- 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}
- 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
.
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integrate(1/(a+z^3), z)
Type: Union(Expression(Integer),...)
- Reduce commands must end with a semicolon ;
But it must be there for Reduce.
- 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
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integrate((x^2+2*x*log(x)+5)/(sin(x^2+x^3-x^4)^2), x)
Type: Union(Expression(Integer),...)
- 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
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sqrt{49/100}
- 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:
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sqrt{49/100}
- Axiom sometimes interprets commands in unexpected ways
This command appears to work
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integrate(x^5 ln[x],x)
Type: Union(Expression(Integer),...)
But notice that
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5 ln[x]
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:
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integrate(x^5*log(x),x)
Type: Union(Expression(Integer),...)
- 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.
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integrate(sin(x),x)
Type: Union(Expression(Integer),...)
- 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.
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solve{xy=1,x}
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
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a:={xy=1,x}
Type: Variable(x)
which is just x
to
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b:=(xy=1,x)
Type: Tuple(Any)
solve normally operates on such a tuple and
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c:=[xy=1,x]
Type: List(Any)
which is a list and finally
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c:=set [xy=1,x]
Type: Set(Any)
which is how to construct a set.
Also notice that multiplication must be written using *
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solve(x*y=1,x)
Type: List(Equation(Fraction(Polynomial(Integer))))
- 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.
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integrate(x^4/(sinh(x))^2,x=%minusInfinity..%plusInfinity)
Type: Union(pole: potentialPole,...)
- 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:
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asin(1/2)@Float
Type: Float
- 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
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r:Fraction Integer:=1.544
Type: Fraction(Integer)
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eq1:=90*%pi/180-asin(n*sin(34*%pi/180)/r)=asin(n/r)
Type: Equation(Expression(Integer))
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s:=solve(eq1,n)
Type: List(Equation(Expression(Integer)))
Axiom thinks there are two solutions, unfortunately only one
is valid:
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eval(eq1,s.1)::Equation Expression Float
Type: Equation(Expression(Float))
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eval(eq1,s.2)::Equation Expression Float
Type: Equation(Expression(Float))
- Coercion is sometimes necessary
For example
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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.
- Use either
differentiate
or the abbreviation D
Since sin(x) cannot be interpreted as a univariate polynomial,
you must specify the integration variable.
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differentiate(sin(x),x)
Type: Expression(Integer)
- MathAction requires that Axiom library code must beging with
)abbrev
.
Typing )abb
is not enough even though that works in Axiom itself.