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Algebra


Indefinite Integration

Axiom can do indefinite integration using Trager's algorithm.

This algorithm is a decision procedure for a certain class of integrals.
This means that if the integrand exists then we get an answer.
If the original integral is returned then it cannot be integrated.

Type Towers

This matrix contains entries which are polynomials.
Each polynomial has a coefficient which is a complex number.

The inverse operation generates another matrix.
In this case the elements of the matrix are fractions.
Each fraction is the ratio of two polynomials.
Each polynomial has complex coefficients.

Coercion

This shows how we form a polynomial which has fractional coefficients.

We would like this to be a fraction of polynomials with integer coefficients.

In Axiom the display of a form is controlled by the type.

Limits

Axiom is capable of computing limits in terms of the parameters.

It is also capable of taking limits from one direction.