[fixed by #4000] x^2 for x over QQ is really frickin' slow compared to over ZZ (nearly factor of 100!!)

[williamstein]

wstein@sage:~$ sage
----------------------------------------------------------------------
| Sage Version 3.4.1, Release Date: 2009-04-21                       |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
sage: R.<x> = ZZ[]
sage: timeit('x^2')
625 loops, best of 3: 1.4 µs per loop
sage: R.<x> = QQ[]
sage: timeit('x^2')
625 loops, best of 3: 118 µs per loop
sage: %prun x**2
         34 function calls in 0.001 CPU seconds

   Ordered by: internal time

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
        1    0.000    0.000    0.001    0.001 <string>:1(<module>)
        1    0.000    0.000    0.000    0.000 polynomial_element_generic.py:590(__init__)
        4    0.000    0.000    0.000    0.000 polynomial_element_generic.py:656(__getitem__)
        3    0.000    0.000    0.000    0.000 {method 'poldegree' of 'sage.libs.pari.gen.gen' objects}
        3    0.000    0.000    0.000    0.000 polynomial_element_generic.py:874(degree)
        2    0.000    0.000    0.000    0.000 {method 'Polrev' of 'sage.libs.pari.gen.gen' objects}
        1    0.000    0.000    0.000    0.000 polynomial_ring.py:211(_element_constructor_)
        1    0.000    0.000    0.000    0.000 polynomial_ring.py:741(gen)
        9    0.000    0.000    0.000    0.000 {isinstance}
        3    0.000    0.000    0.000    0.000 {max}
        1    0.000    0.000    0.000    0.000 {hasattr}
        1    0.000    0.000    0.000    0.000 polynomial_ring.py:810(is_sparse)
        1    0.000    0.000    0.000    0.000 {method 'type' of 'sage.libs.pari.gen.gen' objects}
        1    0.000    0.000    0.000    0.000 {len}
        1    0.000    0.000    0.000    0.000 {sage.rings.fraction_field_element.is_FractionFieldElement}
        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}

sage: R.<x> = ZZ[]
sage: %prun x**2
         3 function calls in 0.000 CPU seconds

   Ordered by: internal time

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
        1    0.000    0.000    0.000    0.000 <string>:1(<module>)
        1    0.000    0.000    0.000    0.000 polynomial_ring.py:741(gen)
        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}

Component: basic arithmetic

Reviewer: David Loeffler

Issue created by migration from https://trac.sagemath.org/ticket/6063

[aghitza]

comment:1

See also #4000, which might be the best way to fix this.

[williamstein]

comment:2

This is because polynomials over QQ are still pure Python. This is an enhancement, not a bug.

[sagetrac-jrp]

comment:3

This appears to be fixed now - the QQ one is even slightly faster.

[loefflerd]

comment:4

Yes, this is fixed. Release manager: please close this ticket.

[jdemeyer]

Reviewer: David Loeffler