The exact limit of an expression as a variable approaches a point. Gives a value, inf or -inf, divergent (the one-sided limits differ), or unsupported when gtmath cannot decide -- never a numeric guess.
expr (symbolic) -- e.g. sin(x)/xwrt (string) -- the variable, unquoted (e.g. x)point (symbolic) -- the point approached, e.g. 0direction (string) -- optional: "left", "right" or "two_sided" (the default)The Taylor polynomial of an expression about a point, through the given order (at most 32). Only the truncated polynomial -- no claim about the remainder.
expr (symbolic) -- e.g. exp(x)wrt (string) -- the variable, unquotedpoint (symbolic) -- the expansion point, e.g. 0order (number) -- the highest power keptThe exact definite integral between two bounds; a bound may be inf or -inf, a multiple of pi (defint(sin(x)^2, x, 0, 2*pi) = pi) or a symbol (defint(x^2, x, 0, a) = a^3/3). Returns unsupported (rather than a guess) when gtmath cannot prove the result, for example across a pole.
expr (symbolic) -- e.g. x^2wrt (string) -- the variable, unquotedlower (symbolic) -- the lower bound, or -infupper (symbolic) -- the upper bound, or infThe exact limit of a polynomial or rational expression as the variable goes to inf (default) or -inf.
expr (symbolic) -- e.g. (2*x^2+1)/(x^2-3)wrt (string) -- the variable, unquoted (e.g. x)direction (string) -- optional: "positive" (default) or "negative"The leading term of the Laurent expansion of a rational expression at a pole.
expr (symbolic) -- a rational expressionwrt (string) -- the variable, unquoted (e.g. x)point (number) -- the poleThe principal part (all negative-power terms) of a rational expression's Laurent expansion at a pole.
expr (symbolic) -- a rational expressionwrt (string) -- the variable, unquoted (e.g. x)point (number) -- the poleThe signed area between a curve and the axis over an interval (area below the axis counts negative).
curve (symbolic) -- e.g. xwrt (string) -- the variable, unquoted (e.g. x)lower (symbolic) -- left boundupper (symbolic) -- right boundThe signed area between an upper and a lower curve over an interval.
upper_curve (symbolic) -- e.g. xlower_curve (symbolic) -- e.g. x^2wrt (string) -- the variable, unquoted (e.g. x)lower (symbolic) -- left boundupper (symbolic) -- right boundThe total (unsigned) area between two polynomial curves, splitting the interval where they cross.
first (symbolic) -- a polynomialsecond (symbolic) -- a polynomialwrt (string) -- the variable, unquoted (e.g. x)lower (symbolic) -- left boundupper (symbolic) -- right boundThe exact arc length of y = f(x) over an interval, when the integral is one gtmath can do exactly.
curve (symbolic) -- e.g. xwrt (string) -- the variable, unquoted (e.g. x)lower (symbolic) -- left boundupper (symbolic) -- right boundThe line integral of a scalar field along a parameterized curve (with respect to arc length).
field (symbolic) -- e.g. x + ycoords (string) -- the coordinate names as a list, e.g. [x, y, z]curve (array) -- the curve's coordinates in the parameter, e.g. [t, t]param (string) -- the parameter, e.g. tlower (symbolic) -- parameter startupper (symbolic) -- parameter endThe line integral (work) of a vector field along a parameterized curve: the integral of F . dr.
field (array) -- the field's components, e.g. [y, x]coords (string) -- the coordinate names as a list, e.g. [x, y, z]curve (array) -- e.g. [t, t^2]param (string) -- the parameterlower (symbolic) -- parameter startupper (symbolic) -- parameter endThe flux of a vector field through a parameterized surface r(u, v), oriented by r_u x r_v.
field (array) -- e.g. [0, 0, 1]coords (string) -- the coordinate names as a list, e.g. [x, y, z]surface (array) -- e.g. [u, v, 0]u (string) -- first parameteru_lower (symbolic) -- u_upper (symbolic) -- v (string) -- second parameterv_lower (symbolic) -- v_upper (symbolic) -- The area of a parameterized surface r(u, v) over a parameter rectangle.
surface (array) -- e.g. [u, v, 0]u (string) -- first parameteru_lower (symbolic) -- u_upper (symbolic) -- v (string) -- second parameterv_lower (symbolic) -- v_upper (symbolic) -- The integral of a scalar field over a parameterized volume; orientation says whether the Jacobian is "nonnegative" or "nonpositive".
field (symbolic) -- e.g. 1coords (string) -- the coordinate names as a list, e.g. [x, y, z]volume (array) -- e.g. [u, v, w]orientation (string) -- "nonnegative" or "nonpositive"u (string) -- u_lower (symbolic) -- u_upper (symbolic) -- v (string) -- v_lower (symbolic) -- v_upper (symbolic) -- w (string) -- w_lower (symbolic) -- w_upper (symbolic) -- The stationary points of a polynomial, each with its multiplicity and whether it is a local minimum, maximum or degenerate. Roots gtmath cannot find exactly are reported as an unresolved factor.
poly (symbolic) -- e.g. x^3 - 3*xwrt (string) -- the variable, unquoted (e.g. x)Where a polynomial is increasing/decreasing and concave up/down, as intervals.
poly (symbolic) -- e.g. x^3 - 3*xwrt (string) -- the variable, unquoted (e.g. x)The absolute minimum and maximum of a polynomial on a closed interval, with where they occur.
poly (symbolic) -- e.g. x^3 - 3*xwrt (string) -- the variable, unquoted (e.g. x)lower (number) -- left endupper (number) -- right endThe tangent line to y = p(x) at a point, for a polynomial p.
poly (symbolic) -- e.g. x^2wrt (string) -- the variable, unquoted (e.g. x)point (number) -- the x-coordinateThe normal line to y = p(x) at a point, for a polynomial p (a vertical line when the tangent is horizontal).
poly (symbolic) -- e.g. x^2wrt (string) -- the variable, unquoted (e.g. x)point (number) -- the x-coordinateThe linear approximation of a polynomial at a point.
poly (symbolic) -- e.g. x^3wrt (string) -- the variable, unquoted (e.g. x)point (number) -- the x-coordinatedy/dx for a relation F(x, y) = 0, by implicit differentiation.
relation (symbolic) -- F, meaning F = 0, e.g. x^2 + y^2 - 25x (string) -- the independent variabley (string) -- the dependent variableSubstitutes several variables at once: substAll(e, [x, y], [1, t]).
expr (expression) -- names (name list) -- values (expression list) --