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!''}) | $$f(\text{``Hello, world!''})$$ |
| f | f | $$f$$ |
| 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