<<< native [ EArray [ AlignCenter , AlignCenter ] [ [ [ EText TextNormal "Bernoulli Trials" ] , [ EGrouped [ EGrouped [ EIdentifier "P" , ESymbol Open "(" , EIdentifier "E" , ESymbol Close ")" ] , ESymbol Rel "=" , EDelimited "(" ")" [ Right (EFraction NormalFrac (EIdentifier "n") (EIdentifier "k")) ] , ESubsup (EIdentifier "p") (EGrouped []) (EIdentifier "k") , ESubsup (EGrouped [ ESymbol Open "(" , ENumber "1" , ESymbol Bin "-" , EIdentifier "p" , ESymbol Close ")" ]) (EGrouped []) (EGrouped [ EIdentifier "n" , ESymbol Bin "-" , EIdentifier "k" ]) ] ] ] , [ [ EText TextNormal "Cauchy-Schwarz Inequality" ] , [ EGrouped [ ESubsup (EDelimited "(" ")" [ Right (EUnderover False (ESymbol Op "\8721") (EGrouped [ EIdentifier "k" , ESymbol Rel "=" , ENumber "1" ]) (EIdentifier "n")) , Right (ESubsup (EIdentifier "a") (EIdentifier "k") (EGrouped [])) , Right (ESubsup (EIdentifier "b") (EIdentifier "k") (EGrouped [])) ]) (EGrouped []) (ENumber "2") , ESymbol Rel "\8804" , EDelimited "(" ")" [ Right (EUnderover False (ESymbol Op "\8721") (EGrouped [ EIdentifier "k" , ESymbol Rel "=" , ENumber "1" ]) (EIdentifier "n")) , Right (ESubsup (EIdentifier "a") (EIdentifier "k") (ENumber "2")) ] , EDelimited "(" ")" [ Right (EUnderover False (ESymbol Op "\8721") (EGrouped [ EIdentifier "k" , ESymbol Rel "=" , ENumber "1" ]) (EIdentifier "n")) , Right (ESubsup (EIdentifier "b") (EIdentifier "k") (ENumber "2")) ] ] ] ] , [ [ EText TextNormal "Cauchy Formula" ] , [ EGrouped [ EIdentifier "f" , ESymbol Open "(" , EIdentifier "z" , ESymbol Close ")" , ESpace (1 % 6) , ESymbol Bin "\183" , ESubsup (EIdentifier "Ind") (EIdentifier "\947") (EGrouped []) , ESymbol Open "(" , EIdentifier "z" , ESymbol Close ")" , ESymbol Rel "=" , EFraction NormalFrac (ENumber "1") (EGrouped [ ENumber "2" , EIdentifier "\960" , EIdentifier "i" ]) , EUnderover False (ESymbol Op "\8750") (EIdentifier "\947") (EGrouped []) , EFraction NormalFrac (EGrouped [ EIdentifier "f" , ESymbol Open "(" , EIdentifier "\958" , ESymbol Close ")" ]) (EGrouped [ EIdentifier "\958" , ESymbol Bin "-" , EIdentifier "z" ]) , ESpace (1 % 6) , EIdentifier "d" , EIdentifier "\958" ] ] ] , [ [ EText TextNormal "Cross Product" ] , [ EGrouped [ ESubsup (EIdentifier "V") (ENumber "1") (EGrouped []) , ESymbol Bin "\215" , ESubsup (EIdentifier "V") (ENumber "2") (EGrouped []) , ESymbol Rel "=" , EDelimited "|" "|" [ Right (EArray [ AlignCenter , AlignCenter , AlignCenter ] [ [ [ EIdentifier "i" ] , [ EIdentifier "j" ] , [ EIdentifier "k" ] ] , [ [ EFraction NormalFrac (EGrouped [ ESymbol Ord "\8706" , EIdentifier "X" ]) (EGrouped [ ESymbol Ord "\8706" , EIdentifier "u" ]) ] , [ EFraction NormalFrac (EGrouped [ ESymbol Ord "\8706" , EIdentifier "Y" ]) (EGrouped [ ESymbol Ord "\8706" , EIdentifier "u" ]) ] , [ ENumber "0" ] ] , [ [ EFraction NormalFrac (EGrouped [ ESymbol Ord "\8706" , EIdentifier "X" ]) (EGrouped [ ESymbol Ord "\8706" , EIdentifier "v" ]) ] , [ EFraction NormalFrac (EGrouped [ ESymbol Ord "\8706" , EIdentifier "Y" ]) (EGrouped [ ESymbol Ord "\8706" , EIdentifier "v" ]) ] , [ ENumber "0" ] ] ]) ] ] ] ] , [ [ EText TextNormal "Vandermonde Determinant" ] , [ EGrouped [ EDelimited "|" "|" [ Right (EArray [ AlignCenter , AlignCenter , AlignCenter , AlignCenter ] [ [ [ ENumber "1" ] , [ ENumber "1" ] , [ ESymbol Ord "\8943" ] , [ ENumber "1" ] ] , [ [ ESubsup (EIdentifier "v") (ENumber "1") (EGrouped []) ] , [ ESubsup (EIdentifier "v") (ENumber "2") (EGrouped []) ] , [ ESymbol Ord "\8943" ] , [ ESubsup (EIdentifier "v") (EIdentifier "n") (EGrouped []) ] ] , [ [ ESubsup (EIdentifier "v") (ENumber "1") (ENumber "2") ] , [ ESubsup (EIdentifier "v") (ENumber "2") (ENumber "2") ] , [ ESymbol Ord "\8943" ] , [ ESubsup (EIdentifier "v") (EIdentifier "n") (ENumber "2") ] ] , [ [ ESymbol Rel "\8942" ] , [ ESymbol Rel "\8942" ] , [ ESymbol Rel "\8945" ] , [ ESymbol Rel "\8942" ] ] , [ [ ESubsup (EIdentifier "v") (ENumber "1") (EGrouped [ EIdentifier "n" , ESymbol Bin "-" , ENumber "1" ]) ] , [ ESubsup (EIdentifier "v") (ENumber "2") (EGrouped [ EIdentifier "n" , ESymbol Bin "-" , ENumber "1" ]) ] , [ ESymbol Ord "\8943" ] , [ ESubsup (EIdentifier "v") (EIdentifier "n") (EGrouped [ EIdentifier "n" , ESymbol Bin "-" , ENumber "1" ]) ] ] ]) ] , ESymbol Rel "=" , EUnderover False (ESymbol Op "\8719") (EGrouped [ ENumber "1" , ESymbol Rel "\8804" , EIdentifier "i" , ESymbol Rel "<" , EIdentifier "j" , ESymbol Rel "\8804" , EIdentifier "n" ]) (EGrouped []) , ESymbol Open "(" , ESubsup (EIdentifier "v") (EIdentifier "j") (EGrouped []) , ESymbol Bin "-" , ESubsup (EIdentifier "v") (EIdentifier "i") (EGrouped []) , ESymbol Close ")" ] ] ] , [ [ EText TextNormal "Lorenz Equations" ] , [ EArray [ AlignCenter , AlignCenter , AlignCenter ] [ [ [ EUnderover False (EIdentifier "x") (EGrouped []) (ESymbol Accent "\729") ] , [ ESymbol Rel "=" ] , [ EGrouped [ EIdentifier "\963" , ESymbol Open "(" , EIdentifier "y" , ESymbol Bin "-" , EIdentifier "x" , ESymbol Close ")" ] ] ] , [ [ EUnderover False (EIdentifier "y") (EGrouped []) (ESymbol Accent "\729") ] , [ ESymbol Rel "=" ] , [ EGrouped [ EIdentifier "\961" , EIdentifier "x" , ESymbol Bin "-" , EIdentifier "y" , ESymbol Bin "-" , EIdentifier "x" , EIdentifier "z" ] ] ] , [ [ EUnderover False (EIdentifier "z") (EGrouped []) (ESymbol Accent "\729") ] , [ ESymbol Rel "=" ] , [ EGrouped [ ESymbol Bin "-" , EIdentifier "\946" , EIdentifier "z" , ESymbol Bin "+" , EIdentifier "x" , EIdentifier "y" ] ] ] ] ] ] , [ [ EText TextNormal "Maxwell's Equations" ] , [ EDelimited "{" "" [ Right (EArray [ AlignCenter , AlignCenter , AlignCenter ] [ [ [ EGrouped [ ESymbol Ord "\8711" , ESpace (0 % 1) , ESymbol Bin "\215" , EUnderover False (EIdentifier "B") (EGrouped []) (ESymbol Accent "\8636") , ESymbol Bin "-" , ESpace (1 % 6) , EFraction NormalFrac (ENumber "1") (EIdentifier "c") , ESpace (1 % 6) , EFraction NormalFrac (EGrouped [ ESymbol Ord "\8706" , ESpace (0 % 1) , EUnderover False (EIdentifier "E") (EGrouped []) (ESymbol Accent "\8636") ]) (EGrouped [ ESymbol Ord "\8706" , ESpace (0 % 1) , EIdentifier "t" ]) ] ] , [ ESymbol Rel "=" ] , [ EGrouped [ EFraction NormalFrac (EGrouped [ ENumber "4" , EIdentifier "\960" ]) (EIdentifier "c") , ESpace (1 % 6) , EUnderover False (EIdentifier "j") (EGrouped []) (ESymbol Accent "\8636") ] ] ] , [ [ EGrouped [ ESymbol Ord "\8711" , ESpace (0 % 1) , ESymbol Bin "\183" , EUnderover False (EIdentifier "E") (EGrouped []) (ESymbol Accent "\8636") ] ] , [ ESymbol Rel "=" ] , [ EGrouped [ ENumber "4" , EIdentifier "\960" , EIdentifier "\961" ] ] ] , [ [ EGrouped [ ESymbol Ord "\8711" , ESpace (0 % 1) , ESymbol Bin "\215" , EUnderover False (EIdentifier "E") (EGrouped []) (ESymbol Accent "\8636") , ESpace (1 % 6) , ESymbol Bin "+" , ESpace (1 % 6) , EFraction NormalFrac (ENumber "1") (EIdentifier "c") , ESpace (1 % 6) , EFraction NormalFrac (EGrouped [ ESymbol Ord "\8706" , ESpace (0 % 1) , EUnderover False (EIdentifier "B") (EGrouped []) (ESymbol Accent "\8636") ]) (EGrouped [ ESymbol Ord "\8706" , ESpace (0 % 1) , EIdentifier "t" ]) ] ] , [ ESymbol Rel "=" ] , [ EUnderover False (ENumber "0") (EGrouped []) (ESymbol Accent "\8636") ] ] , [ [ EGrouped [ ESymbol Ord "\8711" , ESpace (0 % 1) , ESymbol Bin "\183" , EUnderover False (EIdentifier "B") (EGrouped []) (ESymbol Accent "\8636") ] ] , [ ESymbol Rel "=" ] , [ ENumber "0" ] ] ]) ] ] ] , [ [ EText TextNormal "Einstein Field Equations" ] , [ EGrouped [ ESubsup (EIdentifier "R") (EGrouped [ EIdentifier "\956" , EIdentifier "\957" ]) (EGrouped []) , ESymbol Bin "-" , EFraction NormalFrac (ENumber "1") (ENumber "2") , ESpace (1 % 6) , ESubsup (EIdentifier "g") (EGrouped [ EIdentifier "\956" , EIdentifier "\957" ]) (EGrouped []) , ESpace (1 % 6) , EIdentifier "R" , ESymbol Rel "=" , EFraction NormalFrac (EGrouped [ ENumber "8" , EIdentifier "\960" , EIdentifier "G" ]) (ESubsup (EIdentifier "c") (EGrouped []) (ENumber "4")) , ESpace (1 % 6) , ESubsup (EIdentifier "T") (EGrouped [ EIdentifier "\956" , EIdentifier "\957" ]) (EGrouped []) ] ] ] , [ [ EText TextNormal "Ramanujan Identity" ] , [ EGrouped [ EFraction NormalFrac (ENumber "1") (EGrouped [ ESymbol Open "(" , ESqrt (EGrouped [ EIdentifier "\966" , ESqrt (ENumber "5") ]) , ESymbol Bin "-" , EIdentifier "\966" , ESymbol Close ")" , ESubsup (EIdentifier "e") (EGrouped []) (EFraction NormalFrac (ENumber "25") (EIdentifier "\960")) ]) , ESymbol Rel "=" , ENumber "1" , ESymbol Bin "+" , EFraction NormalFrac (ESubsup (EIdentifier "e") (EGrouped []) (EGrouped [ ESymbol Bin "-" , ENumber "2" , EIdentifier "\960" ])) (EGrouped [ ENumber "1" , ESymbol Bin "+" , EFraction NormalFrac (ESubsup (EIdentifier "e") (EGrouped []) (EGrouped [ ESymbol Bin "-" , ENumber "4" , EIdentifier "\960" ])) (EGrouped [ ENumber "1" , ESymbol Bin "+" , EFraction NormalFrac (ESubsup (EIdentifier "e") (EGrouped []) (EGrouped [ ESymbol Bin "-" , ENumber "6" , EIdentifier "\960" ])) (EGrouped [ ENumber "1" , ESymbol Bin "+" , EFraction NormalFrac (ESubsup (EIdentifier "e") (EGrouped []) (EGrouped [ ESymbol Bin "-" , ENumber "8" , EIdentifier "\960" ])) (EGrouped [ ENumber "1" , ESymbol Bin "+" , ESymbol Ord "\8230" ]) ]) ]) ]) ] ] ] , [ [ EText TextNormal "Another Ramanujan identity" ] , [ EGrouped [ EUnderover False (ESymbol Op "\8721") (EGrouped [ EIdentifier "k" , ESymbol Rel "=" , ENumber "1" ]) (EIdentifier "\8734") , EFraction NormalFrac (ENumber "1") (ESubsup (ENumber "2") (EGrouped []) (EGrouped [ ESymbol Open "\8970" , EIdentifier "k" , ESymbol Bin "\183" , ESpace (0 % 1) , EIdentifier "\966" , ESymbol Close "\8971" ])) , ESymbol Rel "=" , EFraction NormalFrac (ENumber "1") (EGrouped [ ESubsup (ENumber "2") (EGrouped []) (ENumber "0") , ESymbol Bin "+" , EFraction NormalFrac (ENumber "1") (EGrouped [ ESubsup (ENumber "2") (EGrouped []) (ENumber "1") , ESymbol Bin "+" , ESymbol Ord "\8943" ]) ]) ] ] ] , [ [ EText TextNormal "Rogers-Ramanujan Identity" ] , [ EGrouped [ ENumber "1" , ESymbol Bin "+" , EGrouped [ EUnderover False (ESymbol Op "\8721") (EGrouped [ EIdentifier "k" , ESymbol Rel "=" , ENumber "1" ]) (EIdentifier "\8734") , EFraction NormalFrac (ESubsup (EIdentifier "q") (EGrouped []) (EGrouped [ ESubsup (EIdentifier "k") (EGrouped []) (ENumber "2") , ESymbol Bin "+" , EIdentifier "k" ])) (EGrouped [ ESymbol Open "(" , ENumber "1" , ESymbol Bin "-" , EIdentifier "q" , ESymbol Close ")" , ESymbol Open "(" , ENumber "1" , ESymbol Bin "-" , ESubsup (EIdentifier "q") (EGrouped []) (ENumber "2") , ESymbol Close ")" , ESymbol Ord "\8943" , ESymbol Open "(" , ENumber "1" , ESymbol Bin "-" , ESubsup (EIdentifier "q") (EGrouped []) (EIdentifier "k") , ESymbol Close ")" ]) ] , ESymbol Rel "=" , EGrouped [ EUnderover False (ESymbol Op "\8719") (EGrouped [ EIdentifier "j" , ESymbol Rel "=" , ENumber "0" ]) (EIdentifier "\8734") , EFraction NormalFrac (ENumber "1") (EGrouped [ ESymbol Open "(" , ENumber "1" , ESymbol Bin "-" , ESubsup (EIdentifier "q") (EGrouped []) (EGrouped [ ENumber "5" , EIdentifier "j" , ESymbol Bin "+" , ENumber "2" ]) , ESymbol Close ")" , ESymbol Open "(" , ENumber "1" , ESymbol Bin "-" , ESubsup (EIdentifier "q") (EGrouped []) (EGrouped [ ENumber "5" , EIdentifier "j" , ESymbol Bin "+" , ENumber "3" ]) , ESymbol Close ")" ]) ] , ESymbol Pun "," , EText TextNormal "\8287\8202" , EText TextNormal "\8287\8202" , EGrouped [ EIdentifier "f" , EIdentifier "o" , EIdentifier "r" ] , ESpace (2 % 9) , ESymbol Op "|" , EIdentifier "q" , ESymbol Op "|" , ESymbol Rel "<" , ENumber "1" , EIdentifier "." ] ] ] , [ [ EText TextNormal "Commutative Diagram" ] , [ EArray [ AlignCenter , AlignCenter , AlignCenter ] [ [ [ EIdentifier "H" ] , [ ESymbol Accent "\8592" ] , [ EIdentifier "K" ] ] , [ [ ESymbol Rel "\8595" ] , [ ESpace (0 % 1) ] , [ ESymbol Rel "\8593" ] ] , [ [ EIdentifier "H" ] , [ ESymbol Accent "\8594" ] , [ EIdentifier "K" ] ] ] ] ] ] ] >>> typst upright("Bernoulli Trials") & P paren.l E paren.r eq lr((n / k)) p_()^k paren.l 1 hyph.minus p paren.r_()^(n hyph.minus k)\ upright("Cauchy-Schwarz Inequality") & lr((sum_(k eq 1)^n a_k^() b_k^()))_()^2 lt.eq lr((sum_(k eq 1)^n a_k^2)) lr((sum_(k eq 1)^n b_k^2))\ upright("Cauchy Formula") & f paren.l z paren.r thin dot.c "Ind"_gamma^() paren.l z paren.r eq frac(1, 2 pi i) integral.cont_gamma^() frac(f paren.l xi paren.r, xi hyph.minus z) thin d xi\ upright("Cross Product") & V_1^() times V_2^() eq mat(delim: "|", i, j, k; frac(diff X, diff u), frac(diff Y, diff u), 0; frac(diff X, diff v), frac(diff Y, diff v), 0)\ upright("Vandermonde Determinant") & mat(delim: "|", 1, 1, dots.h.c, 1; v_1^(), v_2^(), dots.h.c, v_n^(); v_1^2, v_2^2, dots.h.c, v_n^2; dots.v, dots.v, dots.down, dots.v; v_1^(n hyph.minus 1), v_2^(n hyph.minus 1), dots.h.c, v_n^(n hyph.minus 1)) eq product_(1 lt.eq i lt j lt.eq n)^() paren.l v_j^() hyph.minus v_i^() paren.r\ upright("Lorenz Equations") & x^(˙)_() & eq & sigma paren.l y hyph.minus x paren.r\ y^(˙)_() & eq & rho x hyph.minus y hyph.minus x z\ z^(˙)_() & eq & hyph.minus beta z plus x y\ upright("Maxwell's Equations") & {nabla zws times B^harpoon.lt_() hyph.minus thin 1 / c thin frac(diff zws E^harpoon.lt_(), diff zws t) & eq & frac(4 pi, c) thin j^harpoon.lt_()\ nabla zws dot.c E^harpoon.lt_() & eq & 4 pi rho\ nabla zws times E^harpoon.lt_() thin plus thin 1 / c thin frac(diff zws B^harpoon.lt_(), diff zws t) & eq & 0^harpoon.lt_()\ nabla zws dot.c B^harpoon.lt_() & eq & 0\ upright("Einstein Field Equations") & R_(mu nu)^() hyph.minus 1 / 2 thin g_(mu nu)^() thin R eq frac(8 pi G, c_()^4) thin T_(mu nu)^()\ upright("Ramanujan Identity") & frac(1, paren.l sqrt(phi sqrt(5)) hyph.minus phi paren.r e_()^(25 / pi)) eq 1 plus frac(e_()^(hyph.minus 2 pi), 1 plus frac(e_()^(hyph.minus 4 pi), 1 plus frac(e_()^(hyph.minus 6 pi), 1 plus frac(e_()^(hyph.minus 8 pi), 1 plus dots.h))))\ upright("Another Ramanujan identity") & sum_(k eq 1)^oo 1 / 2_()^(⌊ k dot.c zws phi ⌋) eq frac(1, 2_()^0 plus frac(1, 2_()^1 plus dots.h.c))\ upright("Rogers-Ramanujan Identity") & 1 plus sum_(k eq 1)^oo frac(q_()^(k_()^2 plus k), paren.l 1 hyph.minus q paren.r paren.l 1 hyph.minus q_()^2 paren.r dots.h.c paren.l 1 hyph.minus q_()^k paren.r) eq product_(j eq 0)^oo frac(1, paren.l 1 hyph.minus q_()^(5 j plus 2) paren.r paren.l 1 hyph.minus q_()^(5 j plus 3) paren.r) comma upright("  ") upright("  ") f o r med bar.v q bar.v lt 1 dot.basic\ upright("Commutative Diagram") & H & arrow.l & K\ arrow.b & zws & arrow.t\ H & arrow.r & K