#6482: [with patch, needs review] multivariate polynomial substitution has a
design flaw
---------------------------------+------------------------------------------
Reporter: was | Owner: malb
Type: defect | Status: new
Priority: critical | Milestone: sage-4.1.2
Component: commutative algebra | Keywords:
Reviewer: | Author:
Merged: |
---------------------------------+------------------------------------------
Comment(by malb):
'''Performance'''
{{{
#!python
sage: P.<a,b,c,d,e> = PolynomialRing(QQ)
sage: f = P.random_element(degree=3,terms=50)
sage: g = {a:b,b:c,c:d,d:e,e:a}
sage: %timeit f.subs(g)
1000 loops, best of 3: 271 µs per loop
}}}
{{{
#!python
sage: phi = P.hom([b,c,d,e,a])
sage: %timeit phi(f)
1000 loops, best of 3: 939 µs per loop
}}}
{{{
#!python
sage: phi(f)
-a^2*b - 11/2*b^3 - 8*a^2*c + 1/51*b*c^2 + 1/2*c^3 - a^2*d + 1/3*a*b*d -
2/11*a*c*d + 195*b*c*d + 1/3*a*d^2 + 2*b*d^2 - c*d^2 - 2/3*a^2*e +
1/2*a*b*e - 203*b^2*e + 1/4*a*c*e + b*c*e - 5*c^2*e + 6*a*e^2 + b*e^2 -
1/3*c*e^2 - 5*d*e^2 + 3*e^3 + 1/3*a^2 - a*b - 7/48*a*c - 2*b*c - 53/2*c^2
- 1/3*a*d - 1/2*b*d + c*d - d^2 - a*e - 4*b*e - d*e + 13*e^2 - 2*a - 1/2*b
- c + 9/2*d - 1/2
sage: f.sub
f.sub_m_mul_q f.subs f.substitute
sage: f.subs(g)
-a^2*b - 11/2*b^3 - 8*a^2*c + 1/51*b*c^2 + 1/2*c^3 - a^2*d + 1/3*a*b*d -
2/11*a*c*d + 195*b*c*d + 1/3*a*d^2 + 2*b*d^2 - c*d^2 - 2/3*a^2*e +
1/2*a*b*e - 203*b^2*e + 1/4*a*c*e + b*c*e - 5*c^2*e + 6*a*e^2 + b*e^2 -
1/3*c*e^2 - 5*d*e^2 + 3*e^3 + 1/3*a^2 - a*b - 7/48*a*c - 2*b*c - 53/2*c^2
- 1/3*a*d - 1/2*b*d + c*d - d^2 - a*e - 4*b*e - d*e + 13*e^2 - 2*a - 1/2*b
- c + 9/2*d - 1/2
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6482#comment:5>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected]
To unsubscribe from this group, send email to
[email protected]
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en
-~----------~----~----~----~------~----~------~--~---
