#7581: use prCopyR to coerce multivariate polynomials in the simple case
-----------------------------------+----------------------------------------
   Reporter:  malb                 |       Owner:  malb           
       Type:  enhancement          |      Status:  positive_review
   Priority:  major                |   Milestone:  sage-4.3       
  Component:  commutative algebra  |    Keywords:                 
Work_issues:                       |      Author:  Martin Albrecht
   Upstream:  N/A                  |    Reviewer:  Simon King     
     Merged:                       |  
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Comment(by SimonKing):

 Replying to [comment:15 SimonKing]:
 > Replying to [comment:12 SimonKing]:
 > ...
 > > So, 0.41s for imap and only 0.02s for fetch, in a situation where
 (even with your patch) Sage needs 5.43s!
 >
 > Oops, I was copying the wrong number. With your patch, it is 1.18 s.
 However, it'd be great if this could be improved to, say, 0.5s.
 >

 Double oops. I have my children in the office and am a bit distracted.

 OK.

 We have
 {{{
 > system("--ticks-per-sec",1000);
 > ring r1 = 0, (x(1..10000)),dp;
 > poly p = x(10000);
 > ring r2 = 0, (x(1..10001)), dp;
 > int t = timer;
 > imap(r1,p)+x(10001);
 x(10000)+x(10001)
 > timer-t;
 410
 }}}

 while we have (with your patch)
 {{{
 sage: R1 = PolynomialRing(QQ,'x',10001,order='deglex')
 sage: R2 = PolynomialRing(QQ,'x',10002,order='deglex')
 sage: x10000 = R1('x10000')
 sage: x10001 = R2('x10001')
 sage: %time R2(x10000) + x10001
 CPU times: user 0.74 s, sys: 0.00 s, total: 0.74 s
 Wall time: 0.73 s
 x10000 + x10001
 }}}

 I think this is equivalent to what I did in Singular. In other words, your
 patch is not far from native Singular.

 This confirms my positive review.

 Cheers,

 Simon

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7581#comment:16>
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