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author Robert McIntyre <rlm@mit.edu>
date Fri, 28 Oct 2011 00:03:05 -0700
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1:8d8278e09888 2:b4de894a1e2e
1 #+TITLE: Notes for SICM
2
3 * Complex numbers
4
5
6 * Multidimensional Structures
7 ** Tuples
8 - Tuples are a new data type: sequences with /spin/. A tuple can be either spin-up or spin-down.
9 - A pair of compatible tuples can be *contracted* into a single number.
10 - Tuples are compatible if they have the same length and opposite
11 spin, and if their corresponding pairs of items are either both
12 numbers or both compatible tuples.
13 - To contract tuples, take the sum of the products of corresponding
14 pairs of items. (To take the product of compatible tuples,
15 contract them.)
16
17 *Generic Arithmetic:* To multiply two tuples, check to see if they are
18 compatible. If they are, contract them. If they aren't, multiply each
19 item of the second tuple by the first tuple.
20
21 To multiply a tuple by a number, multiply each element of the tuple by
22 the number.
23
24 ** Matrices
25 Uses incanter matrices.