Fungrim entry: bf8f37

Symbol: CurvePath —

\left(f(t),\, t : a \rightsquigarrow b\right)

— Path along a curve

►CurvePath(f(t), For(t, a, b)) —

\left(f(t),\, t : a \rightsquigarrow b\right)

— Represents the path traced by

f(t)

t

follows the path

a \rightsquigarrow b

►CurvePath(Mul(R, Exp(Mul(ConstI, t))), For(t, 0, Mul(2, Pi))) —

\left(R {e}^{i t},\, t : 0 \rightsquigarrow 2 \pi\right)

— Represents the circular path counterclockwise around the origin, starting at

R

►CurvePath(Mul(R, Exp(Mul(ConstI, t))), For(t, 0, Neg(Mul(2, Pi)))) —

\left(R {e}^{i t},\, t : 0 \rightsquigarrow -2 \pi\right)

— Represents the circular path clockwise around the origin, starting at

R

►Path(Pos(Infinity), CurvePath(Exp(Mul(ConstI, t)), For(t, Div(Pi, 2), Div(Mul(3, Pi), 2))), Pos(Infinity)) —

+\infty \rightsquigarrow \left({e}^{i t},\, t : \pi / 2 \rightsquigarrow 3 \pi / 2\right) \rightsquigarrow +\infty

— Represents the Hankel contour starting at

+\infty

, moving along a straight line above the real axis to

i

, moving in a half-circle around the origin to

-i

, and returning to

+\infty

along a straight line below the real axis.

Definitions:

Fungrim symbol	Notation	Short description
`CurvePath`	$\left(f(t),\, t : a \rightsquigarrow b\right)$	Path along a curve
`Path`	$a \rightsquigarrow b \rightsquigarrow c$	Line path
`Exp`	${e}^{z}$	Exponential function
`ConstI`	$i$	Imaginary unit
`Pi`	$\pi$	The constant pi (3.14...)
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("bf8f37"),
    SymbolDefinition(CurvePath, CurvePath(f(t), For(t, a, b)), "Path along a curve"),
    CodeExample(CurvePath(f(t), For(t, a, b)), "Represents the path traced by", f(t), "as", t, "follows the path", Path(a, b), "."),
    CodeExample(CurvePath(Mul(R, Exp(Mul(ConstI, t))), For(t, 0, Mul(2, Pi))), "Represents the circular path counterclockwise around the origin, starting at", R, "."),
    CodeExample(CurvePath(Mul(R, Exp(Mul(ConstI, t))), For(t, 0, Neg(Mul(2, Pi)))), "Represents the circular path clockwise around the origin, starting at", R, "."),
    CodeExample(Path(Pos(Infinity), CurvePath(Exp(Mul(ConstI, t)), For(t, Div(Pi, 2), Div(Mul(3, Pi), 2))), Pos(Infinity)), "Represents the Hankel contour starting at", Pos(Infinity), ", moving along a straight line above the real axis to", i, ", moving in a half-circle around the origin to", Neg(i), ", and returning to", Pos(Infinity), "along a straight line below the real axis."))

Topics using this entry

Operators