Why a new formula symbol?
What is the chinese formula symbol 大 good for. What is that kind of mathematical operation, that needs a new symbol to be introduced into mathematical notation.
The purpose of the operator 大 is to change the value of variables. It is the mathematical equivalent to an assignment in programming languages, which is the most elementary operation of all computational steps. It is supported by all
computer algebra systems and it seems to be most intuitive to change the value
of variables during a computation. Strangely enough the operation does not
yet have a proper mathematical operator.
Mathematical definition
The symbol 大 can be used to denote a value assignment operator. Above the
operator we place the variable to which a new value should be assigned. Below
we write the new value. The whole operator with its two arguments atop and
below is applied to a formula, which we want to evaluate with the newly assigned
parameters. This is mathematically precise and intuitive at the same time.
Prevailing mathematical notation knows this operation as the bar operator. Its
symbol is a vertical line with the value assignment in the lines index position.
Other than all other mathematical operators, the bar operator is applied from
the right hand side, which makes it difficult to integrate in larger formulas.
Furthermore a mathematician is required states an equality in the operators
index position, where by nature no equality holds.
Examples
The following example demonstrates the use of the 大 operator in
an operator sequence. Read from left to right we can interpret it as assigning 8
to x, then multiplying x with 5 and finaly evaluating x + 2. Alternatively, we
can stick to the operators definition and evaluate from right to left.
Operator theory allows operators to be taken to the power of any integer number. The result is a repeated application of that operator. Computer programmers know this construction as loops with deterministic length.
