intaf.spad line 1 [edit on github]
This internal package rationalises integrands on curves of the form: y^2 = a x^2 + b x + c y^2 = (a x + b) / (c x + d) f(x, y) = 0 where f has degree 1 in x The rationalization is done for integration, limited integration, extended integration and the risch differential equation.
lift(u, k) is undocumented
multivariate(u, k, f) is undocumented
palgLODE0(op, g, x, y, d, p) returns the solution of op f = g. Argument y is an algebraic function of x satisfying d(x)^2y(x)^2 = P(x).
palgLODE0(op, g, x, y, z, t, c) returns the solution of op f = g. Argument y is an algebraic function of x satisfying x = eval(t, z, ry) and c = d/dz t; r is rational function of x, c and t are rational functions of z.
palgRDE0(f, g, x, y, foo, d, p) returns a function z(x, y) such that dz/dx + n * df/dx z(x, y) = g(x, y) if such a z exists, and "failed" otherwise. Argument y is an algebraic function of x satisfying d(x)^2y(x)^2 = P(x). Argument foo, called by foo(a, b, x), is a function that solves du/dx + n * da/dx u(x) = u(x) for an unknown u(x) not involving y.
palgRDE0(f, g, x, y, foo, t, c) returns a function z(x, y) such that dz/dx + n * df/dx z(x, y) = g(x, y) if such a z exists, and "failed" otherwise. Argument y is an algebraic function of x satisfying x = eval(t, z, ry) and c = d/dz t; r is rational function of x, c and t are rational functions of z. Argument foo, called by foo(a, b, x), is a function that solves du/dx + n * da/dx u(x) = u(x) for an unknown u(x) not involving y.
palgint0(f, x, y, d, p) returns the integral of f(x, y)dx where y is an algebraic function of x satisfying d(x)^2 y(x)^2 = P(x).
palgint0(f, x, y, z, t, c) returns the integral of f(x, y)dx where y is an algebraic function of x satisfying x = eval(t, z, ry) and c = d/dz t; r is rational function of x, c and t are rational functions of z. Argument z is a dummy variable not appearing in f(x, y).
rationalize_ir(irf, k1) eliminates square root k1 from the integration result.
univariate(f, k, k, p) is undocumented