Module multi 

Values of several ordered infinitesimals: dt, dx declared much smaller than dt, and so on.

An infinitesimal declared much smaller than another is smaller than every positive number made from it (Scale), so the values a program makes from the two are the rational functions of the smaller over the values of the larger, R(dt)(dx), ordered by the transfer principle one infinitesimal at a time, the smallest first: a rational function of dx has, for every small enough dx beside a fixed dt, the sign of its lowest-order coefficient in dx, and that coefficient’s sign is decided among the values of dt. So dx < dt^n for every standard n, and dx/dt^1000 is infinitesimal.

A Multi holds a value at the smallest infinitesimal it involves, as a rational function of a root dx^(1/q) whose coefficients involve only larger infinitesimals: reduced, its denominator comonic, on the least root that holds it. A value of one infinitesimal is held as its real closure’s own (Closed) and a standard number as an algebraic number, so a value has one form whatever route made it.

A value prints as an exact fraction of polynomials in the infinitesimals, in ascending powers of the smallest and each coefficient in the larger ones: dt + dx, dx/dt, 1/(dt + dx), (1 + dt)·dx.

Structs

MultiPowerError

Why a power of a value of several infinitesimals is refused, with the infinitesimal and the root of it its degree is counted in.

Enums

Multi

A value of several ordered infinitesimals. See the module documentation.