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  1. Omitting the {axiom} enviroment

    You have to use \begin{axiom} ... \end{axiom} or \begin{reduce} ... \end{reduce} before and after the command like this:

        \begin{reduce}
        int(1/(a+z^3), z);
        \end{reduce}
    

  2. Axiom commands do not end with ;

    Oh yes, note that for Axiom you don't end the command with ; and the command for integration in Axiom is integrate.

    fricas
    integrate(1/(a+z^3), z)
    
\label{eq1}{\left(
\begin{array}{@{}l}
\displaystyle
-{{\sqrt{3}}\ {\log \left({{{{z}^{2}}\ {{\root{3}\of{{a}^{2}}}^{2}}}-{a \  z \ {\root{3}\of{{a}^{2}}}}+{{a}^{2}}}\right)}}+ \
\
\displaystyle
{2 \ {\sqrt{3}}\ {\log \left({{z \ {\root{3}\of{{a}^{2}}}}+ a}\right)}}+ 
\
\
\displaystyle
{6 \ {\arctan \left({{{2 \  z \ {\sqrt{3}}\ {\root{3}\of{{a}^{2}}}}-{a \ {\sqrt{3}}}}\over{3 \  a}}\right)}}
(1)
    Type: Union(Expression(Integer),...)

  3. Reduce commands must end with a semicolon ;

    But it must be there for Reduce.

    r^2+r+1;
    reduce
    \displaylines{\qdd
r^{2}
+r
+1
\cr}
 

  4. In Axiom ln is written log

    This won't work:

        \begin{axiom}integrate((x^2+2*x*ln(x)+5)/(sin(x^2+x^3-x^4)^2), x)\end{axiom}
    

    Put the \begin{axiom} and \end{axiom} on separate lines and notice that in Axiom ln is written log

    fricas
    integrate((x^2+2*x*log(x)+5)/(sin(x^2+x^3-x^4)^2), x)
    
\label{eq2}\int^{
\displaystyle
x}{{{-{2 \  \%G \ {\log \left({\%G}\right)}}-{{\%G}^{2}}- 5}\over{{{\cos \left({{{\%G}^{4}}-{{\%G}^{3}}-{{\%G}^{2}}}\right)}^{2}}- 1}}\ {d \%G}}(2)
    Type: Union(Expression(Integer),...)

  5. Don't put a \ in front of the axiom command

    This is wrong:

        \begin{axiom}
        \sqrt{49/100}
        \end{axiom}
    

    Begin each comment with an explanation. Don't put \ in front of the Axiom command.

    Do it like this:

        Some explanation
        \begin{axiom}
        sqrt{49/100}
        \end{axiom}
    

    Some explanation

    fricas
    sqrt{49/100}
    
\label{eq3}7 \over{10}(3)
    Type: AlgebraicNumber?

  6. No $ before and after

    This is wrong:

        \begin{axiom}
        $ \sqrt{49/100} $
        \end{axiom}
    

    Don't put $ before and after $ and there is no \ in front.

    Just do it like this:

        \begin{axiom}
        sqrt{49/100}
        \end{axiom}
    

    and what you will see is this:

    fricas
    sqrt{49/100}
    
\label{eq4}7 \over{10}(4)
    Type: AlgebraicNumber?

  7. Axiom sometimes interprets commands in unexpected ways

    This command appears to work

    fricas
    integrate(x^5 ln[x],x)
    
\label{eq5}{{x}^{6}}\over 6(5)
    Type: Union(Expression(Integer),...)

    But notice that

    fricas
    5 ln[x]
    
\label{eq6}5(6)
    Type: UnivariatePolynomial(ln[x],Integer)

    is something strange. Oddly perhaps, Axiom interprets 5 as a UnivariatePolynomial and 'ln[x]' as a subscripted Symbol and the result is a univariate polynomial in the variable 'ln[x]'.

    So perhaps what you meant to write was:

    fricas
    integrate(x^5*log(x),x)
    
\label{eq7}{{6 \ {{x}^{6}}\ {\log \left({x}\right)}}-{{x}^{6}}}\over{36}(7)
    Type: Union(Expression(Integer),...)

  8. Use braces not parenthesis after begin and end

    The command:

        \begin(axiom)
        integrate(sin(x))
        \end(axiom)
    

    wont work.

    Use "braces" like this { } not parenthesis ( ) around {axiom}.

    Finally, unless the expression is a univariate polynomial, then you must also specify the variable with which to integrate.

    fricas
    integrate(sin(x),x)
    
\label{eq8}-{\cos \left({x}\right)}(8)
    Type: Union(Expression(Integer),...)

  9. Use parenthesis not braces in Axiom commands

    This command:

        \begin{axiom}
        solve{xy=1,x}
        \end{axiom}
    

    uses {} after the solve operation. This is syntactically correct but it probably doesn't do what you might expect.

    fricas
    solve{xy=1,x}
    
\label{eq9}\left[{x = 0}\right](9)
    Type: List(Equation(Fraction(Polynomial(Integer))))

    In Axiom {...,...} is executed as a block of commands which returns the result of the last command in the sequence. Compare

    fricas
    a:={xy=1,x}
    
\label{eq10}x(10)
    Type: Variable(x)

    which is just x to

    fricas
    b:=(xy=1,x)
    
\label{eq11}\left[{xy = 1}, \: x \right](11)
    Type: Tuple(Any)

    solve normally operates on such a tuple and

    fricas
    c:=[xy=1,x]
    
\label{eq12}\left[{xy = 1}, \: x \right](12)
    Type: List(Any)

    which is a list and finally

    fricas
    c:=set [xy=1,x]
    
\label{eq13}\left\{{xy = 1}, \: x \right\}(13)
    Type: Set(Any)

    which is how to construct a set.

    Also notice that multiplication must be written using *

    fricas
    solve(x*y=1,x)
    
\label{eq14}\left[{x ={1 \over y}}\right](14)
    Type: List(Equation(Fraction(Polynomial(Integer))))

  10. Use %minusInfinity and %plusInfinity

    I'd like to see if Axiom can do my favorite definite integral:

        \begin{axiom}
        integrate(x^4/(sinh(x))^2,x,-inf,inf)
        \end{axiom}
    

    In Axiom use %minusInfinity and %plusInfinity instead of -inf and inf.

    fricas
    integrate(x^4/(sinh(x))^2,x=%minusInfinity..%plusInfinity)
    
\label{eq15}\verb#"potentialPole"#(15)
    Type: Union(pole: potentialPole,...)

  11. Numeric conversions

    The results of calculations depend on the type of the inputs You can tell Axiom that you would like the result expressed as a floating point number (if possible) using @. For example:

    fricas
    asin(1/2)@Float
    
\label{eq16}0.5235987755 \<u> 9829887308(16)
    Type: Float

  12. Axiom prefers symbolic calculations

    The trig functions are expressed in radians so use \pi/2 instead 90 and 34\pi/180 instead of 34. Finally, because Axiom prefers symbolic calculations express 1.544 as a rational number

    fricas
    r:Fraction Integer:=1.544
    
\label{eq17}{193}\over{125}(17)
    Type: Fraction(Integer)
    fricas
    eq1:=90*%pi/180-asin(n*sin(34*%pi/180)/r)=asin(n/r)
    
\label{eq18}{{-{2 \ {\arcsin \left({{{125}\  n \ {\sin \left({{{17}\  \pi}\over{9
0}}\right)}}\over{193}}\right)}}+ \pi}\over 2}={\arcsin \left({{{1
25}\  n}\over{193}}\right)}(18)
    Type: Equation(Expression(Integer))
    fricas
    s:=solve(eq1,n)
    
\label{eq19}\begin{array}{@{}l}
\displaystyle
\left[{n = -{{{386}\ {{e}^{{{17}\  \pi \ {\sqrt{- 1}}}\over{9
0}}}}\over{{125}\ {\sqrt{-{{{e}^{{{17}\  \pi \ {\sqrt{- 1}}}\over{9
0}}}^{4}}+{6 \ {{{e}^{{{17}\  \pi \ {\sqrt{- 1}}}\over{90}}}^{2}}}- 1}}}}}, \: \right.
\
\
\displaystyle
\left.{n ={{{386}\ {{e}^{{{17}\  \pi \ {\sqrt{- 1}}}\over{90}}}}\over{{1
25}\ {\sqrt{-{{{e}^{{{17}\  \pi \ {\sqrt{- 1}}}\over{90}}}^{4}}+{6 \ {{{e}^{{{17}\  \pi \ {\sqrt{- 1}}}\over{90}}}^{2}}}- 1}}}}}\right] (19)
    Type: List(Equation(Expression(Integer)))

    Axiom thinks there are two solutions, unfortunately only one is valid:

    fricas
    eval(eq1,s.1)::Equation Expression Float
    
\label{eq20}\begin{array}{@{}l}
\displaystyle
{
\begin{array}{@{}l}
\displaystyle
{\arcsin \left({{{1.1183858069 \<u> 414936603}\ {{e}^{{0.593411
9456 \</u> 7807205615}\ {\sqrt{-{1.0}}}}}}\over{\sqrt{-{{1.0}\ {{{e}^{{0.5934119456 \<u> 7807205615}\ {\sqrt{-{1.0}}}}}^{4}}}+{{6.0}\ {{{e}^{{0.5934119456 \</u> 7807205615}\ {\sqrt{-{1.0}}}}}^{2}}}-{1.0}}}}\right)}+ 
\
\
\displaystyle
{1.5707963267 \<u> 948966192}
(20)
    Type: Equation(Expression(Float))
    fricas
    eval(eq1,s.2)::Equation Expression Float
    
\label{eq21}\begin{array}{@{}l}
\displaystyle
{
\begin{array}{@{}l}
\displaystyle
-{{1.0}\ {\arcsin \left({{{1.1183858069 \<u> 414936603}\ {{e}^{{0.5
934119456 \</u> 7807205615}\ {\sqrt{-{1.0}}}}}}\over{\sqrt{-{{1.0}\ {{{e}^{{0.5934119456 \<u> 7807205615}\ {\sqrt{-{1.0}}}}}^{4}}}+{{6.0}\ {{{e}^{{0.5934119456 \</u> 7807205615}\ {\sqrt{-{1.0}}}}}^{2}}}-{1.0}}}}\right)}}+{1.5707963267 \<u> 948966192}
(21)
    Type: Equation(Expression(Float))

  13. Coercion is sometimes necessary

    For example

    fricas
    integrate((4 - x**2)**.5::Expression Fraction Integer, x)
    There are no library operations named ** Use HyperDoc Browse or issue )what op ** to learn if there is any operation containing " ** " in its name.
    Cannot find a definition or applicable library operation named ** with argument type(s) Variable(x) PositiveInteger
    Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.

  14. Use either differentiate or the abbreviation D

    Since sin(x) cannot be interpreted as a univariate polynomial, you must specify the integration variable.

    fricas
    differentiate(sin(x),x)
    
\label{eq22}\cos \left({x}\right)(22)
    Type: Expression(Integer)

  15. MathAction requires that Axiom library code must beging with )abbrev. Typing )abb is not enough even though that works in Axiom itself.



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