**3 was coming back as being a perfect power with exponent of 1, i.e. (2**5*3**3, 1). It should be False to indicate that it is not a perfect power.

2302: canonical integer-base powers

79b57df

When a power of a prime factor of a power's base shares a gcd with the denominator of the base's exponent, e.g. in (2**4*3)**(1/6) the 4 shares a gcd of 2 with 6, then that prime will be factored out of the base: e.g. to give 2**(2/3)*3**(1/6).

test issue 1095

2e45a8e

don't special-case 1.0 in flatten

2d59c9a

Real(1.0) was being changed to S.One by flatten. This was removed since no other Real was being treated that way, e.g. -1.0 is retained. A couple of test were changed.

remove doctest for deprecated block_diag

8902307

remove SKIP after modifying matrices.txt example

47177f7

1777: powsimp obeys power rules

73a1738

Bases having a common exponent should not combine unless the bases are positive or the exponents are integers. The exception being that a negative base or a base with an unknown sign can join non-negative bases.

powsimp gets a force argument (default False)

9c3de7b

2333: powsimp cleanup

6b57151

Some condensation of code was done and the portion where c_exp was traversed while being deleted and reconstructed was re-written.

smichr closed this May 6, 2011

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2302 Canonical powers and fix to perfect_power #267

2302 Canonical powers and fix to perfect_power #267

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2302 Canonical powers and fix to perfect_power #267

2302 Canonical powers and fix to perfect_power #267

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