Edit detail for Common Mistakes revision 1 of 3

changed:
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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ドル$ and 34ドル\pi/180$ instead of 34ドル$. Finally, because Axiom
 prefers symbolic calculations express 1ドル.544$ 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.