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The arithmetic operations are one together recurring that perfectly fits the notion of graph. In particular, a complete equation is a tree set of operations. We're talking about graph when a node has multiple parents. An equation where some words are repeated will form a graph where a repeated word is associated with a single node, and each parent node will go on this node.

The neurons of algebraic distribution concern all the multiplication of terms.

We note each node on a two-dimensional grid where is the number of nodes. Each square of the grid hosts a number positive or zero. This number is the number of links that connect two different nodes (in both directions). The diagonal axis of the grid corresponds to a diagonal of numbers zero, with the understanding that there is no node in relation to himself.

Also, when and/or shall include at least an addition or subtraction so distribution is to multiply each term the sum of by each term sum of .

Generally speaking, the distribution is to develop each term sum one by one.

- initial process

- iterative process
- calculate the term following multiplied by the previous term
- calculate the term following multiplied by the previous term
- develop the term following each product 3 final process

- Cancel and cancel

It will take alternate distribution and the simplification of the product.

There are more than 2 items produced to distribute, to first simplify the products obtained with the first two elements then repeat with two following. A special case of the product of terms is the term raised to the power ; What is the product of equal terms ??

The two branches on the right are the operands of the operation (here the addition). For each operation, there are 6 configurations.

So there is an initial background where each neuron has its own function and its own form. I also note that there is only a single main command for an equation: calculate the result of the equation giving a numerical value to each variable. Related variables, to always express the values by using the equation of this variable. For free variables, any numeric value is correct. Finally, for the unknown variables it comes to seek his equation based on the knowledge of the equations on the variables and the values of the free variables.

To calculate the unknown variables, it must be remembered that the mathematical reasoning and algebra accept 2/3 variables to numeric values and one unknown. And usually, for a real function to a real variable, there is that two unknown variables; It is necessary and sufficient to create an intermediate unknown variable to get actually 2/3 variables to numeric values and one unknown.

Other operators are necessary to allow a set of mathematical sequences. Some instructions are needed:

- declaring a free variable
- declaration of a bound variable
- declaration of an unknown variable
- equality operator to check
- 5 own equality operator
- 6 comparison operators
- 7 conditional operator: a comparison test, a new sequence if the test result is checked, a new sequence (optional) if the test result is denied.

These instructions are defined by templates of neurons. Construction of neurons is done during syntactic analysis of these instructions by specializing each template.

The constructive form is just the composition of the operator according to a human-readable representation. Also, the first neuron is called the whole equation.

Finally, a heuristic decides the best form to give an equation considering the different models of algebraic operations:

- commutativity.
- neutral elements,
- absorbing elements,
- distribution.
- factorization.

Last edited Dec 11, 2016 at 10:48 PM by skercrow, version 3