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Algebraic Line

The core feature of the program is representation of the algebraic variable as a mobile point that can be moved along the algebraic line (see movie on the home page). This feature makes it possible to operate with expressions and propositions as if they were numerical quantities.

As a result, ALNUSET can facilitate understanding in these areas:
  • The structure of expressions. Demo
  • The definition of expressions in numerical sets. Demo
  • The properties of expressions. Demo
  • Polynomial roots. Demo
  • The truth value of propositions. Demo
  • Construction of truth set for propositions. Demo

Expressions can be edited through a linear editor or a bidimensional editor in the Algebraic Line.
Moreover, in the Algebraic Line it is possible:
•    To construct expressions thug geometrical models
•    To find polynomial roots
•    To find the truth set of propositions 

 

Geometrical model of operations to construct expressions

It is possible to construct expressions through three geometrical models that correspond to the operations: addition/subtraction, multiplication/division, integer power/rational power.

These three geometrical models can be also applied on variables and expressions:

Polynomial roots

It is possible to construct polynomial roots once a polynomial expression is inserted in the Algebraic Line.
The exact root is determined by a specific function of the system and it is represented on the linea s a point.

Truth set of algebraic propositions


It is possible to find the truth set of propositions through a specific graphical editor once that roots of polynomial associated to the proposition have been represented on the line.

The constructed truth set can be validated through a specific feedback. In a specific window named “Sets” propositions and numerical sets are associated to a little ball (red/green) under the control of the system. The green (/red) colour of the proposition marker means that the value assumed by the variable on the line during the drag makes the proposition true (/false). The green  (/red) colour of the numerical set means that the value of the variable on the line during the drag is (is not) an element of the numerical set.
The concordance of colour between the ball of the proposition (that indicates its false/truth value) and the ball of the set (that indicates if the current value of the variable it contains) validate the constructed numerical set as truth set of the proposition.