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     1.4 +#+TITLE: Notes for SICM
     1.5 +
     1.6 +* Complex numbers
     1.7 +
     1.8 +
     1.9 +* Multidimensional Structures
    1.10 +** Tuples
    1.11 +- Tuples are a new data type: sequences with /spin/. A tuple can be either spin-up or spin-down.
    1.12 +- A pair of compatible tuples can be *contracted* into a single number.
    1.13 +  - Tuples are compatible if they have the same length and opposite
    1.14 +    spin, and if their corresponding pairs of items are either both
    1.15 +    numbers or both compatible tuples.
    1.16 +  - To contract tuples, take the sum of the products of corresponding
    1.17 +    pairs of items. (To take the product of compatible tuples,
    1.18 +    contract them.)
    1.19 +
    1.20 +*Generic Arithmetic:* To multiply two tuples, check to see if they are
    1.21 + compatible. If they are, contract them. If they aren't, multiply each
    1.22 + item of the second tuple by the first tuple.
    1.23 +
    1.24 +To multiply a tuple by a number, multiply each element of the tuple by
    1.25 +the number.
    1.26 +
    1.27 +** Matrices
    1.28 +Uses incanter matrices.