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### various expressions

Major elements to construct expressions are the following:

- addition, subtraction, multiplication, division, exponentiation
  The exponentiation is denoted by ``^'`. (This differs from C language.) Division denoted by ``/'` is used to operate in a field, for example, `2/3` results in a rational number `2/3`. For integer division and polynomial division, both including remainder operation, built-in functions are provided.

      x+1  A^2*B*afo X/3

- programming variables with indices
  An element of a vector, a matrix or a list can be referred to by indexing. Note that the indices begin with number 0. When the referred element is again a vector, a matrix or a list, repeated indexing is also effective.

      V[0] M[1][2]

- comparison operation
  There are comparison operations ``=='` for equivalence, ``!='` for non-equivalence, ``>'`, ``<'`,``>='`, and ``<='` for larger or smaller. The results of these operations are either value 1 for the truth, or 0 for the false.
- logical expression
  There are two binary logical operations ``&&'` for logical ``conjunction'`(and), ``||'` for logical ``disjunction'`(or), and one unary logical operation ``!'` for logical ``negation'`(not). The results of these operations are either value 1 for the truth, and 0 for the false.
- assignment
  Value assignment of a program variable is usually done by ``='`. There are special assignments combined with arithmetic operations. (``+='`, ``-='`, ``*='`, ``/='`, ``^='`)

      A = 2  A *= 3 (the same as A = A*3; The other combination are alike.)

- function call
  A function call is also an expression.
- ``++'`, ``--'`
  These operators are attached to or before a program variable, and denote special operations and values.

      A++  the expression value is the previous value of A, and A = A+1
      A--  the expression value is the previous value of A, and A = A-1
      ++A  A = A+1, and the expression value is the value after increment of A
      --A  A = A-1, and the expression value is the value after decrement of A

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