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author Robert McIntyre <rlm@mit.edu>
date Fri, 28 Oct 2011 00:03:05 -0700
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     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.