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From: | Raymond Rogers |
Subject: | Re: [Axiom-developer] problems with integrate |
Date: | Sat, 22 Nov 2014 11:03:00 -0500 |
User-agent: | Mozilla/5.0 (X11; Linux x86_64; rv:31.0) Gecko/20100101 Thunderbird/31.2.0 |
On 11/22/2014 09:47 AM, Waldek Hebisch
wrote:
A clue for someone competent? In any case a work around forTim Daly wrote:Question from Thomas Baruchel integrate((16*x^14-125*x^10+150*x^6+375*x^2)/(256*x^16+480*x^12+1025*x^8+750*x^4 +625),x=0..1) 5 (1) -- 77 Type: Union(f1: OrderedCompletion(_expression_(Integer)),...) (2) -> integrate((16*x^14-125*x^10+150*x^6+375*x^2)/(256*x^16+480*x^12+1025*x^8+750*x^4 +625),x) 7 3 5x + 35x (2) ------------------- 8 4 176x + 165x + 275 Type: Union(_expression_(Integer),...) (3) -> D( (5*x^7+35*x^3)/(176*x^8+165*x^4+275) ,x) 14 10 6 2 - 80x - 2575x + 350x + 2625x (3) ------------------------------------------- 16 12 8 4 2816x + 5280x + 11275x + 8250x + 6875 Type: Fraction(Polynomial(Integer))AFAICS logarithmic terms got lost. FriCAS on the same input produces ugly, long answer containing several logarithmic terms. The above agrees with rational part of FriCAS answer. Old code contained a bug which sometimes caused such effect. Thomas Baruchel 54) -> cc (54) -> 16 12 8 4 (54) 256x + 480x + 1025x + 750x + 625 Type: Polynomial(Integer) (55) -> D(complexIntegrate(x^2*(1)/(cc),x),x) (55) -> 2 x (55) -------------------------------------- 16 12 8 4 256x + 480x + 1025x + 750x + 625 Type: _expression_(Integer) (56) -> D(integrate(x^2*(1)/(cc),x),x) (56) -> 14 10 6 2 768x - 11360x - 10125x + 8625x (56) ------------------------------------------------------------- 16 12 8 4 7040000x + 13200000x + 28187500x + 20625000x + 17187500 Type: _expression_(Integer) ----------------------------------------- This particular case: (57) -> bb (57) -> 14 10 6 2 (57) 16x - 125x + 150x + 375x Type: Polynomial(Integer) (58) -> cc (58) -> 16 12 8 4 (58) 256x + 480x + 1025x + 750x + 625 Type: Polynomial(Integer) (59) -> D(integrate(bb/(cc),x),x) (59) -> 14 10 6 2 - 80x - 2575x + 350x + 2625x (59) ------------------------------------------- 16 12 8 4 2816x + 5280x + 11275x + 8250x + 6875 Type: _expression_(Integer) (60) -> D(complexIntegrate(bb/(cc),x),x) (60) -> 14 10 6 2 16x - 125x + 150x + 375x (60) -------------------------------------- 16 12 8 4 256x + 480x + 1025x + 750x + 625 Type: _expression_(Integer) |
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