Axiom - Test

118 days ago by PatrickHammer

show(integrate(x/sqrt(x^4+10*x^2-96*x-71),x)) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}\int \frac{x}{\sqrt{x^{4} + 10 \, x^{2} - 96 \, x - 71}}\,{d x}
\newcommand{\Bold}[1]{\mathbf{#1}}\int \frac{x}{\sqrt{x^{4} + 10 \, x^{2} - 96 \, x - 71}}\,{d x}

Like we can see, Sage's default library (Maxima) for integration failed.. but now let's try with Axiom!
f=x/sqrt(x^4+10*x^2-96*x-71) axiom("f:="+str(f)) show(f) print "integrated by Axiom:" show(axiom("integrate(f,x)")) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{x}{\sqrt{x^{4} + 10 \, x^{2} - 96 \, x - 71}}

integrated by Axiom:

\newcommand{\Bold}[1]{\mathbf{#1}} {\log  \left( {{{{\left( {x^6}+{{15} \  {x^4}} -{{80} \  {x^3}}+{{27} \  {x^2}} -{{528} \  x}+{781}  \right)} \  {\sqrt {{{x^4}+{{10} \  {x^2}} -{{96} \  x} -{71}}}}}+{x^8}+{{20} \  {x^6}} -{{128} \  {x^5}}+{{54} \  {x^4}} -{{1408} \  {x^3}}+{{3124} \  {x^2}}+{10001}}}  \right)} \over 8   
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{x}{\sqrt{x^{4} + 10 \, x^{2} - 96 \, x - 71}}

integrated by Axiom:

\newcommand{\Bold}[1]{\mathbf{#1}} {\log  \left( {{{{\left( {x^6}+{{15} \  {x^4}} -{{80} \  {x^3}}+{{27} \  {x^2}} -{{528} \  x}+{781}  \right)} \  {\sqrt {{{x^4}+{{10} \  {x^2}} -{{96} \  x} -{71}}}}}+{x^8}+{{20} \  {x^6}} -{{128} \  {x^5}}+{{54} \  {x^4}} -{{1408} \  {x^3}}+{{3124} \  {x^2}}+{10001}}}  \right)} \over 8
%axiom fib(n)==if n < 2 then 1 else fib(n-1)+fib(n-2) S:=[fib(i) for i in 0..10] 
        
  [1,1,2,3,5,8,13,21,34,55,89]
                                                                        
Type: List(PositiveInteger)
  [1,1,2,3,5,8,13,21,34,55,89]
                                                                                                                                                                                                                   Type: List(PositiveInteger)

let's take it back to Sage, axiom("S") automatically is a Python list if S was a Axiom list:
"Python-greetings "+" ".join([str(i) for i in axiom("S")]) 
        
'Python-greetings 1 1 2 3 5 8 13 21 34 55 89'
'Python-greetings 1 1 2 3 5 8 13 21 34 55 89'