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lojbau mekso: Mathematical Expressions in Lojban
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The following cmavo are discussed in this section:
jo'i JOhI start vector
te'u TEhU end vector
pi'a VUhU matrix row combiner
sa'i VUhU matrix column combiner
A mathematical vector is a list of numbers, and a mathematical
matrix is a table of numbers. Lojban considers matrices to be
built up out of vectors, which are in turn built up out of
operands.
``jo'i'', the only cmavo of selma'o JOhI, is the vector indicator: it has a syntax reminiscent of a forethought operator, but has very high precedence. The components must be simple operands rather than full expressions (unless parenthesized). A vector can have any number of components; ``te'u'' is the elidable terminator. An example:
15.1) li jo'i paboi reboi te'u su'i jo'i ciboi voboi
du li jo'i voboi xaboi
the-number array( one, two ) plus array( three, four)
equals the-number array( four, six)
(1,2) + (3,4) = (4,6)
Vectors can be combined into matrices using either ``pi'a'',
the matrix row operator, or ``sa'i'', the matrix column
operator. The first combines vectors representing rows of the
matrix, and the second combines vectors representing columns of
the matrix. Both of them allow any number of arguments:
additional arguments are tacked on with the null operator
``ge'a''.
Therefore, the ``magic square'' matrix
15.2) jo'i biboi paboi xa pi'a jo'i ciboi muboi ze
ge'a jo'i voboi soboi re
the-vector (8 1 6) matrix-row the-vector (3 5 7)
, the-vector (4 9 2)
or as
15.3) jo'i biboi ciboi vo sa'i jo'i paboi muboi so
ge'a jo'i xaboi zeboi re
the-vector (8 3 4) matrix-column the-vector (1 5 9)
, the-vector (6 7 2)
The regular mekso operators can be applied to vectors and to
matrices, since grammatically both of these are expressions. It
is usually necessary to parenthesize matrices when used with
operators in order to avoid incorrect groupings. There are no
VUhU operators for the matrix operators of inner or outer
products, but appropriate operators can be created using a
suitable symbolic lerfu word or string prefixed by ``ma'o''.
Matrices of more than two dimensions can be built up using either ``pi'a'' or ``sa'i'' with an appropriate subscript numbering the dimension. When subscripted, there is no difference between ``pi'a'' and ``sa'i''.
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Previous
Infix operators revisited |
lojbau mekso: Mathematical Expressions in Lojban
The Lojban Reference Grammar |
Next
Reverse Polish notation |