I'll open this script. This is just a Tioga document in our environment. I can mail all or part of it around.

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Expressions in documents are represented as decorated characters. I can copy them from one document to another using usual editor character copy (examples) To play with their substructure, however, I bring them back to a CR tool (show it).

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 X expression 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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CaminoReal offers a system evaluator that can be applied to any expression. For example, 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 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 check individual entries of the matrix (DoIT), and next see what the entries of the selected matrix actually are using the Eval function (DoIT):

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Each time we 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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Let's check the matrix identity:

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by first copying the evluated left side to the right, and then redoing the left side. Because of CaminoReal's current philosophy of computation, we have to replace the first element X by X in the matrix of gcd's in order to invert it.

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 proofreading. 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].

Create the following matrix, illustrating copying using the editor

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Play with in-place eval of elements, illustrating that deriv(int) = id.

Let X be defined to be:

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Let X be defined to be:

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Let X be the Sylvester matrix of X andX :

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Then the resultant is the determinant of X , i.e.

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Leave Matheval on.

Let the arguments be:

and:

We load these in to CaminoReal viewers, and compute gcd. It will be done using the SAC-2 algebra system on the Vax.

Now by turning Matheval off, I can show you what those args were, and so I can check the gcd computation.

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