Hi, In Sage 7.5.rc1:
sage: var('x y')
(x, y)
sage: z = (x^18 + 60*x^17 + 331776*(x^2 - 1)*y^16 + 1599*x^16 + 25880*x^15 +
110
....: 592*(x^4 + 15*x^3 + 99*x^2 + 485*x + 1200)*y^14 + 266700*x^14 +
1555560*x^
....: 13 - 9216*(17*x^6 + 60*x^5 - 417*x^4 - 3040*x^3 - 13425*x^2 - 31020*x
- 16
....: 975)*y^12 + 3533300*x^12 - 4005000*x^11 + 9216*(9*x^8 - 60*x^7 - 509*x
^6 -
....: 2430*x^5 - 9525*x^4 - 24260*x^3 - 71775*x^2 - 227250*x - 290600)*y^10
- 1
....: 7787450*x^10 - 18420000*x^9 + 5760*(7*x^10 + 90*x^9 + 473*x^8 + 2460*x
^7 +
....: 10050*x^6 + 15200*x^5 + 53790*x^4 + 120900*x^3 + 198455*x^2 + 741350*x
+
....: 1103625)*y^8 + 15656250*x^8 + 31485000*x^7 - 192*(143*x^12 + 675*x^11
- 10
....: 43*x^10 - 7575*x^9 - 52650*x^8 - 224850*x^7 - 156150*x^6 + 1001250*x^5
+ 3
....: 726075*x^4 + 6217375*x^3 + 4145625*x^2 + 19413125*x + 33330000)*y^6 +
3527
....: 500*x^6 + 12975000*x^5 + 96*(93*x^14 - 105*x^13 - 1693*x^12 - 13470*x^
11 -
....: 99575*x^10 - 222675*x^9 - 149025*x^8 - 1024500*x^7 - 2270025*x^6 +
236662
....: 5*x^5 + 9545625*x^4 + 11931250*x^3 + 451875*x^2 + 11346875*x +
28273125)*y
....: ^4 + 80032500*x^4 + 102025000*x^3 + 192*(x^16 + 30*x^15 + 399*x^14 +
3955*
....: x^13 + 19950*x^12 + 3765*x^11 + 19850*x^10 + 197000*x^9 + 47025*x^8 +
7700
....: 0*x^7 + 646875*x^6 - 598125*x^5 - 2642500*x^4 - 2896875*x^3 + 1117500*
x^2
....: + 1581250*x - 687500)*y^2 - 78609375*x^2 - 180937500*x - 150390625)/(x
^14
....: + (x^2 - 1)*y^12 - x^12 - 6*(x^4 - x^2)*y^10 + 15*(x^6 - x^4)*y^8 - 20
*(x^
....: 8 - x^6)*y^6 + 15*(x^10 - x^8)*y^4 - 6*(x^12 - x^10)*y^2)
sage: z.numerator()
x^18 + 192*x^16*y^2 + 8928*x^14*y^4 - 27456*x^12*y^6 + 40320*x^10*y^8 +
82944*x^8*y^10 - 156672*x^6*y^12 + 110592*x^4*y^14 + 331776*x^2*y^16 + 60*x^
17 + 5760*x^15*y^2 - 10080*x^13*y^4 - 129600*x^11*y^6 + 518400*x^9*y^8 -
552960*x^7*y^10 - 552960*x^5*y^12 + 1658880*x^3*y^14 + 1599*x^16 + 76608*x^
14*y^2 - 162528*x^12*y^4 + 200256*x^10*y^6 + 2724480*x^8*y^8 - 4690944*x^6*y
^10 + 3843072*x^4*y^12 + 10948608*x^2*y^14 - 331776*y^16 + 25880*x^15 +
759360*x^13*y^2 - 1293120*x^11*y^4 + 1454400*x^9*y^6 + 14169600*x^7*y^8 -
22394880*x^5*y^10 + 28016640*x^3*y^12 + 53637120*x*y^14 + 266700*x^14 +
3830400*x^12*y^2 - 9559200*x^10*y^4 + 10108800*x^8*y^6 + 57888000*x^6*y^8 -
87782400*x^4*y^10 + 123724800*x^2*y^12 + 132710400*y^14 + 1555560*x^13 +
722880*x^11*y^2 - 21376800*x^9*y^4 + 43171200*x^7*y^6 + 87552000*x^5*y^8 -
223580160*x^3*y^10 + 285880320*x*y^12 + 3533300*x^12 + 3811200*x^10*y^2 -
14306400*x^8*y^4 + 29980800*x^6*y^6 + 309830400*x^4*y^8 - 661478400*x^2*y^10
+ 156441600*y^12 - 4005000*x^11 + 37824000*x^9*y^2 - 98352000*x^7*y^4 -
192240000*x^5*y^6 + 696384000*x^3*y^8 - 2094336000*x*y^10 - 17787450*x^10 +
9028800*x^8*y^2 - 217922400*x^6*y^4 - 715406400*x^4*y^6 + 1143100800*x^2*y^8
- 49260256*y^10 - 18420000*x^9 + 14784000*x^7*y^2 + 227196000*x^5*y^4 -
1193736000*x^3*y^6 + 45421568*x*y^8 + 15656250*x^8 + 124200000*x^6*y^2 +
916380000*x^4*y^4 - 795960000*x^2*y^6 + 1658880*y^8 + 31485000*x^7 -
114840000*x^5*y^2 + 1145400000*x^3*y^4 - 53134896*x*y^6 + 3527500*x^6 -
507360000*x^4*y^2 + 43380000*x^2*y^4 - 59506352*y^6 + 12975000*x^5 -
556200000*x^3*y^2 + 1089300000*x*y^4 + 80032500*x^4 + 214560000*x^2*y^2 +
63224816*y^4 + 102025000*x^3 + 303600000*x*y^2 - 78609375*x^2 - 132000000*y^
2 - 180937500*x - 150390625
sage: z.denominator()
------------------------------------------------------------------------
Sage hangs then for ever, without any noticeable CPU activity...
(Note that the numerator returned by Sage is correct.)
Is this a known issue ?
Eric.
PS: I am attaching the fraction in a file for the ease of cut and paste in
a Sage session.
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fraction.sage
Description: Binary data
