Edit detail for Common Mistakes revision 1 of 3

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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'.
  \begin{axiom}
  integrate(1/(a+z^3), z)
  \end{axiom}

3 Reduce commands must end with a semicolon ;

  But it must be there for Reduce.
  \begin{reduce}
  r^2+r+1;
  \end{reduce}

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


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


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

7 Axiom sometimes interprets commands in unexpected ways

  This command appears to work
  \begin{axiom}
  integrate(x^5 ln[x],x)
  \end{axiom}

  But notice that
  \begin{axiom}
  5 ln[x]
  \end{axiom}

  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:
  \begin{axiom}
  integrate(x^5*log(x),x)
  \end{axiom}

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.
  \begin{axiom}
  integrate(sin(x),x)
  \end{axiom}

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

  In Axiom {...,...} is executed as a block of commands which
  returns the result of the last command in the sequence. Compare
  \begin{axiom}
  a:={xy=1,x}
  \end{axiom}
  which is just 'x' to
  \begin{axiom}
  b:=(xy=1,x)
  \end{axiom}
  solve normally operates on such a *tuple* and
  \begin{axiom}
  c:=[xy=1,x]
  \end{axiom}
  which is a list and finally
  \begin{axiom}
  c:=set [xy=1,x]
  \end{axiom}
  which is how to construct a set.

  Also notice that multiplication must be written using *
  \begin{axiom}
  solve(x*y=1,x)
  \end{axiom}

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.
   \begin{axiom}
   integrate(x^4/(sinh(x))^2,x=%minusInfinity..%plusInfinity)
   \end{axiom}

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:
   \begin{axiom}
   asin(1/2)@Float
   \end{axiom}

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
   \begin{axiom}
   r:Fraction Integer:=1.544
   eq1:=90*%pi/180-asin(n*sin(34*%pi/180)/r)=asin(n/r)
   s:=solve(eq1,n)
   \end{axiom}

   Axiom thinks there are two solutions, unfortunately only one
   is valid:
   \begin{axiom}
   eval(eq1,s.1)::Equation Expression Float
   eval(eq1,s.2)::Equation Expression Float
   \end{axiom}

13 Reduce commands must end with a semicolon ;

   Like this
   \begin{reduce}
   r^2+r+1;
   \end{reduce}

14 Coercion is sometimes necessary

   For example
   \begin{axiom}
   integrate((4 - x**2)**.5::Expression Fraction Integer, x)
   \end{axiom}

15 Use either 'differentiate' or the abbreviation 'D'

   Since sin(x) cannot be interpreted as a univariate polynomial,
   you must specify the integration variable.
   \begin{axiom}
   differentiate(sin(x),x)
   \end{axiom}

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