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Algebraic Manipulator

The Algebraic Manipulator is mainly for:

  • transforming algebraic expressions and propositions through a set of basic commands. These commands correspond to the basic properties of operations, to equality and inequality properties, and to basic operations on propositions and sets.
  • creating new rules (user rules) once they are proved.

These functions can be extremely useful for:

  • Exploring algebraic rules. Demo
  • Transforming expressions and solving propositions. Demo


Each command produces the result represented by its icon.
In the Algebraic Manipulator it is possible:
  • The exploration of the hierarchical structure of expressions
  • The construction of a new rule once it has been proved.  

Exploring the hierarchical structure of expressions

By dragging the mouse pointer over the elements of the expression or proposition (operators, number, letters, brackets…), the system dynamically displays the meaningful part of the expression or proposition determined by such pointer.
In this way it is possible to explore all meaningful parts of an expression in the different levels of its hierarchical structure.

Creating a new rule

It is possible to create new transformational rules (user rules) once that these new rules have been proved using the basic commands available in the interface or new, previously proved rules.
For example,  it is possible to automatically add the new rule a2-b2=(a+b)*(a-b) in the interface once that it has been proved. This rule can be used in the following transformations.