fexpr to LaTeX test sheet

Converted 298 formulas (2875 leaves, 35520 bytes) to LaTeX in 0.000337 seconds.

fexpr Generated LaTeX KaTeX display
f(0)f(0)$$f(0)$$
f("Hello, world!")f(\text{``Hello, world!''})$$f(\text{``Hello, world!''})$$
ff$$f$$
f_f$$f$$
f_(0)f_{0}$$f_{0}$$
f()f()$$f()$$
Add(Add(Add(f(a, b), c_(n)), f_(x, y)), f_())f(a, b) + c_{n} + f_{x, y} + f_{}$$f(a, b) + c_{n} + f_{x, y} + f_{}$$
f(alpha, beta, chi, delta, ell, epsilon, eta)f(\alpha, \beta, \chi, \delta, \ell, \varepsilon, \eta)$$f(\alpha, \beta, \chi, \delta, \ell, \varepsilon, \eta)$$
f(gamma, iota, kappa, lamda, mu, nu, omega, phi)f(\gamma, \iota, \kappa, \lambda, \mu, \nu, \omega, \phi)$$f(\gamma, \iota, \kappa, \lambda, \mu, \nu, \omega, \phi)$$
f(pi, rho, sigma, tau, theta, varphi, vartheta, xi, zeta)f(\pi, \rho, \sigma, \tau, \theta, \varphi, \vartheta, \xi, \zeta)$$f(\pi, \rho, \sigma, \tau, \theta, \varphi, \vartheta, \xi, \zeta)$$
f(Delta, GreekGamma, GreekPi, Lamda, Omega, Phi, Psi, Sigma, Theta, Xi)f(\Delta, \Gamma, \Pi, \Lambda, \Omega, \Phi, \Psi, \Sigma, \Theta, \Xi)$$f(\Delta, \Gamma, \Pi, \Lambda, \Omega, \Phi, \Psi, \Sigma, \Theta, \Xi)$$
f(alpha_, beta_, chi_, delta_, ell_, epsilon_, eta_)f(\alpha, \beta, \chi, \delta, \ell, \varepsilon, \eta)$$f(\alpha, \beta, \chi, \delta, \ell, \varepsilon, \eta)$$
f(gamma_, iota_, kappa_, lamda_, mu_, nu_, omega_, phi_)f(\gamma, \iota, \kappa, \lambda, \mu, \nu, \omega, \phi)$$f(\gamma, \iota, \kappa, \lambda, \mu, \nu, \omega, \phi)$$
f(pi_, rho_, sigma_, tau_, theta_, varphi_, vartheta_, xi_, zeta)f(\pi, \rho, \sigma, \tau, \theta, \varphi, \vartheta, \xi, \zeta)$$f(\pi, \rho, \sigma, \tau, \theta, \varphi, \vartheta, \xi, \zeta)$$
f(Delta_, GreekGamma_, GreekPi_, Lamda_, Omega_, Phi_, Psi_, Sigma_, Theta_, Xi_)f(\Delta, \Gamma, \Pi, \Lambda, \Omega, \Phi, \Psi, \Sigma, \Theta, \Xi)$$f(\Delta, \Gamma, \Pi, \Lambda, \Omega, \Phi, \Psi, \Sigma, \Theta, \Xi)$$
f(alpha(x), beta(x), chi(x), delta(x), ell(x), epsilon(x), eta(x))f\!\left(\alpha(x), \beta(x), \chi(x), \delta(x), \ell(x), \varepsilon(x), \eta(x)\right)$$f\!\left(\alpha(x), \beta(x), \chi(x), \delta(x), \ell(x), \varepsilon(x), \eta(x)\right)$$
f(gamma(x), iota(x), kappa(x), lamda(x), mu(x), nu(x), omega(x), phi(x))f\!\left(\gamma(x), \iota(x), \kappa(x), \lambda(x), \mu(x), \nu(x), \omega(x), \phi(x)\right)$$f\!\left(\gamma(x), \iota(x), \kappa(x), \lambda(x), \mu(x), \nu(x), \omega(x), \phi(x)\right)$$
f(pi(x), rho(x), sigma(x), tau(x), theta(x), varphi(x), vartheta(x), xi(x), zeta(x))f\!\left(\pi(x), \rho(x), \sigma(x), \tau(x), \theta(x), \varphi(x), \vartheta(x), \xi(x), \zeta(x)\right)$$f\!\left(\pi(x), \rho(x), \sigma(x), \tau(x), \theta(x), \varphi(x), \vartheta(x), \xi(x), \zeta(x)\right)$$
f(Delta(x), GreekGamma(x), GreekPi(x), Lamda(x), Omega(x), Phi(x), Psi(x), Sigma(x), Theta(x), Xi(x))f\!\left(\Delta(x), \Gamma(x), \Pi(x), \Lambda(x), \Omega(x), \Phi(x), \Psi(x), \Sigma(x), \Theta(x), \Xi(x)\right)$$f\!\left(\Delta(x), \Gamma(x), \Pi(x), \Lambda(x), \Omega(x), \Phi(x), \Psi(x), \Sigma(x), \Theta(x), \Xi(x)\right)$$
f(alpha_(n), beta_(n), chi_(n), delta_(n), ell_(n), epsilon_(n), eta_(n))f\!\left(\alpha_{n}, \beta_{n}, \chi_{n}, \delta_{n}, \ell_{n}, \varepsilon_{n}, \eta_{n}\right)$$f\!\left(\alpha_{n}, \beta_{n}, \chi_{n}, \delta_{n}, \ell_{n}, \varepsilon_{n}, \eta_{n}\right)$$
f(gamma_(n), iota_(n), kappa_(n), lamda_(n), mu_(n), nu_(n), omega_(n), phi_(n))f\!\left(\gamma_{n}, \iota_{n}, \kappa_{n}, \lambda_{n}, \mu_{n}, \nu_{n}, \omega_{n}, \phi_{n}\right)$$f\!\left(\gamma_{n}, \iota_{n}, \kappa_{n}, \lambda_{n}, \mu_{n}, \nu_{n}, \omega_{n}, \phi_{n}\right)$$
f(pi_(n), rho_(n), sigma_(n), tau_(n), theta_(n), varphi_(n), vartheta_(n), xi_(n), zeta_(n))f\!\left(\pi_{n}, \rho_{n}, \sigma_{n}, \tau_{n}, \theta_{n}, \varphi_{n}, \vartheta_{n}, \xi_{n}, \zeta_{n}\right)$$f\!\left(\pi_{n}, \rho_{n}, \sigma_{n}, \tau_{n}, \theta_{n}, \varphi_{n}, \vartheta_{n}, \xi_{n}, \zeta_{n}\right)$$
f(Delta_(n), GreekGamma_(n), GreekPi_(n), Lamda_(n), Omega_(n), Phi_(n), Psi_(n), Sigma_(n), Theta_(n), Xi_(n))f\!\left(\Delta_{n}, \Gamma_{n}, \Pi_{n}, \Lambda_{n}, \Omega_{n}, \Phi_{n}, \Psi_{n}, \Sigma_{n}, \Theta_{n}, \Xi_{n}\right)$$f\!\left(\Delta_{n}, \Gamma_{n}, \Pi_{n}, \Lambda_{n}, \Omega_{n}, \Phi_{n}, \Psi_{n}, \Sigma_{n}, \Theta_{n}, \Xi_{n}\right)$$
f(a)(b)f(a)(b)$$f(a)(b)$$
Mul(f, g)(x)\left(f g\right)(x)$$\left(f g\right)(x)$$
Add(f, g)(x)\left(f + g\right)(x)$$\left(f + g\right)(x)$$
c_(m, n, p)(x, y, z)c_{m, n, p}(x, y, z)$$c_{m, n, p}(x, y, z)$$
f_(Div(-3, 2))(Div(-3, 2))f_{-3 / 2}\!\left(-\frac{3}{2}\right)$$f_{-3 / 2}\!\left(-\frac{3}{2}\right)$$
Mul(2, Pi, NumberI)2 \pi i$$2 \pi i$$
Mul(-2, Pi, NumberI)-2 \pi i$$-2 \pi i$$
Add(2, x)2 + x$$2 + x$$
Sub(2, x)2 - x$$2 - x$$
Add(2, Neg(x))2 + \left(-x\right)$$2 + \left(-x\right)$$
Sub(2, Neg(x))2 - \left(-x\right)$$2 - \left(-x\right)$$
Add(2, Sub(x, y))2 + \left(x - y\right)$$2 + \left(x - y\right)$$
Sub(2, Add(x, y))2 - \left(x + y\right)$$2 - \left(x + y\right)$$
Sub(2, Sub(x, y))2 - \left(x - y\right)$$2 - \left(x - y\right)$$
Add(-3, -4, -5)-3-4-5$$-3-4-5$$
Add(-3, Mul(-4, x), -5)-3-4 x-5$$-3-4 x-5$$
Add(-3, Mul(-4, x), Pos(5))-3-4 x+5$$-3-4 x+5$$
Add(-3, Div(Mul(-4, x), 7), -5)-3-\frac{4 x}{7}-5$$-3-\frac{4 x}{7}-5$$
Add(-3, Div(Mul(4, x), 7), -5)-3 + \frac{4 x}{7}-5$$-3 + \frac{4 x}{7}-5$$
Mul(0, 1)0 \cdot 1$$0 \cdot 1$$
Mul(3, Pow(2, n))3 \cdot {2}^{n}$$3 \cdot {2}^{n}$$
Mul(3, Pow(-1, n))3 \cdot {\left(-1\right)}^{n}$$3 \cdot {\left(-1\right)}^{n}$$
Mul(-3, Pow(-1, n))-3 \cdot {\left(-1\right)}^{n}$$-3 \cdot {\left(-1\right)}^{n}$$
Mul(-1, -2, -3)-1 \cdot \left(-2\right) \cdot \left(-3\right)$$-1 \cdot \left(-2\right) \cdot \left(-3\right)$$
Div(-1, 3)-\frac{1}{3}$$-\frac{1}{3}$$
Div(Mul(-5, Pi), 3)-\frac{5 \pi}{3}$$-\frac{5 \pi}{3}$$
Div(Neg(Mul(5, Pi)), 3)-\frac{5 \pi}{3}$$-\frac{5 \pi}{3}$$
Div(Add(Add(Mul(-5, Pow(x, 2)), Mul(4, x)), 1), Add(Mul(3, x), y))\frac{-5 {x}^{2} + 4 x + 1}{3 x + y}$$\frac{-5 {x}^{2} + 4 x + 1}{3 x + y}$$
Pow(2, n){2}^{n}$${2}^{n}$$
Pow(-1, n){\left(-1\right)}^{n}$${\left(-1\right)}^{n}$$
Pow(10, Pow(10, -10)){10}^{{10}^{-10}}$${10}^{{10}^{-10}}$$
Pow(2, Div(-1, 3)){2}^{-1 / 3}$${2}^{-1 / 3}$$
Pow(2, Div(-1, Mul(3, n))){2}^{-1 / \left(3 n\right)}$${2}^{-1 / \left(3 n\right)}$$
Equal(Add(Pow(Sin(x), 2), Pow(Cos(x), 2)), 1)\sin^{2}\!\left(x\right) + \cos^{2}\!\left(x\right) = 1$$\sin^{2}\!\left(x\right) + \cos^{2}\!\left(x\right) = 1$$
Set(Set(), Set(1), Set(1, 2, 3))\left\{\left\{\right\}, \left\{1\right\}, \left\{1, 2, 3\right\}\right\}$$\left\{\left\{\right\}, \left\{1\right\}, \left\{1, 2, 3\right\}\right\}$$
Tuple(Tuple(), Tuple(1), Tuple(1, 2, 3))\left(\left(\right), \left(1\right), \left(1, 2, 3\right)\right)$$\left(\left(\right), \left(1\right), \left(1, 2, 3\right)\right)$$
List(List(), List(1), List(1, 2, 3))\left[\left[\right], \left[1\right], \left[1, 2, 3\right]\right]$$\left[\left[\right], \left[1\right], \left[1, 2, 3\right]\right]$$
Set(f(x), For(x, CC))\left\{ f(x) : x \in \mathbb{C} \right\}$$\left\{ f(x) : x \in \mathbb{C} \right\}$$
Set(f(x), For(x, CC), NotEqual(x, 0))\left\{ f(x) : x \in \mathbb{C}\,\mathbin{\operatorname{and}}\, x \ne 0 \right\}$$\left\{ f(x) : x \in \mathbb{C}\,\mathbin{\operatorname{and}}\, x \ne 0 \right\}$$
List(Floor(x), Ceil(x), Abs(x), RealAbs(x), Conjugate(z), Sqrt(x))\left[\left\lfloor x \right\rfloor, \left\lceil x\right\rceil, \left|x\right|, \left|x\right|, \overline{z}, \sqrt{x}\right]$$\left[\left\lfloor x \right\rfloor, \left\lceil x\right\rceil, \left|x\right|, \left|x\right|, \overline{z}, \sqrt{x}\right]$$
List(Floor(Div(1, 2)), Ceil(Div(1, 2)), Abs(Div(1, 2)), RealAbs(Div(1, 2)), Conjugate(Div(1, 2)), Sqrt(Div(1, 2)))\left[\left\lfloor \frac{1}{2} \right\rfloor, \left\lceil \frac{1}{2}\right\rceil, \left|\frac{1}{2}\right|, \left|\frac{1}{2}\right|, \overline{\frac{1}{2}}, \sqrt{\frac{1}{2}}\right]$$\left[\left\lfloor \frac{1}{2} \right\rfloor, \left\lceil \frac{1}{2}\right\rceil, \left|\frac{1}{2}\right|, \left|\frac{1}{2}\right|, \overline{\frac{1}{2}}, \sqrt{\frac{1}{2}}\right]$$
And(Equal(Length(Tuple(1, 2, 3)), 3), Equal(Cardinality(Set()), 0))\# \left(1, 2, 3\right) = 3 \;\mathbin{\operatorname{and}}\; \# \left\{\right\} = 0$$\# \left(1, 2, 3\right) = 3 \;\mathbin{\operatorname{and}}\; \# \left\{\right\} = 0$$
Tuple(Parentheses(x), Brackets(x), Braces(x), AngleBrackets(x))\left(\left(x\right), \left[x\right], \left\{x\right\}, \left\langle x\right\rangle\right)$$\left(\left(x\right), \left[x\right], \left\{x\right\}, \left\langle x\right\rangle\right)$$
Tuple(Parentheses(Div(1, 2)), Brackets(Div(1, 2)), Braces(Div(1, 2)), AngleBrackets(Div(1, 2)))\left(\left(\frac{1}{2}\right), \left[\frac{1}{2}\right], \left\{\frac{1}{2}\right\}, \left\langle \frac{1}{2}\right\rangle\right)$$\left(\left(\frac{1}{2}\right), \left[\frac{1}{2}\right], \left\{\frac{1}{2}\right\}, \left\langle \frac{1}{2}\right\rangle\right)$$
Concatenation(A, B)A \,^\frown B$$A \,^\frown B$$
Equal(Concatenation(Tuple(a, b), Tuple(c, d, e), Tuple()), Tuple(a, b, c, d, e))\left(a, b\right) \,^\frown \left(c, d, e\right) \,^\frown \left(\right) = \left(a, b, c, d, e\right)$$\left(a, b\right) \,^\frown \left(c, d, e\right) \,^\frown \left(\right) = \left(a, b, c, d, e\right)$$
Equal(f(x), Cases(Case(y, P(x)), Case(Neg(y), Q(x))))f(x) = \begin{cases} y, & P(x)\\-y, & Q(x)\\ \end{cases}$$f(x) = \begin{cases} y, & P(x)\\-y, & Q(x)\\ \end{cases}$$
Equal(f(x), Cases(Case(y, P(x)), Case(Neg(y), Q(x)), Case(0, Otherwise)))f(x) = \begin{cases} y, & P(x)\\-y, & Q(x)\\0, & \text{otherwise}\\ \end{cases}$$f(x) = \begin{cases} y, & P(x)\\-y, & Q(x)\\0, & \text{otherwise}\\ \end{cases}$$
And(Equal(True, Not(False)), Equal(False, Not(True)))\operatorname{True} = \operatorname{not} \operatorname{False} \;\mathbin{\operatorname{and}}\; \operatorname{False} = \operatorname{not} \operatorname{True}$$\operatorname{True} = \operatorname{not} \operatorname{False} \;\mathbin{\operatorname{and}}\; \operatorname{False} = \operatorname{not} \operatorname{True}$$
All(Greater(x, 0), For(x, S))x > 0 \;\text{ for all } x \in S$$x > 0 \;\text{ for all } x \in S$$
All(Greater(x, 0), For(x, S), P(x))x > 0 \;\text{ for all } x \in S \text{ with } P(x)$$x > 0 \;\text{ for all } x \in S \text{ with } P(x)$$
Exists(Greater(x, 0), For(x, S))x > 0 \;\text{ for some } x \in S$$x > 0 \;\text{ for some } x \in S$$
Exists(Greater(x, 0), For(x, S), P(x))x > 0 \;\text{ for some } x \in S \text{ with } P(x)$$x > 0 \;\text{ for some } x \in S \text{ with } P(x)$$
Logic(All(Greater(x, 0), For(x, S)))\forall x \in S : \, x > 0$$\forall x \in S : \, x > 0$$
Logic(All(Greater(x, 0), For(x, S), P(x)))\forall x \in S, \,P(x) : \, x > 0$$\forall x \in S, \,P(x) : \, x > 0$$
Logic(Exists(Greater(x, 0), For(x, S)))\exists x \in S : \, x > 0$$\exists x \in S : \, x > 0$$
Logic(Exists(Greater(x, 0), For(x, S), P(x)))\exists x \in S, \,P(x) : \, x > 0$$\exists x \in S, \,P(x) : \, x > 0$$
Or(Q, And(P, Q, Not(P), Or(Q, P), Not(Or(Q, P))))Q \;\mathbin{\operatorname{or}}\; \left(P \;\mathbin{\operatorname{and}}\; Q \;\mathbin{\operatorname{and}}\; \operatorname{not} P \;\mathbin{\operatorname{and}}\; \left(Q \;\mathbin{\operatorname{or}}\; P\right) \;\mathbin{\operatorname{and}}\; \operatorname{not} \,\left(Q \;\mathbin{\operatorname{or}}\; P\right)\right)$$Q \;\mathbin{\operatorname{or}}\; \left(P \;\mathbin{\operatorname{and}}\; Q \;\mathbin{\operatorname{and}}\; \operatorname{not} P \;\mathbin{\operatorname{and}}\; \left(Q \;\mathbin{\operatorname{or}}\; P\right) \;\mathbin{\operatorname{and}}\; \operatorname{not} \,\left(Q \;\mathbin{\operatorname{or}}\; P\right)\right)$$
Logic(Or(Q, And(P, Q, Not(P), Or(Q, P), Not(Or(Q, P)))))Q \,\lor\, \left(P \,\land\, Q \,\land\, \neg P \,\land\, \left(Q \,\lor\, P\right) \,\land\, \neg \left(Q \,\lor\, P\right)\right)$$Q \,\lor\, \left(P \,\land\, Q \,\land\, \neg P \,\land\, \left(Q \,\lor\, P\right) \,\land\, \neg \left(Q \,\lor\, P\right)\right)$$
Equivalent(A, B)A \iff B$$A \iff B$$
Equivalent(Not(Equal(x, y)), NotEqual(x, y))\left(\operatorname{not} \,\left(x = y\right)\right) \iff \left(x \ne y\right)$$\left(\operatorname{not} \,\left(x = y\right)\right) \iff \left(x \ne y\right)$$
Implies(P, And(R, S))P \;\implies\; \left(R \;\mathbin{\operatorname{and}}\; S\right)$$P \;\implies\; \left(R \;\mathbin{\operatorname{and}}\; S\right)$$
Implies(Element(x, QQ), Element(x, RR))x \in \mathbb{Q} \;\implies\; x \in \mathbb{R}$$x \in \mathbb{Q} \;\implies\; x \in \mathbb{R}$$
And(Less(x, y), Less(x, y, z), LessEqual(x, y), LessEqual(x, y, z))x < y \;\mathbin{\operatorname{and}}\; x < y < z \;\mathbin{\operatorname{and}}\; x \le y \;\mathbin{\operatorname{and}}\; x \le y \le z$$x < y \;\mathbin{\operatorname{and}}\; x < y < z \;\mathbin{\operatorname{and}}\; x \le y \;\mathbin{\operatorname{and}}\; x \le y \le z$$
And(Greater(x, y), Greater(x, y, z), GreaterEqual(x, y), GreaterEqual(x, y, z))x > y \;\mathbin{\operatorname{and}}\; x > y > z \;\mathbin{\operatorname{and}}\; x \ge y \;\mathbin{\operatorname{and}}\; x \ge y \ge z$$x > y \;\mathbin{\operatorname{and}}\; x > y > z \;\mathbin{\operatorname{and}}\; x \ge y \;\mathbin{\operatorname{and}}\; x \ge y \ge z$$
Subset(Primes, NN, ZZ, QQ, RR, CC)\mathbb{P} \subset \mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}$$\mathbb{P} \subset \mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}$$
Subset(QQ, AlgebraicNumbers, CC)\mathbb{Q} \subset \overline{\mathbb{Q}} \subset \mathbb{C}$$\mathbb{Q} \subset \overline{\mathbb{Q}} \subset \mathbb{C}$$
SubsetEqual(S, QQ)S \subseteq \mathbb{Q}$$S \subseteq \mathbb{Q}$$
NotElement(123456789012345678901234567890, SetMinus(QQ, ZZ))123456789012345678901234567890 \notin \mathbb{Q} \setminus \mathbb{Z}$$123456789012345678901234567890 \notin \mathbb{Q} \setminus \mathbb{Z}$$
KroneckerDelta(x, Div(1, 2))\delta_{(x,1 / 2)}$$\delta_{(x,1 / 2)}$$
Set(Interval(a, b), OpenInterval(a, b), ClosedOpenInterval(a, b), OpenClosedInterval(a, b))\left\{\left[a, b\right], \left(a, b\right), \left[a, b\right), \left(a, b\right]\right\}$$\left\{\left[a, b\right], \left(a, b\right), \left[a, b\right), \left(a, b\right]\right\}$$
Set(Interval(a, Div(1, 2)), OpenInterval(a, Div(1, 2)), ClosedOpenInterval(a, Div(1, 2)), OpenClosedInterval(a, Div(1, 2)))\left\{\left[a, 1 / 2\right], \left(a, 1 / 2\right), \left[a, 1 / 2\right), \left(a, 1 / 2\right]\right\}$$\left\{\left[a, 1 / 2\right], \left(a, 1 / 2\right), \left[a, 1 / 2\right), \left(a, 1 / 2\right]\right\}$$
Set(RealBall(m, r), OpenRealBall(m, r))\left\{\left[m \pm r\right], \left(m \pm r\right)\right\}$$\left\{\left[m \pm r\right], \left(m \pm r\right)\right\}$$
Set(ClosedComplexDisk(m, r), OpenComplexDisk(m, r))\left\{\overline{D}(m, r), D(m, r)\right\}$$\left\{\overline{D}(m, r), D(m, r)\right\}$$
Set(Undefined, UnsignedInfinity, Pos(Infinity), Neg(Infinity))\left\{\mathfrak{u}, \hat{\infty}, +\infty, -\infty\right\}$$\left\{\mathfrak{u}, \hat{\infty}, +\infty, -\infty\right\}$$
Equal(RealSignedInfinities, Set(Pos(Infinity), Neg(Infinity)))\{\pm \infty\} = \left\{+\infty, -\infty\right\}$$\{\pm \infty\} = \left\{+\infty, -\infty\right\}$$
Equal(ComplexSignedInfinities, Set(Mul(Exp(Mul(NumberI, theta)), Infinity), For(theta, OpenClosedInterval(Neg(Pi), Pi))))\{[e^{i \theta}] \infty\} = \left\{ e^{i \theta} \cdot \infty : \theta \in \left(-\pi, \pi\right] \right\}$$\{[e^{i \theta}] \infty\} = \left\{ e^{i \theta} \cdot \infty : \theta \in \left(-\pi, \pi\right] \right\}$$
Equal(RealInfinities, Union(RealSignedInfinities, Set(UnsignedInfinity)))\{\hat{\infty}, \pm \infty\} = \{\pm \infty\} \cup \left\{\hat{\infty}\right\}$$\{\hat{\infty}, \pm \infty\} = \{\pm \infty\} \cup \left\{\hat{\infty}\right\}$$
Equal(ComplexInfinities, Union(ComplexSignedInfinities, Set(UnsignedInfinity)))\{\hat{\infty}, [e^{i \theta}] \infty\} = \{[e^{i \theta}] \infty\} \cup \left\{\hat{\infty}\right\}$$\{\hat{\infty}, [e^{i \theta}] \infty\} = \{[e^{i \theta}] \infty\} \cup \left\{\hat{\infty}\right\}$$
Equal(ExtendedRealNumbers, Union(RR, RealSignedInfinities))\overline{\mathbb{R}} = \mathbb{R} \cup \{\pm \infty\}$$\overline{\mathbb{R}} = \mathbb{R} \cup \{\pm \infty\}$$
Equal(SignExtendedComplexNumbers, Union(CC, ComplexSignedInfinities))\overline{\mathbb{C}}_{[e^{i \theta}] \infty} = \mathbb{C} \cup \{[e^{i \theta}] \infty\}$$\overline{\mathbb{C}}_{[e^{i \theta}] \infty} = \mathbb{C} \cup \{[e^{i \theta}] \infty\}$$
Equal(ProjectiveRealNumbers, Union(RR, Set(UnsignedInfinity)))\hat{\mathbb{R}}_{\infty} = \mathbb{R} \cup \left\{\hat{\infty}\right\}$$\hat{\mathbb{R}}_{\infty} = \mathbb{R} \cup \left\{\hat{\infty}\right\}$$
Equal(ProjectiveComplexNumbers, Union(CC, Set(UnsignedInfinity)))\hat{\mathbb{C}}_{\infty} = \mathbb{C} \cup \left\{\hat{\infty}\right\}$$\hat{\mathbb{C}}_{\infty} = \mathbb{C} \cup \left\{\hat{\infty}\right\}$$
Equal(RealSingularityClosure, Union(RR, Set(UnsignedInfinity), RealSignedInfinities, Set(Undefined)))\overline{\mathbb{R}}_{\text{Sing}} = \mathbb{R} \cup \left\{\hat{\infty}\right\} \cup \{\pm \infty\} \cup \left\{\mathfrak{u}\right\}$$\overline{\mathbb{R}}_{\text{Sing}} = \mathbb{R} \cup \left\{\hat{\infty}\right\} \cup \{\pm \infty\} \cup \left\{\mathfrak{u}\right\}$$
Equal(ComplexSingularityClosure, Union(CC, Set(UnsignedInfinity), ComplexSignedInfinities, Set(Undefined)))\overline{\mathbb{C}}_{\text{Sing}} = \mathbb{C} \cup \left\{\hat{\infty}\right\} \cup \{[e^{i \theta}] \infty\} \cup \left\{\mathfrak{u}\right\}$$\overline{\mathbb{C}}_{\text{Sing}} = \mathbb{C} \cup \left\{\hat{\infty}\right\} \cup \{[e^{i \theta}] \infty\} \cup \left\{\mathfrak{u}\right\}$$
Set(Mul(Infinity, Infinity), Mul(Mul(a, b), Infinity), Mul(NumberI, Infinity), Mul(Infinity, NumberI))\left\{\infty \cdot \infty, a b \cdot \infty, i \cdot \infty, \infty i\right\}$$\left\{\infty \cdot \infty, a b \cdot \infty, i \cdot \infty, \infty i\right\}$$
ArgMin(Add(f(x), g(x)), For(x, RR), NotEqual(x, 0))\mathop{\operatorname{arg\,min}\,}\limits_{x \in \mathbb{R},\,x \ne 0} \left[f(x) + g(x)\right]$$\mathop{\operatorname{arg\,min}\,}\limits_{x \in \mathbb{R},\,x \ne 0} \left[f(x) + g(x)\right]$$
List(ArgMin(f(x), For(x, S)), ArgMax(f(x), For(x, S)), ArgMin(f(x), For(x, S), P(x)), ArgMax(f(x), For(x, S), P(x)))\left[\mathop{\operatorname{arg\,min}\,}\limits_{x \in S} f(x), \mathop{\operatorname{arg\,max}\,}\limits_{x \in S} f(x), \mathop{\operatorname{arg\,min}\,}\limits_{x \in S,\,P(x)} f(x), \mathop{\operatorname{arg\,max}\,}\limits_{x \in S,\,P(x)} f(x)\right]$$\left[\mathop{\operatorname{arg\,min}\,}\limits_{x \in S} f(x), \mathop{\operatorname{arg\,max}\,}\limits_{x \in S} f(x), \mathop{\operatorname{arg\,min}\,}\limits_{x \in S,\,P(x)} f(x), \mathop{\operatorname{arg\,max}\,}\limits_{x \in S,\,P(x)} f(x)\right]$$
List(Minimum(f(x), For(x, S)), Maximum(f(x), For(x, S)), Minimum(f(x), For(x, S), P(x)), Maximum(f(x), For(x, S), P(x)))\left[\mathop{\min\,}\limits_{x \in S} f(x), \mathop{\max\,}\limits_{x \in S} f(x), \mathop{\min\,}\limits_{x \in S,\,P(x)} f(x), \mathop{\max\,}\limits_{x \in S,\,P(x)} f(x)\right]$$\left[\mathop{\min\,}\limits_{x \in S} f(x), \mathop{\max\,}\limits_{x \in S} f(x), \mathop{\min\,}\limits_{x \in S,\,P(x)} f(x), \mathop{\max\,}\limits_{x \in S,\,P(x)} f(x)\right]$$
List(ArgMinUnique(f(x), For(x, S)), ArgMaxUnique(f(x), For(x, S)), ArgMinUnique(f(x), For(x, S), P(x)), ArgMaxUnique(f(x), For(x, S), P(x)))\left[\mathop{\operatorname{arg\,min*}\,}\limits_{x \in S} f(x), \mathop{\operatorname{arg\,max*}\,}\limits_{x \in S} f(x), \mathop{\operatorname{arg\,min*}\,}\limits_{x \in S,\,P(x)} f(x), \mathop{\operatorname{arg\,max*}\,}\limits_{x \in S,\,P(x)} f(x)\right]$$\left[\mathop{\operatorname{arg\,min*}\,}\limits_{x \in S} f(x), \mathop{\operatorname{arg\,max*}\,}\limits_{x \in S} f(x), \mathop{\operatorname{arg\,min*}\,}\limits_{x \in S,\,P(x)} f(x), \mathop{\operatorname{arg\,max*}\,}\limits_{x \in S,\,P(x)} f(x)\right]$$
List(Infimum(f(x), For(x, S)), Supremum(f(x), For(x, S)), Infimum(f(x), For(x, S), P(x)), Supremum(f(x), For(x, S), P(x)))\left[\mathop{\operatorname{inf}\,}\limits_{x \in S} f(x), \mathop{\operatorname{sup}\,}\limits_{x \in S} f(x), \mathop{\operatorname{inf}\,}\limits_{x \in S,\,P(x)} f(x), \mathop{\operatorname{sup}\,}\limits_{x \in S,\,P(x)} f(x)\right]$$\left[\mathop{\operatorname{inf}\,}\limits_{x \in S} f(x), \mathop{\operatorname{sup}\,}\limits_{x \in S} f(x), \mathop{\operatorname{inf}\,}\limits_{x \in S,\,P(x)} f(x), \mathop{\operatorname{sup}\,}\limits_{x \in S,\,P(x)} f(x)\right]$$
List(Solutions(Q(x), For(x, S)), Zeros(f(x), For(x, S)), Solutions(Q(x), For(x, S), P(x)), Zeros(f(x), For(x, S), P(x)))\left[\mathop{\operatorname{solutions}\,}\limits_{x \in S} Q(x), \mathop{\operatorname{zeros}\,}\limits_{x \in S} f(x), \mathop{\operatorname{solutions}\,}\limits_{x \in S,\,P(x)} Q(x), \mathop{\operatorname{zeros}\,}\limits_{x \in S,\,P(x)} f(x)\right]$$\left[\mathop{\operatorname{solutions}\,}\limits_{x \in S} Q(x), \mathop{\operatorname{zeros}\,}\limits_{x \in S} f(x), \mathop{\operatorname{solutions}\,}\limits_{x \in S,\,P(x)} Q(x), \mathop{\operatorname{zeros}\,}\limits_{x \in S,\,P(x)} f(x)\right]$$
List(UniqueSolution(Q(x), For(x, S)), UniqueZero(f(x), For(x, S)), UniqueSolution(Q(x), For(x, S), P(x)), UniqueZero(f(x), For(x, S), P(x)))\left[\mathop{\operatorname{solution*}\,}\limits_{x \in S} Q(x), \mathop{\operatorname{zero*}\,}\limits_{x \in S} f(x), \mathop{\operatorname{solution*}\,}\limits_{x \in S,\,P(x)} Q(x), \mathop{\operatorname{zero*}\,}\limits_{x \in S,\,P(x)} f(x)\right]$$\left[\mathop{\operatorname{solution*}\,}\limits_{x \in S} Q(x), \mathop{\operatorname{zero*}\,}\limits_{x \in S} f(x), \mathop{\operatorname{solution*}\,}\limits_{x \in S,\,P(x)} Q(x), \mathop{\operatorname{zero*}\,}\limits_{x \in S,\,P(x)} f(x)\right]$$
Sum(Add(f(n), g(n)), For(n, a, b))\sum_{n=a}^{b} \left(f(n) + g(n)\right)$$\sum_{n=a}^{b} \left(f(n) + g(n)\right)$$
Sum(f(n), For(n, ZZ))\sum_{n \in \mathbb{Z}} f(n)$$\sum_{n \in \mathbb{Z}} f(n)$$
Sum(f(n), For(n, ZZ), NotEqual(n, 0))\sum_{\textstyle{n \in \mathbb{Z} \atop n \ne 0}} f(n)$$\sum_{\textstyle{n \in \mathbb{Z} \atop n \ne 0}} f(n)$$
Sum(f(n), For(n, a, b), NotEqual(n, 0))\sum_{\textstyle{n=a \atop n \ne 0}}^{b} f(n)$$\sum_{\textstyle{n=a \atop n \ne 0}}^{b} f(n)$$
Sum(f(n), For(n, a, b))\sum_{n=a}^{b} f(n)$$\sum_{n=a}^{b} f(n)$$
Product(Add(f(n), g(n)), For(n, a, b))\prod_{n=a}^{b} \left(f(n) + g(n)\right)$$\prod_{n=a}^{b} \left(f(n) + g(n)\right)$$
Product(f(n), For(n, NN))\prod_{n \in \mathbb{N}} f(n)$$\prod_{n \in \mathbb{N}} f(n)$$
Product(f(n), For(n, NN), NotEqual(g(n), 0))\prod_{\textstyle{n \in \mathbb{N} \atop g(n) \ne 0}} f(n)$$\prod_{\textstyle{n \in \mathbb{N} \atop g(n) \ne 0}} f(n)$$
Product(f(n), For(n, a, b), NotEqual(n, 0))\prod_{\textstyle{n=a \atop n \ne 0}}^{b} f(n)$$\prod_{\textstyle{n=a \atop n \ne 0}}^{b} f(n)$$
Product(f(n), For(n, a, b))\prod_{n=a}^{b} f(n)$$\prod_{n=a}^{b} f(n)$$
Equal(Set(f(n), For(n, ZZ)), Union(Set(f(n), For(n, ZZ), IsEven(n)), Set(f(n), For(n, ZZ), IsOdd(n))))\left\{ f(n) : n \in \mathbb{Z} \right\} = \left\{ f(n) : n \in \mathbb{Z}\,\mathbin{\operatorname{and}}\, n \text{ even} \right\} \cup \left\{ f(n) : n \in \mathbb{Z}\,\mathbin{\operatorname{and}}\, n \text{ odd} \right\}$$\left\{ f(n) : n \in \mathbb{Z} \right\} = \left\{ f(n) : n \in \mathbb{Z}\,\mathbin{\operatorname{and}}\, n \text{ even} \right\} \cup \left\{ f(n) : n \in \mathbb{Z}\,\mathbin{\operatorname{and}}\, n \text{ odd} \right\}$$
Equal(Primes, Set(p, For(p, NN), IsPrime(p)))\mathbb{P} = \left\{ p : p \in \mathbb{N}\,\mathbin{\operatorname{and}}\, p \text{ prime} \right\}$$\mathbb{P} = \left\{ p : p \in \mathbb{N}\,\mathbin{\operatorname{and}}\, p \text{ prime} \right\}$$
Equal(Sum(f(n), Element(n, ZZ)), Add(Sum(f(n), Element(n, ZZ), IsOdd(n)), Sum(f(n), Element(n, ZZ), IsEven(n))))\sum_{n \in \mathbb{Z}} f(n) = \sum_{\textstyle{n \in \mathbb{Z} \atop n \text{ odd}}} f(n) + \sum_{\textstyle{n \in \mathbb{Z} \atop n \text{ even}}} f(n)$$\sum_{n \in \mathbb{Z}} f(n) = \sum_{\textstyle{n \in \mathbb{Z} \atop n \text{ odd}}} f(n) + \sum_{\textstyle{n \in \mathbb{Z} \atop n \text{ even}}} f(n)$$
Set(DivisorSum(f(d), For(d, n)), DivisorSum(f(d), For(d, n), IsOdd(d)), DivisorSum(Add(f(d), g(d)), For(d, n)))\left\{\sum_{d \mid n} f(d), \sum_{d \mid n,\, d \text{ odd}} f(d), \sum_{d \mid n} \left(f(d) + g(d)\right)\right\}$$\left\{\sum_{d \mid n} f(d), \sum_{d \mid n,\, d \text{ odd}} f(d), \sum_{d \mid n} \left(f(d) + g(d)\right)\right\}$$
Set(DivisorProduct(f(d), For(d, n)), DivisorProduct(f(d), For(d, n), IsOdd(d)), DivisorProduct(Add(f(d), g(d)), For(d, n)))\left\{\prod_{d \mid n} f(d), \prod_{d \mid n,\, d \text{ odd}} f(d), \prod_{d \mid n} \left(f(d) + g(d)\right)\right\}$$\left\{\prod_{d \mid n} f(d), \prod_{d \mid n,\, d \text{ odd}} f(d), \prod_{d \mid n} \left(f(d) + g(d)\right)\right\}$$
Set(PrimeSum(f(p), For(p)), PrimeSum(f(p), For(p), NotElement(p, S)), PrimeProduct(f(p), For(p)), PrimeProduct(f(p), For(p), NotElement(p, S)))\left\{\sum_{p} f(p), \sum_{p \notin S} f(p), \prod_{p} f(p), \prod_{p \notin S} f(p)\right\}$$\left\{\sum_{p} f(p), \sum_{p \notin S} f(p), \prod_{p} f(p), \prod_{p \notin S} f(p)\right\}$$
Integral(f(x), For(x, Neg(Infinity), Infinity))\int_{-\infty}^{\infty} f(x) \, dx$$\int_{-\infty}^{\infty} f(x) \, dx$$
Integral(f(x), For(x, RR))\int_{x \in \mathbb{R}} f(x) \, dx$$\int_{x \in \mathbb{R}} f(x) \, dx$$
Integral(Add(f(x), Div(g(x), h(x))), For(x, a, b))\int_{a}^{b} \left(f(x) + \frac{g(x)}{h(x)}\right) \, dx$$\int_{a}^{b} \left(f(x) + \frac{g(x)}{h(x)}\right) \, dx$$
Set(Derivative(f(x_), For(x_, x)), Derivative(f(x_), For(x_, Div(x, y))), Derivative(Gamma(x_), For(x_, 1)))\left\{f'\!\left(x\right), f'\!\left(\frac{x}{y}\right), \Gamma'\!\left(1\right)\right\}$$\left\{f'\!\left(x\right), f'\!\left(\frac{x}{y}\right), \Gamma'\!\left(1\right)\right\}$$
Set(Derivative(f(x_), For(x_, x, 0)), Derivative(f(x_), For(x_, x, 1)), Derivative(f(x_), For(x_, x, 2)), Derivative(f(x_), For(x_, x, 3)), Derivative(f(x_), For(x_, x, 4)), Derivative(f(x_), For(x_, x, n)), Derivative(f(x_), For(x_, x, Add(Mul(2, n), 3))))\left\{{f}^{(0)}\!\left(x\right), f'\!\left(x\right), f''\!\left(x\right), f'''\!\left(x\right), {f}^{(4)}\!\left(x\right), {f}^{(n)}\!\left(x\right), {f}^{(2 n + 3)}\!\left(x\right)\right\}$$\left\{{f}^{(0)}\!\left(x\right), f'\!\left(x\right), f''\!\left(x\right), f'''\!\left(x\right), {f}^{(4)}\!\left(x\right), {f}^{(n)}\!\left(x\right), {f}^{(2 n + 3)}\!\left(x\right)\right\}$$
Set(Derivative(f(Add(x, 1)), For(x, x)), Derivative(f(Add(x, 1)), For(x, x, 0)), Derivative(f(Add(x, 1)), For(x, x, 1)), Derivative(f(Add(x, 1)), For(x, x, n)))\left\{\frac{d}{d x}\, f\!\left(x + 1\right), \frac{d^{0}}{{d x}^{0}}\, f\!\left(x + 1\right), \frac{d}{d x}\, f\!\left(x + 1\right), \frac{d^{n}}{{d x}^{n}}\, f\!\left(x + 1\right)\right\}$$\left\{\frac{d}{d x}\, f\!\left(x + 1\right), \frac{d^{0}}{{d x}^{0}}\, f\!\left(x + 1\right), \frac{d}{d x}\, f\!\left(x + 1\right), \frac{d^{n}}{{d x}^{n}}\, f\!\left(x + 1\right)\right\}$$
Set(Derivative(Add(f(x), g(x)), For(x, Add(y, 3))), Derivative(Add(f(x), g(x)), For(x, Add(y, 3), 5)))\left\{\left[\frac{d}{d x}\, \left[f(x) + g(x)\right] \right]_{x = y + 3}, \left[\frac{d^{5}}{{d x}^{5}}\, \left[f(x) + g(x)\right] \right]_{x = y + 3}\right\}$$\left\{\left[\frac{d}{d x}\, \left[f(x) + g(x)\right] \right]_{x = y + 3}, \left[\frac{d^{5}}{{d x}^{5}}\, \left[f(x) + g(x)\right] \right]_{x = y + 3}\right\}$$
Set(RealDerivative(f(x), For(x, 1)), ComplexDerivative(f(x), For(x, 1)), ComplexBranchDerivative(f(x), For(x, 1)), MeromorphicDerivative(f(x), For(x, 1)))\left\{f'\!\left(1\right), f'\!\left(1\right), f'\!\left(1\right), f'\!\left(1\right)\right\}$$\left\{f'\!\left(1\right), f'\!\left(1\right), f'\!\left(1\right), f'\!\left(1\right)\right\}$$
Set(Limit(f(x), For(x, a)), Limit(f(x), For(x, a), P(x)))\left\{\lim_{x \to a} f(x), \lim_{x \to a,\,P(x)} f(x)\right\}$$\left\{\lim_{x \to a} f(x), \lim_{x \to a,\,P(x)} f(x)\right\}$$
Set(Limit(f(x), For(x, a)), RealLimit(f(x), For(x, a)), ComplexLimit(f(x), For(x, a)), MeromorphicLimit(f(x), For(x, a)))\left\{\lim_{x \to a} f(x), \lim_{x \to a} f(x), \lim_{x \to a} f(x), \lim_{x \to a} f(x)\right\}$$\left\{\lim_{x \to a} f(x), \lim_{x \to a} f(x), \lim_{x \to a} f(x), \lim_{x \to a} f(x)\right\}$$
Set(LeftLimit(f(x), For(x, 0)), RightLimit(f(x), For(x, 0)))\left\{\lim_{x \to {0}^{-}} f(x), \lim_{x \to {0}^{+}} f(x)\right\}$$\left\{\lim_{x \to {0}^{-}} f(x), \lim_{x \to {0}^{+}} f(x)\right\}$$
Set(SequenceLimit(f(n), For(n, Infinity)), SequenceLimitInferior(f(n), For(n, Infinity)), SequenceLimitSuperior(f(n), For(n, Infinity)))\left\{\lim_{n \to \infty} f(n), \liminf_{n \to \infty} f(n), \limsup_{n \to \infty} f(n)\right\}$$\left\{\lim_{n \to \infty} f(n), \liminf_{n \to \infty} f(n), \limsup_{n \to \infty} f(n)\right\}$$
Sub(Limit(Add(f(x), g(x)), For(x, a)), Limit(Sub(f(x), g(x)), For(x, a)))\lim_{x \to a} \left[f(x) + g(x)\right] - \lim_{x \to a} \left[f(x) - g(x)\right]$$\lim_{x \to a} \left[f(x) + g(x)\right] - \lim_{x \to a} \left[f(x) - g(x)\right]$$
Divides(GCD(a, b), LCM(a, b))\gcd(a, b) \mid \operatorname{lcm}(a, b)$$\gcd(a, b) \mid \operatorname{lcm}(a, b)$$
Set(Exp(x), Exp(Div(3, 2)), Exp(Add(Neg(Pow(x, 2)), x)), Exp(Abs(Im(z))), Exp(Div(3, Add(2, x))), Exp(Sin(x)))\left\{e^{x}, e^{3 / 2}, e^{-{x}^{2} + x}, e^{\left|\operatorname{Im}(z)\right|}, \exp\!\left(\frac{3}{2 + x}\right), \exp\!\left(\sin(x)\right)\right\}$$\left\{e^{x}, e^{3 / 2}, e^{-{x}^{2} + x}, e^{\left|\operatorname{Im}(z)\right|}, \exp\!\left(\frac{3}{2 + x}\right), \exp\!\left(\sin(x)\right)\right\}$$
Add(Sin(x), Cos(x), Tan(x), Cot(x), Sec(x), Csc(x))\sin(x) + \cos(x) + \tan(x) + \cot(x) + \sec(x) + \csc(x)$$\sin(x) + \cos(x) + \tan(x) + \cot(x) + \sec(x) + \csc(x)$$
Add(Sinh(x), Cosh(x), Tanh(x), Coth(x), Sech(x), Csch(x))\sinh(x) + \cosh(x) + \tanh(x) + \coth(x) + \operatorname{sech}(x) + \operatorname{csch}(x)$$\sinh(x) + \cosh(x) + \tanh(x) + \coth(x) + \operatorname{sech}(x) + \operatorname{csch}(x)$$
Add(Asin(x), Acos(x), Atan(x), Acot(x), Asec(x), Acsc(x))\operatorname{asin}(x) + \operatorname{acos}(x) + \operatorname{atan}(x) + \operatorname{acot}(x) + \operatorname{asec}(x) + \operatorname{acsc}(x)$$\operatorname{asin}(x) + \operatorname{acos}(x) + \operatorname{atan}(x) + \operatorname{acot}(x) + \operatorname{asec}(x) + \operatorname{acsc}(x)$$
Add(Asinh(x), Acosh(x), Atanh(x), Acoth(x), Asech(x), Acsch(x))\operatorname{asinh}(x) + \operatorname{acosh}(x) + \operatorname{atanh}(x) + \operatorname{acoth}(x) + \operatorname{asech}(x) + \operatorname{acsch}(x)$$\operatorname{asinh}(x) + \operatorname{acosh}(x) + \operatorname{atanh}(x) + \operatorname{acoth}(x) + \operatorname{asech}(x) + \operatorname{acsch}(x)$$
Exp(Neg(Euler))e^{-\gamma}$$e^{-\gamma}$$
Set(Re(z), Im(z), Atan2(y, x))\left\{\operatorname{Re}(z), \operatorname{Im}(z), \operatorname{atan2}(y, x)\right\}$$\left\{\operatorname{Re}(z), \operatorname{Im}(z), \operatorname{atan2}(y, x)\right\}$$
Add(NumberE, GoldenRatio, CatalanConstant)e + \varphi + G$$e + \varphi + G$$
Add(Sinc(x), Pow(Sinc(x), 2))\operatorname{sinc}(x) + \operatorname{sinc}^{2}\!\left(x\right)$$\operatorname{sinc}(x) + \operatorname{sinc}^{2}\!\left(x\right)$$
AGM(a, b)\operatorname{agm}(a, b)$$\operatorname{agm}(a, b)$$
And(Equal(LogBarnesG(z), Log(BarnesG(z))), Equal(LogGamma(z), Log(Gamma(z))))\log G(z) = \log\!\left(G(z)\right) \;\mathbin{\operatorname{and}}\; \log \Gamma(z) = \log\!\left(\Gamma(z)\right)$$\log G(z) = \log\!\left(G(z)\right) \;\mathbin{\operatorname{and}}\; \log \Gamma(z) = \log\!\left(\Gamma(z)\right)$$
DirichletL(s, chi)L(s, \chi)$$L(s, \chi)$$
DirichletLambda(s, chi)\Lambda(s, \chi)$$\Lambda(s, \chi)$$
Implies(GeneralizedRiemannHypothesis, RiemannHypothesis)\operatorname{GRH} \;\implies\; \operatorname{RH}$$\operatorname{GRH} \;\implies\; \operatorname{RH}$$
Set(ModularJ(tau), ModularLambda(tau), JacobiTheta(n, z, tau))\left\{j(\tau), \lambda(\tau), \theta_{n}\!\left(z, \tau\right)\right\}$$\left\{j(\tau), \lambda(\tau), \theta_{n}\!\left(z, \tau\right)\right\}$$
Set(WeierstrassP(z, tau), WeierstrassSigma(z, tau), WeierstrassZeta(z, tau))\left\{\wp(z, \tau), \sigma(z, \tau), \zeta(z, \tau)\right\}$$\left\{\wp(z, \tau), \sigma(z, \tau), \zeta(z, \tau)\right\}$$
Mul(ChebyshevT(n, x), ChebyshevU(n, x))T_{n}\!\left(x\right) U_{n}\!\left(x\right)$$T_{n}\!\left(x\right) U_{n}\!\left(x\right)$$
Add(FresnelC(z), FresnelS(z))C(z) + S(z)$$C(z) + S(z)$$
Div(EisensteinE(Mul(2, n), tau), EisensteinG(Mul(2, n), tau))\frac{E_{2 n}\!\left(\tau\right)}{G_{2 n}\!\left(\tau\right)}$$\frac{E_{2 n}\!\left(\tau\right)}{G_{2 n}\!\left(\tau\right)}$$
Equal(Div(IncompleteBeta(z, a, b), IncompleteBetaRegularized(z, a, b)), BetaFunction(a, b))\frac{\mathrm{B}_{z}\!\left(a, b\right)}{I_{z}\!\left(a, b\right)} = \mathrm{B}(a, b)$$\frac{\mathrm{B}_{z}\!\left(a, b\right)}{I_{z}\!\left(a, b\right)} = \mathrm{B}(a, b)$$
Set(PolyLog(s, z), HurwitzZeta(s, z), LerchPhi(z, s, a))\left\{\operatorname{Li}_{s}\!\left(z\right), \zeta(s, z), \Phi(z, s, a)\right\}$$\left\{\operatorname{Li}_{s}\!\left(z\right), \zeta(s, z), \Phi(z, s, a)\right\}$$
Equal(PartitionsP(n), Mul(Div(1, n), Sum(Mul(DivisorSigma(1, Sub(n, k)), PartitionsP(k)), For(k, 0, Sub(n, 1)))))p(n) = \frac{1}{n} \sum_{k=0}^{n - 1} \sigma_{1}\!\left(n - k\right) p(k)$$p(n) = \frac{1}{n} \sum_{k=0}^{n - 1} \sigma_{1}\!\left(n - k\right) p(k)$$
MultiZetaValue(a, b, c)\zeta(a, b, c)$$\zeta(a, b, c)$$
RiemannXi(s)\xi(s)$$\xi(s)$$
Mul(LiouvilleLambda(n), EulerPhi(n), MoebiusMu(n))\lambda(n) \varphi(n) \mu(n)$$\lambda(n) \varphi(n) \mu(n)$$
BetaFunction(a, b)\mathrm{B}(a, b)$$\mathrm{B}(a, b)$$
PrimePi(x)\pi(x)$$\pi(x)$$
Equal(Min(a, b), Neg(Max(Neg(a), Neg(b))))\min(a, b) = -\max\!\left(-a, -b\right)$$\min(a, b) = -\max\!\left(-a, -b\right)$$
Equal(Arg(z), Div(Pi, 2))\arg(z) = \frac{\pi}{2}$$\arg(z) = \frac{\pi}{2}$$
NotEqual(Csgn(z), Sign(z))\operatorname{csgn}(z) \ne \operatorname{sgn}(z)$$\operatorname{csgn}(z) \ne \operatorname{sgn}(z)$$
Add(Factorial(0), Factorial(1), Div(1, Factorial(-3)), Factorial(Div(1, 2)), Factorial(Factorial(n)), DoubleFactorial(n))0! + 1! + \frac{1}{\left(-3\right)!} + \left(\frac{1}{2}\right)! + \left(n!\right)! + n!!$$0! + 1! + \frac{1}{\left(-3\right)!} + \left(\frac{1}{2}\right)! + \left(n!\right)! + n!!$$
List(Binomial(x, n), RisingFactorial(x, n), FallingFactorial(x, n), StirlingCycle(x, n), StirlingS1(x, n), StirlingS2(x, n))\left[{x \choose n}, \left(x\right)_{n}, \left(x\right)^{\underline{n}}, \left[{x \atop n}\right], s\!\left(x, n\right), \left\{{x \atop n}\right\}\right]$$\left[{x \choose n}, \left(x\right)_{n}, \left(x\right)^{\underline{n}}, \left[{x \atop n}\right], s\!\left(x, n\right), \left\{{x \atop n}\right\}\right]$$
Add(BellNumber(5), BernoulliB(5), EulerE(5), Fibonacci(5), HarmonicNumber(5), Prime(5), RiemannZetaZero(5))\operatorname{B}_{5} + B_{5} + E_{5} + F_{5} + H_{5} + p_{5} + \rho_{5}$$\operatorname{B}_{5} + B_{5} + E_{5} + F_{5} + H_{5} + p_{5} + \rho_{5}$$
List(LegendreSymbol(p, q), JacobiSymbol(p, q), KroneckerSymbol(p, q))\left[\left(\frac{p}{q}\right), \left(\frac{p}{q}\right), \left(\frac{p}{q}\right)\right]$$\left[\left(\frac{p}{q}\right), \left(\frac{p}{q}\right), \left(\frac{p}{q}\right)\right]$$
Add(ExpIntegralEi(x), ExpIntegralE(n, x), SinIntegral(x), SinhIntegral(x), CosIntegral(x), CoshIntegral(x), LogIntegral(x))\operatorname{Ei}(x) + E_{n}\!\left(x\right) + \operatorname{Si}(x) + \operatorname{Shi}(x) + \operatorname{Ci}(x) + \operatorname{Chi}(x) + \operatorname{li}(x)$$\operatorname{Ei}(x) + E_{n}\!\left(x\right) + \operatorname{Si}(x) + \operatorname{Shi}(x) + \operatorname{Ci}(x) + \operatorname{Chi}(x) + \operatorname{li}(x)$$
Mul(BesselJ(nu, z), BesselI(nu, z), BesselY(nu, z), BesselK(nu, z))J_{\nu}\!\left(z\right) I_{\nu}\!\left(z\right) Y_{\nu}\!\left(z\right) K_{\nu}\!\left(z\right)$$J_{\nu}\!\left(z\right) I_{\nu}\!\left(z\right) Y_{\nu}\!\left(z\right) K_{\nu}\!\left(z\right)$$
Equal(AiryAi(AiryAiZero(n)), AiryBi(AiryBiZero(n)), 0)\operatorname{Ai}\!\left(a_{n}\right) = \operatorname{Bi}\!\left(b_{n}\right) = 0$$\operatorname{Ai}\!\left(a_{n}\right) = \operatorname{Bi}\!\left(b_{n}\right) = 0$$
Equal(BesselJ(nu, BesselJZero(nu, n)), BesselY(nu, BesselYZero(nu, n)), 0)J_{\nu}\!\left(j_{\nu, n}\right) = Y_{\nu}\!\left(y_{\nu, n}\right) = 0$$J_{\nu}\!\left(j_{\nu, n}\right) = Y_{\nu}\!\left(y_{\nu, n}\right) = 0$$
Equal(RiemannZeta(s), Mul(Mul(Mul(Mul(2, Pow(Mul(2, Pi), Sub(s, 1))), Sin(Div(Mul(Pi, s), 2))), Gamma(Sub(1, s))), RiemannZeta(Sub(1, s))))\zeta(s) = 2 {\left(2 \pi\right)}^{s - 1} \sin\!\left(\frac{\pi s}{2}\right) \Gamma\!\left(1 - s\right) \zeta\!\left(1 - s\right)$$\zeta(s) = 2 {\left(2 \pi\right)}^{s - 1} \sin\!\left(\frac{\pi s}{2}\right) \Gamma\!\left(1 - s\right) \zeta\!\left(1 - s\right)$$
Pow(Div(Pow(DedekindEta(Mul(2, tau)), 2), Mul(DedekindEta(tau), DedekindEta(Mul(4, tau)))), 24){\left(\frac{\eta^{2}\!\left(2 \tau\right)}{\eta(\tau) \eta\!\left(4 \tau\right)}\right)}^{24}$${\left(\frac{\eta^{2}\!\left(2 \tau\right)}{\eta(\tau) \eta\!\left(4 \tau\right)}\right)}^{24}$$
Mul(Mul(Erf(z), Erfc(z)), Erfi(z))\operatorname{erf}(z) \operatorname{erfc}(z) \operatorname{erfi}(z)$$\operatorname{erf}(z) \operatorname{erfc}(z) \operatorname{erfi}(z)$$
Mul(EllipticK(m), EllipticE(m), EllipticPi(n, m))K(m) E(m) \Pi(n, m)$$K(m) E(m) \Pi(n, m)$$
Mul(IncompleteEllipticE(z, m), IncompleteEllipticF(z, m), IncompleteEllipticPi(n, z, m))E(z, m) F(z, m) \Pi(n, z, m)$$E(z, m) F(z, m) \Pi(n, z, m)$$
Add(CarlsonRF(x, y, z), CarlsonRG(x, y, z), CarlsonRJ(x, y, z, w), CarlsonRD(x, y, z), CarlsonRC(x, y))R_F(x, y, z) + R_G(x, y, z) + R_J(x, y, z, w) + R_D(x, y, z) + R_C(x, y)$$R_F(x, y, z) + R_G(x, y, z) + R_J(x, y, z, w) + R_D(x, y, z) + R_C(x, y)$$
Mul(Hypergeometric0F1(b, z), Hypergeometric0F1Regularized(b, z))\,{}_0F_1(b, z) \,{}_0{\textbf F}_1(b, z)$$\,{}_0F_1(b, z) \,{}_0{\textbf F}_1(b, z)$$
Mul(Hypergeometric1F1(a, b, z), Hypergeometric1F1Regularized(a, b, z))\,{}_1F_1(a, b, z) \,{}_1{\textbf F}_1(a, b, z)$$\,{}_1F_1(a, b, z) \,{}_1{\textbf F}_1(a, b, z)$$
Hypergeometric2F0(a, b, z)\,{}_2F_0(a, b, z)$$\,{}_2F_0(a, b, z)$$
Mul(HypergeometricU(a, b, z), HypergeometricUStar(a, b, z))U(a, b, z) U^{*}(a, b, z)$$U(a, b, z) U^{*}(a, b, z)$$
Mul(Hypergeometric2F1(a, b, c, z), Hypergeometric2F1Regularized(a, b, c, z))\,{}_2F_1(a, b, c, z) \,{}_2{\textbf F}_1(a, b, c, z)$$\,{}_2F_1(a, b, c, z) \,{}_2{\textbf F}_1(a, b, c, z)$$
Mul(Hypergeometric1F2(a, b, c, z), Hypergeometric1F2Regularized(a, b, c, z))\,{}_1F_2(a, b, c, z) \,{}_1{\textbf F}_2(a, b, c, z)$$\,{}_1F_2(a, b, c, z) \,{}_1{\textbf F}_2(a, b, c, z)$$
Mul(Hypergeometric2F2(a, b, c, d, z), Hypergeometric2F2Regularized(a, b, c, d, z))\,{}_2F_2(a, b, c, d, z) \,{}_2{\textbf F}_2(a, b, c, d, z)$$\,{}_2F_2(a, b, c, d, z) \,{}_2{\textbf F}_2(a, b, c, d, z)$$
Mul(Hypergeometric3F2(a, b, c, d, e, z), Hypergeometric3F2Regularized(a, b, c, d, e, z))\,{}_3F_2(a, b, c, d, e, z) \,{}_3{\textbf F}_2(a, b, c, d, e, z)$$\,{}_3F_2(a, b, c, d, e, z) \,{}_3{\textbf F}_2(a, b, c, d, e, z)$$
Pow(Hypergeometric2F1Regularized(Div(-1, 4), Div(1, 4), Div(1, 2), Div(Sub(x, 1), 2)), 2){\left(\,{}_2{\textbf F}_1\!\left(-\frac{1}{4}, \frac{1}{4}, \frac{1}{2}, \frac{x - 1}{2}\right)\right)}^{2}$${\left(\,{}_2{\textbf F}_1\!\left(-\frac{1}{4}, \frac{1}{4}, \frac{1}{2}, \frac{x - 1}{2}\right)\right)}^{2}$$
Matrix(List(List(a, b, c), List(d, e, f), List(g, h, 0)))\displaystyle{\begin{pmatrix}a & b & c \\d & e & f \\g & h & 0\end{pmatrix}}$$\displaystyle{\begin{pmatrix}a & b & c \\d & e & f \\g & h & 0\end{pmatrix}}$$
Matrix2x2(a, b, c, d)\displaystyle{\begin{pmatrix}a & b \\ c & d\end{pmatrix}}$$\displaystyle{\begin{pmatrix}a & b \\ c & d\end{pmatrix}}$$
Set(RowMatrix(), RowMatrix(a), RowMatrix(a, b), RowMatrix(a, b, c), RowMatrix(a, b, c, d))\left\{\displaystyle{\begin{pmatrix}\end{pmatrix}}, \displaystyle{\begin{pmatrix}a\end{pmatrix}}, \displaystyle{\begin{pmatrix}a & b\end{pmatrix}}, \displaystyle{\begin{pmatrix}a & b & c\end{pmatrix}}, \displaystyle{\begin{pmatrix}a & b & c & d\end{pmatrix}}\right\}$$\left\{\displaystyle{\begin{pmatrix}\end{pmatrix}}, \displaystyle{\begin{pmatrix}a\end{pmatrix}}, \displaystyle{\begin{pmatrix}a & b\end{pmatrix}}, \displaystyle{\begin{pmatrix}a & b & c\end{pmatrix}}, \displaystyle{\begin{pmatrix}a & b & c & d\end{pmatrix}}\right\}$$
Set(ColumnMatrix(), ColumnMatrix(a), ColumnMatrix(a, b), ColumnMatrix(a, b, c), ColumnMatrix(a, b, c, d))\left\{\displaystyle{\begin{pmatrix}\end{pmatrix}}, \displaystyle{\begin{pmatrix}a\end{pmatrix}}, \displaystyle{\begin{pmatrix}a \\ b\end{pmatrix}}, \displaystyle{\begin{pmatrix}a \\ b \\ c\end{pmatrix}}, \displaystyle{\begin{pmatrix}a \\ b \\ c \\ d\end{pmatrix}}\right\}$$\left\{\displaystyle{\begin{pmatrix}\end{pmatrix}}, \displaystyle{\begin{pmatrix}a\end{pmatrix}}, \displaystyle{\begin{pmatrix}a \\ b\end{pmatrix}}, \displaystyle{\begin{pmatrix}a \\ b \\ c\end{pmatrix}}, \displaystyle{\begin{pmatrix}a \\ b \\ c \\ d\end{pmatrix}}\right\}$$
Set(DiagonalMatrix(), DiagonalMatrix(a), DiagonalMatrix(a, b), DiagonalMatrix(a, b, c), DiagonalMatrix(a, b, c, d))\left\{\displaystyle{\begin{pmatrix}\end{pmatrix}}, \displaystyle{\begin{pmatrix}a\end{pmatrix}}, \displaystyle{\begin{pmatrix}a & \\ & b\end{pmatrix}}, \displaystyle{\begin{pmatrix}a & & \\ & b & \\ & & c\end{pmatrix}}, \displaystyle{\begin{pmatrix}a & & & \\ & b & & \\ & & c & \\ & & & d\end{pmatrix}}\right\}$$\left\{\displaystyle{\begin{pmatrix}\end{pmatrix}}, \displaystyle{\begin{pmatrix}a\end{pmatrix}}, \displaystyle{\begin{pmatrix}a & \\ & b\end{pmatrix}}, \displaystyle{\begin{pmatrix}a & & \\ & b & \\ & & c\end{pmatrix}}, \displaystyle{\begin{pmatrix}a & & & \\ & b & & \\ & & c & \\ & & & d\end{pmatrix}}\right\}$$
Matrix(c_(m, n), For(m, 1, N), For(n, 1, 10))\displaystyle{\begin{pmatrix} c_{1, 1} & c_{1, 2} & \cdots & c_{1, 10} \\ c_{2, 1} & c_{2, 2} & \cdots & c_{2, 10} \\ \vdots & \vdots & \ddots & \vdots \\ c_{N, 1} & c_{N, 2} & \cdots & c_{N, 10} \end{pmatrix}}$$\displaystyle{\begin{pmatrix} c_{1, 1} & c_{1, 2} & \cdots & c_{1, 10} \\ c_{2, 1} & c_{2, 2} & \cdots & c_{2, 10} \\ \vdots & \vdots & \ddots & \vdots \\ c_{N, 1} & c_{N, 2} & \cdots & c_{N, 10} \end{pmatrix}}$$
Matrix(ShowExpandedNormalForm(Div(1, Sub(Add(m, n), 1))), For(m, 1, 10), For(n, 1, 10))\displaystyle{\begin{pmatrix} 1 & \frac{1}{2} & \cdots & \frac{1}{10} \\ \frac{1}{2} & \frac{1}{3} & \cdots & \frac{1}{11} \\ \vdots & \vdots & \ddots & \vdots \\ \frac{1}{10} & \frac{1}{11} & \cdots & \frac{1}{19} \end{pmatrix}}$$\displaystyle{\begin{pmatrix} 1 & \frac{1}{2} & \cdots & \frac{1}{10} \\ \frac{1}{2} & \frac{1}{3} & \cdots & \frac{1}{11} \\ \vdots & \vdots & \ddots & \vdots \\ \frac{1}{10} & \frac{1}{11} & \cdots & \frac{1}{19} \end{pmatrix}}$$
Add(ZeroMatrix(2), IdentityMatrix(2), HilbertMatrix(2))0_{2} + I_{2} + H_{2}$$0_{2} + I_{2} + H_{2}$$
Set(SpecialLinearGroup(n, ZZ), GeneralLinearGroup(n, ZZ))\left\{\operatorname{SL}_{n}\!\left(\mathbb{Z}\right), \operatorname{GL}_{n}\!\left(\mathbb{Z}\right)\right\}$$\left\{\operatorname{SL}_{n}\!\left(\mathbb{Z}\right), \operatorname{GL}_{n}\!\left(\mathbb{Z}\right)\right\}$$
Equal(One(QQ), 1)1_{\mathbb{Q}} = 1$$1_{\mathbb{Q}} = 1$$
Equal(Zero(QQ), 0)0_{\mathbb{Q}} = 0$$0_{\mathbb{Q}} = 0$$
List(Polynomials(QQ, x), Polynomials(QQ, x, y), Polynomials(QQ, Tuple()), Polynomials(QQ, Tuple(x)), Polynomials(QQ, Tuple(x, y)))\left[\mathbb{Q}[x], \mathbb{Q}[x, y], \mathbb{Q}[], \mathbb{Q}[x], \mathbb{Q}[x, y]\right]$$\left[\mathbb{Q}[x], \mathbb{Q}[x, y], \mathbb{Q}[], \mathbb{Q}[x], \mathbb{Q}[x, y]\right]$$
List(Polynomials(QQ, x), PolynomialFractions(QQ, x), FormalPowerSeries(QQ, x), FormalLaurentSeries(QQ, x), FormalPuiseuxSeries(QQ, x))\left[\mathbb{Q}[x], \mathbb{Q}(x), \mathbb{Q}[[x]], \mathbb{Q}(\!(x)\!), \mathbb{Q}\!\left\langle\!\left\langle x \right\rangle\!\right\rangle\right]$$\left[\mathbb{Q}[x], \mathbb{Q}(x), \mathbb{Q}[[x]], \mathbb{Q}(\!(x)\!), \mathbb{Q}\!\left\langle\!\left\langle x \right\rangle\!\right\rangle\right]$$
Set(IntegersGreaterEqual(0), IntegersGreaterEqual(n), IntegersLessEqual(0), IntegersLessEqual(n))\left\{\mathbb{Z}_{\ge 0}, \mathbb{Z}_{\ge n}, \{0, -1, \ldots\}, \mathbb{Z}_{\le n}\right\}$$\left\{\mathbb{Z}_{\ge 0}, \mathbb{Z}_{\ge n}, \{0, -1, \ldots\}, \mathbb{Z}_{\le n}\right\}$$
List(Range(a, b), Range(1, b), Range(-3, 5))\left[\{a, a + 1, \ldots, b\}, \{1, 2, \ldots, b\}, \{-3, -2, \ldots, 5\}\right]$$\left[\{a, a + 1, \ldots, b\}, \{1, 2, \ldots, b\}, \{-3, -2, \ldots, 5\}\right]$$
CongruentMod(f(n), 0, p)f(n) \equiv 0 \pmod {p }$$f(n) \equiv 0 \pmod {p }$$
PrimitiveReducedPositiveIntegralBinaryQuadraticForms(D)\mathcal{Q}^{*}_{D}$$\mathcal{Q}^{*}_{D}$$
Set(EllipticRootE(1, tau), EllipticRootE(2, tau), EllipticRootE(3, tau))\left\{e_{1}\!\left(\tau\right), e_{2}\!\left(\tau\right), e_{3}\!\left(\tau\right)\right\}$$\left\{e_{1}\!\left(\tau\right), e_{2}\!\left(\tau\right), e_{3}\!\left(\tau\right)\right\}$$
GaussSum(n, chi)G_{n}\!\left(\chi\right)$$G_{n}\!\left(\chi\right)$$
Set(GlaisherConstant, KhinchinConstant)\left\{A, K\right\}$$\left\{A, K\right\}$$
Decimal("0.3141")0.3141$$0.3141$$
Decimal("0.3141e-27")0.3141 \cdot 10^{-27}$$0.3141 \cdot 10^{-27}$$
Set(DigammaFunction(z), DigammaFunction(z, 1), DigammaFunction(z, n))\left\{\psi(z), \psi'\!\left(z\right), {\psi}^{(n)}\!\left(z\right)\right\}$$\left\{\psi(z), \psi'\!\left(z\right), {\psi}^{(n)}\!\left(z\right)\right\}$$
Set(AiryAi(z, 1), AiryAi(z, 2), AiryBi(z, n), BesselJ(n, z, 1), BesselY(n, z, 2), BesselK(n, z, Add(Mul(3, r), 1)))\left\{\operatorname{Ai}'\!\left(z\right), \operatorname{Ai}''\!\left(z\right), {\operatorname{Bi}}^{(n)}\!\left(z\right), J'_{n}\!\left(z\right), Y''_{n}\!\left(z\right), {K}^{(3 r + 1)}_{n}\!\left(z\right)\right\}$$\left\{\operatorname{Ai}'\!\left(z\right), \operatorname{Ai}''\!\left(z\right), {\operatorname{Bi}}^{(n)}\!\left(z\right), J'_{n}\!\left(z\right), Y''_{n}\!\left(z\right), {K}^{(3 r + 1)}_{n}\!\left(z\right)\right\}$$
Set(HankelH1(n, z), HankelH2(n, z))\left\{H^{(1)}_{n}\!\left(z\right), H^{(2)}_{n}\!\left(z\right)\right\}$$\left\{H^{(1)}_{n}\!\left(z\right), H^{(2)}_{n}\!\left(z\right)\right\}$$
Element(DirichletCharacter(q, k), PrimitiveDirichletCharacters(q))\chi_{q \, . \, k} \in G^{\text{Primitive}}_{q}$$\chi_{q \, . \, k} \in G^{\text{Primitive}}_{q}$$
DirichletCharacter(q, k, n)\chi_{q \, . \, k}(n)$$\chi_{q \, . \, k}(n)$$
JacobiTheta(3, z, tau, 2)\theta''_{3}\!\left(z, \tau\right)$$\theta''_{3}\!\left(z, \tau\right)$$
Set(RiemannZeta(s, 1), RiemannZeta(s, r))\left\{\zeta'\!\left(s\right), {\zeta}^{(r)}\!\left(s\right)\right\}$$\left\{\zeta'\!\left(s\right), {\zeta}^{(r)}\!\left(s\right)\right\}$$
Subscript(x, y){x}_{y}$${x}_{y}$$
Set(BernsteinEllipse(r), UnitCircle, PSL2Z, AGMSequence(n, a, b), CarlsonHypergeometricR, CarlsonHypergeometricT)\left\{\mathcal{E}_{r}, \mathbb{T}, \operatorname{PSL}_2(\mathbb{Z}), \operatorname{agm}_{n}\!\left(a, b\right), R, T\right\}$$\left\{\mathcal{E}_{r}, \mathbb{T}, \operatorname{PSL}_2(\mathbb{Z}), \operatorname{agm}_{n}\!\left(a, b\right), R, T\right\}$$
Mul(Mul(Pow(Fibonacci(n), 2), Pow(x_(a), 2)), Pow(alpha_(n), 2))F_{n}^{2} x_{a}^{2} \alpha_{n}^{2}$$F_{n}^{2} x_{a}^{2} \alpha_{n}^{2}$$
Set(Derivative(ChebyshevT(n, x_), For(x_, x)), Derivative(ChebyshevT(n, x_), For(x_, x, 2)), Derivative(ChebyshevT(n, x_), For(x_, x, 4)))\left\{T'_{n}\!\left(x\right), T''_{n}\!\left(x\right), {T}^{(4)}_{n}\!\left(x\right)\right\}$$\left\{T'_{n}\!\left(x\right), T''_{n}\!\left(x\right), {T}^{(4)}_{n}\!\left(x\right)\right\}$$
Poles(Gamma(z), For(z, CC))\mathop{\operatorname{poles}\,}\limits_{z \in \mathbb{C}} \Gamma(z)$$\mathop{\operatorname{poles}\,}\limits_{z \in \mathbb{C}} \Gamma(z)$$
Equal(Item(Tuple(a, b, c), 2), b){\left(a, b, c\right)}_{2} = b$${\left(a, b, c\right)}_{2} = b$$
Set(Tuple(n, For(n, a, b)), List(Pow(Neg(n), 2), For(n, 1, 100)), Set(f_(n), For(n, 0, N)))\left\{\left(a, a + 1, \ldots, b\right), \left[{\left(-1\right)}^{2}, {\left(-2\right)}^{2}, \ldots, {\left(-100\right)}^{2}\right], \left\{f_{0}, f_{1}, \ldots, f_{N}\right\}\right\}$$\left\{\left(a, a + 1, \ldots, b\right), \left[{\left(-1\right)}^{2}, {\left(-2\right)}^{2}, \ldots, {\left(-100\right)}^{2}\right], \left\{f_{0}, f_{1}, \ldots, f_{N}\right\}\right\}$$
Set(Tuple(1, 0, Repeat(3, N)), Tuple(1, 0, Repeat(1, 2, 3, N)))\left\{\left(1, 0, \underbrace{3, \ldots, 3}_{N \text{ times}}\right), \left(1, 0, \underbrace{1, 2, 3, \ldots, 1, 2, 3}_{\left(1, 2, 3\right) \; N \text{ times}}\right)\right\}$$\left\{\left(1, 0, \underbrace{3, \ldots, 3}_{N \text{ times}}\right), \left(1, 0, \underbrace{1, 2, 3, \ldots, 1, 2, 3}_{\left(1, 2, 3\right) \; N \text{ times}}\right)\right\}$$
Tuple(Sub(A, 2), Sub(A, 1), Step(n, For(n, A, B)), Add(B, 1), Add(B, 2))\left(A - 2, A - 1, A, A + 1, \ldots, B, B + 1, B + 2\right)$$\left(A - 2, A - 1, A, A + 1, \ldots, B, B + 1, B + 2\right)$$
Lattice(1, tau)\Lambda_{(1, \tau)}$$\Lambda_{(1, \tau)}$$
DiscreteLog(n, 2, q)(\epsilon : {2}^{\epsilon} \equiv n \text{ mod }q)$$(\epsilon : {2}^{\epsilon} \equiv n \text{ mod }q)$$
AsymptoticTo(f(n), g(n), n, Infinity)f(n) \sim g(n), \; n \to \infty$$f(n) \sim g(n), \; n \to \infty$$
Set(CoulombF(l, eta, z), CoulombG(l, eta, z), CoulombH(1, l, eta, z), CoulombH(-1, l, eta, z), CoulombH(omega, l, eta, z))\left\{F_{l,\eta}(z), G_{l,\eta}(z), H^{+}_{l,\eta}(z), H^{-}_{l,\eta}(z), H^{\omega}_{l,\eta}(z)\right\}$$\left\{F_{l,\eta}(z), G_{l,\eta}(z), H^{+}_{l,\eta}(z), H^{-}_{l,\eta}(z), H^{\omega}_{l,\eta}(z)\right\}$$
Set(Matrices(CC, n), Matrices(CC, n, m))\left\{\operatorname{M}_{n}(\mathbb{C}), \operatorname{M}_{n \times m}(\mathbb{C})\right\}$$\left\{\operatorname{M}_{n}(\mathbb{C}), \operatorname{M}_{n \times m}(\mathbb{C})\right\}$$
Set(SloaneA(40, n), SloaneA(12345, n), SloaneA("A553322", n))\left\{\text{A000040}\!\left(n\right), \text{A012345}\!\left(n\right), \text{A553322}\!\left(n\right)\right\}$$\left\{\text{A000040}\!\left(n\right), \text{A012345}\!\left(n\right), \text{A553322}\!\left(n\right)\right\}$$
And(EqualAndElement(x, Pi, RR), EqualNearestDecimal(Pi, Decimal("3.14"), 3))x = \pi \in \mathbb{R} \;\mathbin{\operatorname{and}}\; \pi = 3.14 \;\, {\scriptstyle (\text{nearest } 3 \text{ digits})}$$x = \pi \in \mathbb{R} \;\mathbin{\operatorname{and}}\; \pi = 3.14 \;\, {\scriptstyle (\text{nearest } 3 \text{ digits})}$$
Less(0, Same(Div(1, Sqrt(2)), Div(Sqrt(2), 2)), 1)0 < \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} < 1$$0 < \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} < 1$$
Fun(x, Pow(x, 2))x \mapsto {x}^{2}$$x \mapsto {x}^{2}$$
GeneralizedBernoulliB(n, chi)B_{n, \chi}$$B_{n, \chi}$$
HurwitzZeta(s, a, 2)\zeta''\!\left(s, a\right)$$\zeta''\!\left(s, a\right)$$
Set(StieltjesGamma(n), StieltjesGamma(n, a))\left\{\gamma_{n}, \gamma_{n}\!\left(a\right)\right\}$$\left\{\gamma_{n}, \gamma_{n}\!\left(a\right)\right\}$$
And(IsHolomorphicOn(f(z), For(z, CC)), IsMeromorphicOn(g(z), For(z, CC)))f(z) \text{ is holomorphic on } z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; g(z) \text{ is meromorphic on } z \in \mathbb{C}$$f(z) \text{ is holomorphic on } z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; g(z) \text{ is meromorphic on } z \in \mathbb{C}$$
Set(StirlingSeriesRemainder(N, z), LogBarnesGRemainder(N, z))\left\{R_{N}\!\left(z\right), R_{N}\!\left(z\right)\right\}$$\left\{R_{N}\!\left(z\right), R_{N}\!\left(z\right)\right\}$$
AnalyticContinuation(f(z), For(z, a, b))\mathop{\text{Continuation}}\limits_{\displaystyle{z: a \rightsquigarrow b}} \, f(z)$$\mathop{\text{Continuation}}\limits_{\displaystyle{z: a \rightsquigarrow b}} \, f(z)$$
AnalyticContinuation(f(z), For(z, CurvePath(g(t), For(t, a, b))))\mathop{\text{Continuation}}\limits_{\displaystyle{z: \left(g(t),\, t : a \rightsquigarrow b\right)}} \, f(z)$$\mathop{\text{Continuation}}\limits_{\displaystyle{z: \left(g(t),\, t : a \rightsquigarrow b\right)}} \, f(z)$$
BernoulliPolynomial(n, x)B_{n}\!\left(x\right)$$B_{n}\!\left(x\right)$$
Call(f, x)f(x)$$f(x)$$
CallIndeterminate(f, x, v)f(v)$$f(v)$$
CartesianProduct(ZZ, QQ)\mathbb{Z} \times \mathbb{Q}$$\mathbb{Z} \times \mathbb{Q}$$
CartesianPower(RR, 3){\mathbb{R}}^{3}$${\mathbb{R}}^{3}$$
Characteristic(R)\operatorname{char}(R)$$\operatorname{char}(R)$$
Coefficient(f, x, 2)[{x}^{2}] f$$[{x}^{2}] f$$
ComplexZeroMultiplicity(f(z), For(z, a))\mathop{\operatorname{ord}}\limits_{z=a} f(z)$$\mathop{\operatorname{ord}}\limits_{z=a} f(z)$$
Residue(f(z), For(z, a))\mathop{\operatorname{res}}\limits_{z=a} f(z)$$\mathop{\operatorname{res}}\limits_{z=a} f(z)$$
ConreyGenerator(q)g_{q}$$g_{q}$$
CoulombC(l, eta)C_{l}\!\left(\eta\right)$$C_{l}\!\left(\eta\right)$$
CoulombSigma(l, eta)\sigma_{l}\!\left(\eta\right)$$\sigma_{l}\!\left(\eta\right)$$
Cyclotomic(n, x)\Phi_{n}\!\left(x\right)$$\Phi_{n}\!\left(x\right)$$
DedekindEtaEpsilon(a, b, c, d)\varepsilon(a, b, c, d)$$\varepsilon(a, b, c, d)$$
DedekindSum(a, b)s(a, b)$$s(a, b)$$
Where(f(Add(x, 1)), Def(f(t), Div(1, t)))f\!\left(x + 1\right)\; \text{ where } f(t) = \frac{1}{t}$$f\!\left(x + 1\right)\; \text{ where } f(t) = \frac{1}{t}$$
Det(Matrix2x2(a, b, c, d))\operatorname{det} \displaystyle{\begin{pmatrix}a & b \\ c & d\end{pmatrix}}$$\operatorname{det} \displaystyle{\begin{pmatrix}a & b \\ c & d\end{pmatrix}}$$
Det(A)\operatorname{det}(A)$$\operatorname{det}(A)$$
f(a, b, Ellipsis, z)f(a, b, \ldots, z)$$f(a, b, \ldots, z)$$
Equal(DirichletL(DirichletLZero(n, chi), chi), 0)L\!\left(\rho_{n, \chi}, \chi\right) = 0$$L\!\left(\rho_{n, \chi}, \chi\right) = 0$$
DirichletGroup(q)G_{q}$$G_{q}$$
Set(ModularGroupFundamentalDomain, ModularLambdaFundamentalDomain)\left\{\mathcal{F}, \mathcal{F}_{\lambda}\right\}$$\left\{\mathcal{F}, \mathcal{F}_{\lambda}\right\}$$
Path(a, b, c, d)a \rightsquigarrow b \rightsquigarrow c \rightsquigarrow d$$a \rightsquigarrow b \rightsquigarrow c \rightsquigarrow d$$
PolynomialDegree(f)\deg(f)$$\deg(f)$$
RootOfUnity(5)\zeta_{5}$$\zeta_{5}$$
SL2Z\operatorname{SL}_2(\mathbb{Z})$$\operatorname{SL}_2(\mathbb{Z})$$
UpperHalfPlane\mathbb{H}$$\mathbb{H}$$
XGCD(m, n)\operatorname{xgcd}(m, n)$$\operatorname{xgcd}(m, n)$$
JacobiThetaQ(3, z, q)\theta_{3}\!\left(z, q\right)$$\theta_{3}\!\left(z, q\right)$$
KeiperLiLambda(n)\lambda_{n}$$\lambda_{n}$$
Set(LambertW(z), LambertW(z, n), LambertW(z, n, 1), LambertW(z, n, r))\left\{W(z), W_{n}(z), W'_{n}(z), {W}^{(r)}_{n}(z)\right\}$$\left\{W(z), W_{n}(z), W'_{n}(z), {W}^{(r)}_{n}(z)\right\}$$
LandauG(n)g(n)$$g(n)$$
SquaresR(k, n)r_{k}\!\left(n\right)$$r_{k}\!\left(n\right)$$
ModularGroupAction(gamma, tau)\gamma \circ \tau$$\gamma \circ \tau$$
Mod(n, p)n \bmod p$$n \bmod p$$
LessEqual(0, Step(f(n), For(n, a, b)), 1)0 \le f(a) \le f\!\left(a + 1\right) \le \ldots \le f(b) \le 1$$0 \le f(a) \le f\!\left(a + 1\right) \le \ldots \le f(b) \le 1$$
LessEqual(0, Step(f(n), For(n, 1, b)), 1)0 \le f(1) \le f(2) \le \ldots \le f(b) \le 1$$0 \le f(1) \le f(2) \le \ldots \le f(b) \le 1$$
Add(LowerGamma(s, z), UpperGamma(s, z))\gamma(s, z) + \Gamma(s, z)$$\gamma(s, z) + \Gamma(s, z)$$
DigammaFunctionZero(n)x_{n}$$x_{n}$$
Set(EulerPolynomial(n, x), HermiteH(n, x), HilbertClassPolynomial(n, x))\left\{E_{n}\!\left(x\right), H_{n}\!\left(x\right), H_{n}\!\left(x\right)\right\}$$\left\{E_{n}\!\left(x\right), H_{n}\!\left(x\right), H_{n}\!\left(x\right)\right\}$$
JacobiThetaEpsilon(j, a, b, c, d)\varepsilon_{j}\!\left(a, b, c, d\right)$$\varepsilon_{j}\!\left(a, b, c, d\right)$$
JacobiThetaPermutation(j, a, b, c, d)S_{j}\!\left(a, b, c, d\right)$$S_{j}\!\left(a, b, c, d\right)$$
SymmetricPolynomial(k, List(X_(t), For(t, 1, n)))e_{k}\!\left(\left[X_{1}, X_{2}, \ldots, X_{n}\right]\right)$$e_{k}\!\left(\left[X_{1}, X_{2}, \ldots, X_{n}\right]\right)$$
Intersection(A, B)A \cap B$$A \cap B$$
RealAlgebraicNumbers\overline{\mathbb{Q}}_{\mathbb{R}}$$\overline{\mathbb{Q}}_{\mathbb{R}}$$

Untested builtins:

CommutativeRings EqualQSeriesEllipsis EulerQSeries Fields FiniteField GaussLegendreWeight GegenbauerC HypergeometricUStarRemainder IndefiniteIntegralEqual JacobiP LaguerreL LegendreP LegendrePolynomialZero Pol QSeriesCoefficient QuotientRing Rings Root Ser Sets SingularValues Spectrum SphericalHarmonicY Subsets Tuples XX