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# Arrays and Tables

## Definitions for Arrays and Tables

Function: ARRAY (name, dim1, dim2, ..., dimk)
This sets up a k-dimensional array. A maximum of five dimensions may be used. The subscripts for the ith dimension are the integers running from 0 to dimi. If the user assigns to a subscripted variable before declaring the corresponding array, an undeclared array is set up. If the user has more than one array to be set up the same way, they may all be set up at the same time, by ARRAY([list-of-names],dim1, dim2, ..., dimk). Undeclared arrays, otherwise known as hashed arrays (because hash coding is done on the subscripts), are more general than declared arrays. The user does not declare their maximum size, and they grow dynamically by hashing as more elements are assigned values. The subscripts of undeclared arrays need not even be numbers. However, unless an array is rather sparse, it is probably more efficient to declare it when possible than to leave it undeclared. The ARRAY function can be used to transform an undeclared array into a declared array.

Function: ARRAYAPPLY (array,[sub1, ... ,subk])
is like APPLY except the first argument is an array.

Function: ARRAYINFO (a)
returns a list of information about the array a. For hashed arrays it returns a list of "HASHED", the number of subscripts, and the subscripts of every element which has a value. For declared arrays it returns a list of "DECLARED", the number of subscripts, and the bounds that were given the the ARRAY function when it was called on a. Do EXAMPLE(ARRAYINFO); for an example.

Function: ARRAYMAKE (name,[i1,i2,...])
returns name[i1,i2,...].

Variable: ARRAYS
default: [] a list of all the arrays that have been allocated, both declared and undeclared. Functions which deal with arrays are: ARRAY, ARRAYAPPLY, ARRAYINFO, ARRAYMAKE, FILLARRAY, LISTARRAY, and REARRAY.

Function: BASHINDICES (expr)
- transforms the expression expr by giving each summation and product a unique index. This gives CHANGEVAR greater precision when it is working with summations or products. The form of the unique index is J<number>. The quantity <number> is determined by referring to GENSUMNUM, which can be changed by the user. For example, GENSUMNUM:0\$ resets it.

Function: FILLARRAY (array,list-or-array)
fills array from list-or-array. If array is a floating-point (integer) array then list-or-array should be either a list of floating-point (integer) numbers or another floating-point (integer) array. If the dimensions of the arrays are different array is filled in row-major order. If there are not enough elements in list-or-array the last element is used to fill out the rest of array. If there are too many the remaining ones are thrown away. FILLARRAY returns its first argument.

Function: GETCHAR (a, i)
returns the ith character of the quoted string or atomic name a. This function is useful in manipulating the LABELS list.

Function: LISTARRAY (array)
returns a list of the elements of a declared or hashed array. the order is row-major. Elements which you have not defined yet will be represented by #####.

Function: MAKE_ARRAY (type,dim1,dim2,...,dimn)
- creates an array. "type" may be 'ANY, 'FLONUM, 'FIXNUM, 'HASHED or 'FUNCTIONAL. This is similar to the ARRAY command, except that the created array is a functional array object. The advantage of this over ARRAY is that it doesn't have a name, and once a pointer to it goes away, it will also go away. e.g. Y:MAKE_ARRAY(....); Y now points to an object which takes up space, but do Y:FALSE, and Y no longer points to that object, so the object will get garbage collected. Note: the "dimi" here are different from the ARRAY command, since they go from 0 to i-1, i.e. a "dimension" of 10 means you have elements from 0 to 9. Y:MAKE_ARRAY('FUNCTIONAL,'F,'HASHED,1) - The second argument to MAKE_ARRAY in this case is the function to call to calculate array elements, and the rest of the arguments are passed recursively to MAKE_ARRAY to generate the "memory" for the array function object.

Function: REARRAY (array,dim1, ... ,dimk)
can be used to change the size or dimensions of an array. The new array will be filled with the elements of the old one in row-major order. If the old array was too small, FALSE, 0.0 or 0 will be used to fill the remaining elements, depending on the type of the array. The type of the array cannot be changed.

Function: REMARRAY (name1, name2, ...)
removes arrays and array associated functions and frees the storage occupied. If name is ALL then all arrays are removed. It may be necessary to use this function if it is desired to redefine the values in a hashed array.

Variable: USE_FAST_ARRAYS
[TRUE on Lispm] - If TRUE then only two types of arrays are recognized.

1) The art-q array (t in common lisp) which may have several dimensions indexed by integers, and may hold any lisp or macsyma object as an entry. To construct such an array, enter A:MAKE_ARRAY(ANY,3,4); then A will have as value, an array with twelve slots, and the indexing is zero based.

2) The Hash_table array which is the default type of array created if one does B[X+1]:Y^2 (and B is not already an array,a list, or a matrix-- if it were one of these an error would be caused since x+1 would not be a valid subscript for an art-q array,a list or a matrix ). Its indices (also known as keys) may be any object. It only takes ONE KEY at a time (B[X+1,U]:Y would ignore the u) Referencing is done by B[X+1]==> Y^2. Of course the key may be a list, eg B[[x+1,u]]:y would be valid. This is in- compatible with the old Macsyma hash arrays, but saves consing.

An advantage of storing the arrays as values of the symbol is that the usual conventions about local variables of a function apply to arrays as well. The Hash_table type also uses less consing and is more efficient than the old type of macsyma hashar. To obtain consistent behaviour in translated and compiled code set TRANSLATE_FAST_ARRAYS [TRUE] to be TRUE.

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