This is a test of Sage in MathAction.

Sage stands for:

  Software for Algebra and Geometry Experimentation

Sage has native computer algebra capabilities as well as interfaces to other systems such as GAP , PARI , Singular and Maxima.

Sage was recently extended (version 1.4.1.2) to include support for Axiom.

Here is a summary of features

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This is how to enter Sage commands:

  Commands can be used inline, for example: $1+2=\sage{1+2}$ and $\sqrt{1+2}=\sage{sqrt(1+2)}$.
  Or we can evaluate a block of Sage commands:
  \begin{sageblock}
  # do some stuff
  E = EllipticCurve("37a")
  # more stuff
  \end{sageblock}

  Now the elliptic curve $E$ given by $\sage{E}$
  has discriminant $\sage{E.discriminant()}$.

To get this:

Commands can be used inline, for example: and . Or we can evaluate a block of Sage commands:

Now the elliptic curve given by has discriminant .

Maxima commands in Sage look like this:

The \sage commands can occur in other LaTeX contexts such as:

  \begin{equation}
     \int \sage{f} dx = \sage{g}.
  \end{equation}

This produces:

(1)

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Axiom commands in Sage look like this:

The \sage commands can occur in other LaTeX contexts such as:

  \begin{equation}
     {\int \sage{fAxiom} dx} = {\sage{gAxiom}}.
  \end{equation}

This produces:

(2)

Using Axiom to guess integer sequences:

Gives:

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Sage also works in pamphlet files. See SandBoxSagePamphlet