I select the expression in the Tioga document, set a primary selection in the CaminoReal tool, and hit the FromTioga button with the mouse:

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The expression from the Tioga document replaces the primary selection in my CaminoReal tool. Using CaminoReal, I edit the Xexpression to be.

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Then I make it the primary CaminoReal selection, indicate the position in the Tioga document where I want it to go, and bug the ToTioga button in CaminoReal. The new expression replaces the old in the Tioga document. And of course, I can print the modified Tioga document whenever I wish.

I can change the size of an Expression in a Tioga document; let's make this one bigger.

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We said earlier that to do computation, the CaminoReal user must specify a domain, and imbed his expressions as elements of that domain (this was what we did with the SetObject button). CaminoReal offers another style of computation. There is a system evaluator, called Eval, that can be applied to any expression, and determines an appropriate domain for the result. Let's see some examples of its use.

First, suppose we have the following expression in a CaminoReal tool:

This expression asserts that a certain 3 x 3 matrix is equal to the inverse of the product of two other 3 x 3 matrices. The Del operator here denotes gcd. In other words, the ij-th element of the matrix I'm selecting now the greatest common divisor of i and j.

I can apply Eval to any selected subexpression, either putting the result in a new CaminoReal tool, or replacing the primary selection with the result. Replacing the primary selection with the result is often convenient, particularly if I don't want to save the result, because of CaminoReal's Undo button. For example, let's see what the entries of the selected matrix actually are using the Eval function:

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and let's undo the result to get back to the original expression.

Let's see what the product of the two matrices is:

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Let's evaluate the inverse:

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And finally let's check the entire equation:

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I can apply the Eval function to expressions in Tioga documents. This can be quite useful for detecting typographical or other errors, in other words, mathematical spelling checking. For example, before I print a document, I might like to check that my equations don't contain errors. Thus, I want to evaluate them, but discard the result before I print the document.

Here's a Tioga document that contains the script I'm using to make this videotape, and here's the expression we were just working on, in the document. Let's check its correctness in place, by evaluating it with the EvalTiogaInPlace button:

We see that it's correct. Tioga's Reset button allows us to Undo, i.e. go back to the expression we actually want to print.

[Reset].