AsciiMath выражения для рендеринга страниц проекта, содержащие MathJax формулы, функции и иные математические нотации в представленных на сайте задачах
Основные выражения, операции, символы и константы:
| x^y | `x^y` |
| x_n | `x_n` |
| x_n^y | `x_n^y` |
| sqrt(x) | `sqrt(x)` |
| root(n)(x) | `root(n)(x)` |
| abs(x) | `abs(x)` |
| log_{x}(y) | `log_{x}(y)` |
| >= | `>=` |
| = | `=` |
| != | `!=` |
| ~~ | `~~` |
| equiv | `equiv` |
| -= | `-=` |
| +- | `+-` |
| pm | `pm` |
| -: | `-:` |
| div | `div` |
| lfloor n rfloor | `lfloor n rfloor` |
| lceil n rceil | `lceil n rceil` |
| AA | `AA` |
| forall | `forall` |
| EE | `EE` |
| exists | `exists` |
| F_(n-1)+F_(n-2)=(((1+sqrt5)/2)^n-((1+sqrt5)/2)^(-n))/(sqrt5), n>=2 | |
| `F_(n-1)+F_(n-2)=(((1+sqrt5)/2)^n-((1+sqrt5)/2)^(-n))/(sqrt5), n>=2` | |
| times | `times` |
| * | `*` |
| in | `in` |
| notin | `notin` |
| infty | `infty` |
| +infty | `+infty` |
| -infty | `-infty` |
| /_ | `/_` |
| angle | `angle` |
| _|_ | `_|_` |
| bot | `bot` |
| vec(x) | `vec(x)` |
| bar(x+y+z) | `bar(x+y+z)` |
| overline(x+y+z) | `overline(x+y+z)` |
| underline(x+y+z) | `underline(x+y+z)` |
| 30^@ (градусы) | `30^@` |
| circ | `circ` |
| pi | `pi` |
| e | `e` |
| i | `i` |
| phi | `phi` |
| cos/_ (vec x; vec y)= (x_1*y_1+x_2*y_2+x_3*y_3)/ (sqrt(x_1^2+x_2^2+x_3^2)* sqrt(y_1^2+y_2^2+y_3^2)), vec x != vec 0, vec y!= vec 0 | |
| `cos/_ (vec x; vec y)= (x_1*y_1+x_2*y_2+x_3*y_3)/ (sqrt(x_1^2+x_2^2+x_3^2)* sqrt(y_1^2+y_2^2+y_3^2)), vec x != vec 0, vec y!= vec 0` | |
Дифференцирование и интегрирование
| f ' | `f '` |
| f '' | `f ''` |
| dot f | `dot f` |
| ddot f | `ddot f` |
| f^((n)) | `f^((n))` |
| (df)/(dx) | `(df)/(dx)` |
| DD f | `DD f` |
| (partial f)/(partial x) | `(partial f)/(partial x)` |
| nabla f | `nabla f` |
| y=(1+x)/sqrt(1-x), x < 1 => =>(d^100 y)/(dx^100)=((197)!!)/(2^100)*(399-x)/((1-x)^(100.5)) | |
| `y=(1+x)/sqrt(1-x), x < 1 =>` `=>(d^100 y)/(dx^100)=((197)!!)/(2^100)*(399-x)/((1-x)^(100.5))` | |
| int f(x)dx | `int f(x)dx` |
| int_a^b f(x)dx | `int_a^b f(x)dx` |
| int_l f dl | `int_l f dl` |
| iint_D dxdy | `iint_D dxdy` |
| iiint_D dxdydz | `iiint_D dxdydz` |
| oint_L Pdx+Qdy | `oint_L Pdx+Qdy` |
| lim_(x->+infty)(int_0^x e^(t^2)dt)^2/(int_0^x e^(2t^2)dt)=0 | |
| `lim_(x->+infty)(int_0^x e^(t^2)dt)^2/(int_0^x e^(2t^2)dt)=0` | |
Греческие буквы
Строчные греческие буквы
| alpha | `alpha` | xi | `xi` | |
| beta | `beta` | o | `o` | |
| gamma | `gamma` | pi | `pi` | |
| delta | `delta` | |||
| epsilon | `epsilon` | rho | `rho` | |
| varepsilon | `varepsilon` | |||
| zeta | `zeta` | sigma | `sigma` | |
| eta | `eta` | |||
| theta | `theta` | tau | `tau` | |
| vartheta | `vartheta` | upsilon | `upsilon` | |
| iota | `iota` | phi | `phi` | |
| kappa | `kappa` | varphi | `varphi` | |
| lambda | `lambda` | chi | `chi` | |
| mu | `mu` | psi | `psi` | |
| nu | `nu` | omega | `omega` | |
| kappa -=(2pi)/(lambda)=(2pi*nu)/(upsilon_p)=(omega)/(upsilon_p)=E/(hbar*c) | ||||
| `kappa -=(2pi)/(lambda)=(2pi*nu)/(upsilon_p)=(omega)/(upsilon_p)=E/(hbar*c)` | ||||
Прописные греческие буквы, отличающиеся по написанию от латинских
| Gamma | `Gamma` |
| Delta | `Delta` |
| Theta | `Theta` |
| Lambda | `Lambda` |
| Xi | `Xi` |
| Pi | `Pi` |
| Sigma | `Sigma` |
| Phi | `Phi` |
| Psi | `Psi` |
| Omega | `Omega` |
| E K Lambda E I Delta E I A quad Gamma E Omega M E T P I A | |
| `E K Lambda E I Delta E I A quad Gamma E Omega M E T P I A` | |
Особые начертания букв и другие буквы
| NN | `NN` |
| ZZ | `ZZ` |
| `QQ` | |
| RR | `RR` |
| CC | `CC` |
| mathbb(N, Z, Q, R, C) | `mathbb(N, Z, Q, R, C)` |
| nabla | `nabla` |
| aleph | `aleph` |
| mathfrak(C, I, H, R, Z) | `mathfrak(C, I, H, R, Z)` |
| mathcal(E, I, B, F) | `mathcal(E, I, B, F)` |
| mathcal(H, L, M, R) | `mathcal( H, L, M, R)` |
| NN subset ZZ subset QQ subset RR subset CC | |
| `NN subset ZZ subset QQ subset RR subset CC` | |
Стрелки
| Leftarrow | `Leftarrow` |
| mapsto | `mapsto` |
| rightarrow | `rightarrow` |
| to | `to` |
| -> | `->` |
| Rightarrow | `Rightarrow` |
| => | `=>` |
| leftrightarrow | `leftrightarrow` |
| Leftrightarrow | `Leftrightarrow` |
| iff | `iff` |
| <=> | `<=>` |
Многоточия, точки, диакритические знаки и логические символы
| vdots | `vdots` |
| ddots | `ddots` |
| cdots | `cdots` |
| ldots | `ldots` |
| cdot | `cdot` |
| dot(x) | `dot(x)` |
| ddot(x) | `ddot(x)` |
| hat(x) | `hat(x)` |
| tilde(x) | `tilde(x)` |
| bar(x) | `bar(x)` |
| vec(x) | `vec(x)` |
| vee | `vee` |
| vv | `vv` |
| wedge | `wedge` |
| ^^ | `^^` |
| bar(f) | `bar(f)` |
| neg f | `neg f` |
| vdash | `vdash` |
| f(tilde(x)^n)=x_1 ^^ ldots ^^ x_n -> (x_1 oplus ldots oplus x_n) | |
| `f(tilde(x)^n)=x_1 ^^ ldots ^^ x_n -> (x_1 oplus ldots oplus x_n)` | |
Множества и подмножества
| emptyset | `emptyset` |
| in | `in` |
| notin | `notin` |
| subset | `subset` |
| subseteq | `subseteq` |
| supset | `supset` |
| supseteq | `supseteq` |
| cup | `cup` |
| uu | `uu` |
| nn | `nn` |
| oplus | `oplus` |
| times | `times` |
| otimes | `otimes` |
| setminus | `setminus` |
| dot(-) | `dot(-)` |
| -< | `-<` |
| prec | `prec` |
| preceq | `preceq` |
| >- | `>-` |
| succ | `succ` |
| succeq | `succeq` |
| {(B Delta C = X nn A),(X setminus C = A cap B),(C subseteq A nn B):} => {(X = B),(B subseteq A),(C = emptyset):} | |
| `{(B Delta C = X nn A),(X setminus C = A cap B),(C subseteq A nn B):} => {(X = B),(B subseteq A),(C = emptyset):}` | |
Операторы с пределами (один или оба предела могут и не быть)
| lim_(x -> a) f(x) | `lim_(x -> a) f(x)` |
| sum_(k=1)^(n) f(k) | `sum_(k=1)^(n) f(k)` |
| prod_(k=1)^n k | `prod_(k=1)^n k` |
| bigcup_(i=1)^n A_i | `bigcup_(i=1)^n A_i` |
| uuu_(i=1)^n A_i | `uuu_(i=1)^n A_i` |
| bigcap_(i=1)^n A_i | `bigcap_(i=1)^n A_i` |
| nnn_(i=1)^n A_i | `nnn_(i=1)^n A_i` |
| bigvee_(i=1)^n x_i | `bigvee_(i=1)^n x_i` |
| vvv_(i=1)^n x_i | `vvv_(i=1)^n x_i` |
| bigwedge_(i=1)^n x_i | `bigwedge_(i=1)^n x_i` |
| ^^^_(i=1)^n x_i | `^^^_(i=1)^n x_i` |
| phi: 2^S to RR, quad psi: 2^S to RR,quad forall T subseteq S =>psi(T)=sum_(T subseteq Y subseteq S) phi(Y) <=> phi(T)=sum_(T subseteq Y subseteq S) (-1)^(|Y setminus T|) psi(Y) | |
| `phi: 2^S to RR, quad psi: 2^S to RR,quad forall T subseteq S =>psi(T)=sum_(T subseteq Y subseteq S) phi(Y) <=> phi(T)=sum_(T subseteq Y subseteq S) (-1)^(|Y setminus T|) psi(Y)` | |
Матрицы, определители, системы, совокупности и биномиальные коэффициенты
| ((1,2,3),(4,5,6),(7,8,9),(10,11,12)) | `((1,2,3),(4,5,6),(7,8,9),(10,11,12))` |
| [(1,2,3),(4,5,6),(7,8,9),(10,11,12)] | `[(1,2,3),(4,5,6),(7,8,9),(10,11,12)]` |
| ||(1,2,3),(4,5,6),(7,8,9),(10,11,12)|| | `||(1,2,3),(4,5,6),(7,8,9),(10,11,12)||` |
| |(1,2,3,4),(5,6,7,8),(9,10,11,12),(13,14,15,16)| | `|(1,2,3,4),(5,6,7,8),(9,10,11,12),(13,14,15,16)|` |
| {(x+y+z=1), (x+y+t=2), (x+z+t<3), (y+z+t<=4):} | `{(x+y+z=1), (x+y+t=2), (x+z+t<3), (y+z+t<=4):}` |
| [(x+y+z=1), (x+y+t=2), (x+z+t<3), (y+z+t<=4):} | `[(x+y+z=1), (x+y+t=2), (x+z+t<3), (y+z+t<=4):}` |
| ((n),(k)) | `((n),(k))` |
| C_n^k | `C_n^k` |
| {(a_(11)x_1+a_(12)x_2+cdots+a_(1n)x_n=b_1),(a_(21)x_1+a_(22)x_2+cdots+a_(2n)x_n=b_2),(ldots),(a_(m1)x_1+a_(m2)x_2+cdots+a_(mn)x_n=b_m):} <=> ((a_(11),a_(12),ldots,a_(1n)),(a_(21),a_(22),ldots,a_(2n)),(vdots,vdots,ddots,vdots),(a_(m1),a_(m2),ldots,a_(mn)))*((x_1),(x_2),(vdots),(x_n))=((b_1),(b_2),(vdots),(b_m)) | |
| `{(a_(11)x_1+a_(12)x_2+cdots+a_(1n)x_n=b_1),(a_(21)x_1+a_(22)x_2+cdots+a_(2n)x_n=b_2),(ldots),(a_(m1)x_1+a_(m2)x_2+cdots+a_(mn)x_n=b_m):} <=> ((a_(11),a_(12),ldots,a_(1n)),(a_(21),a_(22),ldots,a_(2n)),(vdots,vdots,ddots,vdots),(a_(m1),a_(m2),ldots,a_(mn)))*((x_1),(x_2),(vdots),(x_n))=((b_1),(b_2),(vdots),(b_m))` | |
Замечание к системам: в качестве элемента системы/совокупности может быть другая система/совокупность, например:
| {({(x^2+2x>0),(x^2+2x <3):}),([(x^2-4 <0),(x^2+6x>=0):}):} | `{({(x^2+2x>0),(x^2+2x < 3):}),([(x^2-4 < 0),(x^2+6x>=0):}):}` |
