[index]

Algebra::AlgebraicParser

(Class of Evaluation of Algebraic Expression)

File Name:

• algebraic-parser.rb

SuperClass:

• Object

Included Module:

none.

Class Methods:

Algebra::AlgebraicParser.eval(string, ring)

Calculates the string on ring.

Methods:

none.

Specification:

Evaluation

The value of variable is obtained by the class method indeterminate of ring. The value of numeral is the return value of the class method indeterminate of ring.ground.

require "algebraic-parser"
class A
  def self.indeterminate(str)
    case str
    when "x"; 7
    when "y"; 11
    end
  end
  def A.ground
    Integer
  end
end
p Algebra::AlgebraicParser.eval("x * y - x^2 + x/8", A)
    #=> 7*11 - 7**2 + 7/8 = 28

indeterminate of Integer is defined as following:

def Integer.indeterminate(x)
  eval(x)
end

in algebra-supplement.rb which is required by algebraic-parser.rb

Identifier

Identifier is "a alphabet + some digits". For example,

"a13bc04def0"

is interpreted as

"a13 * b * c04 * d * e * f0".

Operations

The order of strength of operations:

;               intermediate evaluation
+, -            sum, difference
+, -            unary +, unary -
*, /            product, quotient
(juxtaposition) product
**, ^           power

Example:

In Algebra::Polynomial and Algebra::MPolynomial, indeterminate andground are defined suitably. So we can obtain the value of strings as following:

require "algebraic-parser"
require "rational"
require "m-polynomial"
F = Algebra::MPolynomial(Rational)
p Algebra::AlgebraicParser.eval("- (2*y)**3 + x", F) #=> -8y^3 + x

In Algebra::MPolynomial, indeterminate resists the objects representing variables in order that they appear. So we may set the order, using `;'.

F.variables.clear
p Algebra::AlgebraicParser.eval("x; y; - (2*y)**3 + x", F) #=> x - 8y^3