## Symbolic Algebra

Cassiopeia uses MathML content markup to represent equations internally. This means that equations have mathematical meaning and can therefore be processed by the integrated symbolic algebra system. The tight integration with the super-efficient WYSIWYG equation editor gives Cassiopeia a cutting edge.

## Taking derivatives

Press Command-y to create a new equation and then type "y", "=", "a", Ctrl-l, "3", "x", Ctrl-h, "3", ... five times cursor right ..."+", "a", Ctrl-l, "2", "x", Ctrl-h, "2", ...enter x in the Variable field and click on

**Differentiate**. The following equation is generated automatically.

Repeating this process gives

That's one way of taking derivatives. There is another one. Create a new equation with Command-y and then type "z", "=", Ctrl-d

Now Alt-doubleclick on the last equation to simplify. Do this a couple of times until Cassiopeia reaches the end of its wisdom.

In the above example we had to explicitly specify a derivation variable. This would not have been necessary if we entered a function instead of an equation. A function requires the specification of a function variable. Create a copy of the function above (just doubleclick on it), then click into the equation and remove the y on the left of the equal sign. Then type "y", "(", "x", ")". The equation should look as follows now.

The graph plot is inserted into the document below the shift-doubleclicked function or at the current insertion location. Drag the other two functions y' and y'' from the document into the textview on the 2D graph inspector and change the from value to 0. Press <Enter> after modifying a value to trigger redraw.

Play with the x and y limits until your are satisfied with the graph. Then choose Tools - Colors from the Cassiopeia menu, select colors and drag one color on each of the three functions in the tableview.

You might also want to play with the values of the coefficients. Generate a PDF for your document. You should get something like the following:

## Solving Integrals

We want to solve a few integrals now using the integrated symbolic algebra system. Assume you want to calculate the volume of a sphere. Create a new equation with Command-y and type in the infinitesimal volume element in sphere coordinates like so "d", "V", "=", "r", Ctrl-h, "2", Cursor-up, Cursor-right, "s", "i", "n", Ctrl-g "b", "d", "r", ...

Now click into the center of this equation and hit cursor up until the inner integral is selected.

Then press Ctrl-y (see Core - Strokes) to upgrade this integral to a determined integral.

Click into the lower limit cell and enter 0. Hit cursor right four times to get into the upper limit cell (or use the mouse). There enter R.

Press cursor up until the middle integral is selected

and hit Ctrl-y to upgrade that as well.

Enter "0" for the lower limit and "2", Ctrl-g p for the upper limit.

Press cursor up until the outer integral is selected. Upgrade that as well and set the limits 0 and pi.

We are done with the creative part. Cassiopeia can handle the rest of the work. Just Alt-doubleclick on the equation(s) until the result is presented as shown below.

We have started the above integration with a dintegral (Ctrl-i d). A dintegral has a single cell behind the integral sign and is useful for expressions of the form

## News

21.01.2015 | Cassiopeia 1.4.0 released |

14.05.2013 | LaTeX and HTML Generation |

08.05.2013 | Example Paper released |

26.04.2013 | Co-editing in a workgroup |

26.04.2013 | Troubleshooting |

16.04.2013 | Equation Editor Quick Reference |

12.04.2013 | Equation Editor |

04.04.2013 | Links and Bibliography |

01.04.2013 | Books |

30.03.2013 | Documents |

28.03.2013 | Simulations |

16.03.2013 | 2D Graphs |

10.03.2013 | Symbolic Algebra |

08.03.2013 | Getting Started |

07.03.2013 | Installation and Setup |

## Youtube

19.06.2013 | Magnetic Field |

14.06.2013 | Creating Documents |

10.06.2013 | Vector Algebra |

30.05.2013 | Installation and Setup |

30.05.2013 | Blackboard Replacement |

30.05.2013 | Differential Simulations |

29.05.2013 | Installation and Setup |

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