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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)
 (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

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)
 (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}
 (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}  (4) Type: AlgebraicNumber? 7. Axiom sometimes interprets commands in unexpected ways This command appears to work fricas integrate(x^5 ln[x],x)  (5) Type: Union(Expression(Integer),...) But notice that fricas 5 ln[x]  (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)  (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)  (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}  (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}  (10) Type: Variable(x) which is just x to fricas b:=(xy=1,x)  (11) Type: Tuple(Any) solve normally operates on such a tuple and fricas c:=[xy=1,x]  (12) Type: List(Any) which is a list and finally fricas c:=set [xy=1,x]  (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)  (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)  (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  (16) Type: Float 12. Axiom prefers symbolic calculations The trig functions are expressed in radians so use instead and instead of . Finally, because Axiom prefers symbolic calculations express as a rational number fricas r:Fraction Integer:=1.544  (17) Type: Fraction(Integer) fricas eq1:=90*%pi/180-asin(n*sin(34*%pi/180)/r)=asin(n/r)  (18) Type: Equation(Expression(Integer)) fricas s:=solve(eq1,n)  (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  (20) Type: Equation(Expression(Float)) fricas eval(eq1,s.2)::Equation Expression Float  (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)
 (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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