FYI, I did not know Fricas now has a github issues page. So I entered the above there
https://github.com/fricas/fricas/issues/133 On Tuesday, August 8, 2023 at 6:06:20 PM UTC-5 Nasser M. Abbasi wrote: > 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 > > > > > > > > > > > > > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. 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