Search results
Results from the WOW.Com Content Network
The above dyadic functions examples [left and right examples] (using the same / symbol, right example) demonstrate how Boolean values (0s and 1s) can be used as left arguments for the \ expand and / replicate functions to produce exactly opposite results.
The concepts of successor, addition, multiplication and exponentiation are all hyperoperations; the successor operation (producing x + 1 from x) is the most primitive, the addition operator specifies the number of times 1 is to be added to itself to produce a final value, multiplication specifies the number of times a number is to be added to ...
Python supports normal floating point numbers, which are created when a dot is used in a literal (e.g. 1.1), when an integer and a floating point number are used in an expression, or as a result of some mathematical operations ("true division" via the / operator, or exponentiation with a negative exponent).
Modular exponentiation is the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus); that is, c = b e mod m. From the definition of division, it follows that 0 ≤ c < m. For example, given b = 5, e = 3 and m = 13, dividing 5 3 = 125 by 13 leaves a remainder of c = 8.
The result for the above examples would be (in reverse Polish notation) "3 4 +" and "3 4 2 1 − × +", respectively. The shunting yard algorithm will correctly parse all valid infix expressions, but does not reject all invalid expressions. For example, "1 2 +" is not a valid infix expression, but would be parsed as "1 + 2". The algorithm can ...
If exponentiation is indicated by stacked symbols using superscript notation, the usual rule is to work from the top down: [2] [7] a b c = a (b c) which typically is not equal to (a b) c. This convention is useful because there is a property of exponentiation that (a b) c = a bc, so it's unnecessary to use serial exponentiation for this.
The Euclidean method was first introduced in Efficient exponentiation using precomputation and vector addition chains by P.D Rooij. This method for computing x n {\displaystyle x^{n}} in group G , where n is a natural integer, whose algorithm is given below, is using the following equality recursively:
The number n is called the exponent and the expression is known formally as exponentiation of b by n or the exponential of n with base b. It is more commonly expressed as "the nth power of b", "b to the nth power" or "b to the power n". For example, the fourth power of 10 is 10,000 because 10 4 = 10 × 10 × 10 × 10 = 10,000.