I can't understand this behavior of 1.3.9. Starting with fresh session, it
seems the result one time works, and another time fails, using same exact
command. Sometimes trying twice it works.
>fricas --version
FriCAS 1.3.9
based on sbcl 2.3.0
--------------------------------------------------------
1) -> unparse(integrate((2+3*x)/(2^(2/3)-x)/(x^3-1)^(1/2),x)::InputForm)
>> Error detected within library code:
catdef: division by zero
(1) -> unparse(integrate((2+3*x)/(2^(2/3)-x)/(x^3-1)^(1/2),x)::InputForm)
"...57042834961904521699968)*3^(1/2))""
(2) -> unparse(integrate((2+3*x)/(2^(2/3)-x)/(x^3-1)^(1/2),x)::InputForm)
>> Error detected within library code:
catdef: division by zero
------------------------------------------------------------------------------
Here is another fresh session, but now I set setSimplifyDenomsFlag(true)
before anything
1) -> setSimplifyDenomsFlag(true)
(1) false
Type:
Boolean
(2) -> unparse(integrate((2+3*x)/(2^(2/3)-x)/(x^3-1)^(1/2),x)::InputForm)
(2)
"(3^(1/2)*(12*(2^(1/3))^2+18*2^(1/3)+4)^(1/2)*log((((18*x^16+(-102)*x^15+252*
x^14+5580*x^13+(-6348)*x^12+5328*x^11+41976*x^10+(-15168)*x^9+(-47808)*x^7+32
448*x^6+(-9216)*x^5+(-4608)*x^4+(-15360)*x^3+4608*x^2+9216*x+3072)*(2^(1/3))^
2+(4*x^16+306*x^15+(-756)*x^14+1240*x^13+19044*x^12+(-15984)*x^11+9328*x^10+4
5504*x^9+(-10624)*x^7+(-97344)*x^6+27648*x^5+(-1024)*x^4+46080*x^3+(-13824)*x
^2+2048*x+(-9216))*2^(1/3)+((-12)*x^16+68*x^15+2268*x^14+(-3720)*x^13+4232*x^
12+47952*x^11+(-27984)*x^10+10112*x^9+31872*x^7+(-21632)*x^6+(-82944)*x^5+307
2*x^4+10240*x^3+41472*x^2+(-6144)*x+(-2048)))*3^(1/2)*(x^3+(-1))^(1/2)*(12*(2
^(1/3))^2+18*2^(1/3)+4)^(1/2)+((696*x^17+84216*x^14+332688*x^11+(-796224)*x^8
+423168*x^5+(-44544)*x^2)*(2^(1/3))^2+(6960*x^16+244992*x^13+115536*x^10+(-94
6560)*x^7+757248*x^4+(-178176)*x)*2^(1/3)+(29*x^18+41760*x^15+504600*x^12+(-6
10624)*x^9+(-300672)*x^6+445440*x^3+(-59392))))/(x^18+(-24)*x^15+240*x^12+(-1
280)*x^9+3840*x^6+(-6144)*x^3+4096))+(24*2^(1/3)+(-36))*weierstrassPInverse(0
,4,x))/18"
(3) -> unparse(integrate((2+3*x)/(2^(2/3)-x)/(x^3-1)^(1/2),x)::InputForm)
(3)
"(3^(1/2)*(12*(2^(1/3))^2+18*2^(1/3)+4)^(1/2)*log((((18*x^16+(-102)*x^15+252*
x^14+5580*x^13+(-6348)*x^12+5328*x^11+41976*x^10+(-15168)*x^9+(-47808)*x^7+32
448*x^6+(-9216)*x^5+(-4608)*x^4+(-15360)*x^3+4608*x^2+9216*x+3072)*(2^(1/3))^
2+(4*x^16+306*x^15+(-756)*x^14+1240*x^13+19044*x^12+(-15984)*x^11+9328*x^10+4
5504*x^9+(-10624)*x^7+(-97344)*x^6+27648*x^5+(-1024)*x^4+46080*x^3+(-13824)*x
^2+2048*x+(-9216))*2^(1/3)+((-12)*x^16+68*x^15+2268*x^14+(-3720)*x^13+4232*x^
12+47952*x^11+(-27984)*x^10+10112*x^9+31872*x^7+(-21632)*x^6+(-82944)*x^5+307
2*x^4+10240*x^3+41472*x^2+(-6144)*x+(-2048)))*3^(1/2)*(x^3+(-1))^(1/2)*(12*(2
^(1/3))^2+18*2^(1/3)+4)^(1/2)+((696*x^17+84216*x^14+332688*x^11+(-796224)*x^8
+423168*x^5+(-44544)*x^2)*(2^(1/3))^2+(6960*x^16+244992*x^13+115536*x^10+(-94
6560)*x^7+757248*x^4+(-178176)*x)*2^(1/3)+(29*x^18+41760*x^15+504600*x^12+(-6
10624)*x^9+(-300672)*x^6+445440*x^3+(-59392))))/(x^18+(-24)*x^15+240*x^12+(-1
280)*x^9+3840*x^6+(-6144)*x^3+4096))+(24*2^(1/3)+(-36))*weierstrassPInverse(0
,4,x))/18"
Type:
String
(4) -> unparse(integrate((2+3*x)/(2^(2/3)-x)/(x^3-1)^(1/2),x)::InputForm)
>> Error detected within library code:
catdef: division by zero
(4) ->
----------------------------------------------------
So you see, it seems Fricas does not always generate same result. It seems
random to me. There many such integrals that generate division by zero, but
it seems if one tries again it can work. Here is current list of integrals
that show this problem. So I am not sure if trying again in the test
program will solve this or not.
----------------------------------------------------------------
sqlite> select command_in_fricas from main where fricas_anti LIKE '%catdef:
division by zero%';
integrate((1-2^(1/3)*x)/(2^(2/3)+x)/(x^3+1)^(1/2),x, algorithm="fricas")
integrate(1/(2^(2/3)-x)/(x^3-1)^(1/2),x, algorithm="fricas")
integrate(1/(2^(2/3)+x)/(-x^3-1)^(1/2),x, algorithm="fricas")
integrate((2+3*x)/(2^(2/3)-x)/(x^3-1)^(1/2),x, algorithm="fricas")
integrate((1+x+3^(1/2))/(d*x+c)/(-x^3-1)^(1/2),x, algorithm="fricas")
integrate((1+x-3^(1/2))/(d*x+c)/(-x^3-1)^(1/2),x, algorithm="fricas")
integrate(1/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^2,x, algorithm="fricas")
integrate((e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c))^4,x, algorithm="fricas")
integrate(1/(a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(1/2),x, algorithm="fricas")
integrate(1/(-1+cos(x)^2)^(1/2),x, algorithm="fricas")
integrate(1/(-1+cos(x)^2)^(3/2),x, algorithm="fricas")
integrate((d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e)),x, algorithm="fricas")
integrate((d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e))^2,x, algorithm="fricas")
integrate(tan(d*x+c)^(2/3)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm="fricas")
integrate(tan(d*x+c)^(1/3)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm="fricas")
integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(4/3),x, algorithm="fricas")
---------------------------------------------------
Question is: Whey Fricas gives different result for same command?
--Nasser
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