All about simplification

In this post, we list out all the steps the Mathlify library does to "simplify" expressions.

Fraction

• "Hoist" negative denominators to the numerator if necessary so that denominators are always positive. For example, $\frac{5}{-2}$ will be simplified to $\frac{-5}{2}$.
• Extract gcd such that the numerator and denominator are coprime. For example $\frac{15}{6}$ becomes $\frac{5}{2}$ and $\frac{0}{6}$ becomes $\frac{0}{1}$.

Sum

• Combines like terms into a Product of a numerical coefficient and the term
• _combine_like_terms() also combines Numerals such that there are at most one Numeral in a Sum.
• Nested sums are flattened.
• Numerals of 0s are removed.

Product

• Combines Numerals to become a coeff at the start of the product
• Nested products are flattened
• (New feature introduced 24/6/17) Product containing a quotient will be changed into a quotient with the products in the numerator

Expression

The Expression class allow us to modify the underlying type

• Any Bracket class are changed to the underlying type.
• An empty Sum will be changed to a Numeral of 0.
• A singleton Sum will be changed to the underlying type.
• An empty Product will be changed to a Numeral of its coeff
• A product with a single factor and coeff of 1 will be changed to the underlying type
• A product with a coeff of 0 will be changed to a Numeral 0.
• A Quotient with a numerator of Numeral 0 will be changed 0
• A Quotient with a denominator of Numeral 1 will be changed to the underlying numerator type
• A Quotient with Numerals on both numerator and denominator will be changed to a Numeral class
• A Quotient with a negative Numeral or a negative Product will be changed to a product with a coeff of -1
• An Exponent with positive integral Numeral power and a Product base will be cased of a Product of Exponents