texmath 0.12.5.3 → 0.12.5.4

raw patch · 27 files changed

+212/−101 lines, 27 filesPVP ok

version bump matches the API change (PVP)

API changes (from Hackage documentation)

Files

• changelog +12/−0
• src/Text/TeXMath/Readers/OMML.hs +10/−11
• src/Text/TeXMath/Writers/Eqn.hs +3/−1
• src/Text/TeXMath/Writers/OMML.hs +2/−1
• src/Text/TeXMath/Writers/TeX.hs +8/−2
• test/regression/196.test +96/−0
• test/writer/eqn/01.test +1/−1
• test/writer/eqn/02.test +1/−1
• test/writer/eqn/02200_Mathematical_Operators.test +2/−2
• test/writer/eqn/04.test +1/−1
• test/writer/eqn/05.test +1/−1
• test/writer/eqn/11.test +1/−1
• test/writer/eqn/12.test +2/−2
• test/writer/eqn/13.test +1/−1
• test/writer/eqn/binomial_coefficient.test +1/−1
• test/writer/eqn/c.test +1/−1
• test/writer/eqn/complex1.test +2/−2
• test/writer/eqn/complex3.test +53/−53
• test/writer/eqn/href3.test +1/−1
• test/writer/eqn/m.test +1/−1
• test/writer/eqn/maction-05.test +1/−1
• test/writer/eqn/moore_determinant.test +2/−2
• test/writer/eqn/schwinger_dyson.test +1/−1
• test/writer/eqn/sophomores_dream.test +1/−1
• test/writer/eqn/sphere_volume.test +1/−1
• test/writer/omml/subsup.test +5/−10
• texmath.cabal +1/−1

@@ -1,3 +1,15 @@+texmath (0.12.5.4)++  * OMML reader: fix treatment of `eqArr` (#196).+    This change also includes a change to the TeX writer: any array+    with an alternating sequence of R,L alignments will be rendered+    as an aligned environment (not just a single [R,L] as currently).++  * OOML Writer: Add low line char ("_") to `isBarChar` (#193, Hagb).+    Closes jgm/pandoc#8152.++  * Eqn writer: use `-` for minus, `cdots` for cdots (#200).+ texmath (0.12.5.3)    * Eqn writer: avoid empty `{}` (#198).

@@ -42,6 +42,7 @@ import Text.TeXMath.Shared (fixTree, getSpaceWidth, getOperator) import Text.TeXMath.Unicode.ToTeX (getSymbolType) import Text.TeXMath.Unicode.Fonts (getUnicode, textToFont)+import Data.List.Split (splitWhen)  readOMML :: T.Text -> Either T.Text [Exp] readOMML s | Just e <- parseXMLDoc s =@@ -127,15 +128,11 @@ elemToBases _ = Nothing  --- TODO: The right way to do this is to use the ampersand to break the--- text lines into multiple columns. That's tricky, though, and this--- will get us most of the way for the time being.-filterAmpersand :: Exp -> Exp-filterAmpersand (EIdentifier s)   = EIdentifier (T.filter ('&' /=) s)-filterAmpersand (EText tt s)      = EText tt (T.filter ('&' /=) s)-filterAmpersand (EStyled tt exps) = EStyled tt (map filterAmpersand exps)-filterAmpersand (EGrouped exps)   = EGrouped (map filterAmpersand exps)-filterAmpersand e                    = e+breakOnAmpersand :: [Exp] -> [[Exp]]+breakOnAmpersand = splitWhen isAmpersand+ where+  isAmpersand (ESymbol _ "&") = True+  isAmpersand _ = False  elemToOMathRunTextStyle :: Element -> OMathRunTextStyle elemToOMathRunTextStyle element@@ -294,9 +291,11 @@    Just [EDelimited beg end exps] elemToExps' element | isElem "m" "eqArr" element =   let expLst = mapMaybe elemToBases (elChildren element)-      expLst' = map (\es -> [map filterAmpersand es]) expLst+      expLst' = map breakOnAmpersand expLst+      cols = maximum (map length expLst')+      colspecs = take cols $ cycle [AlignRight , AlignLeft]   in-   return [EArray [] expLst']+   return [EArray colspecs expLst'] elemToExps' element | isElem "m" "f" element = do   num <- filterChildName (hasElemName "m" "num") element   den <- filterChildName (hasElemName "m" "den") element

@@ -37,7 +37,7 @@ -- packages (amsmath and amssymb) writeEqn :: DisplayType -> [Exp] -> T.Text writeEqn dt exprs =-  T.intercalate " " $ map writeExp $ everywhere (mkT $ S.handleDownup dt) exprs+  T.unwords $ map writeExp $ everywhere (mkT $ S.handleDownup dt) exprs  -- like writeExp but inserts {} if contents contain a space writeExp' :: Exp -> T.Text@@ -77,6 +77,8 @@   case s of     "{"     -> "\\[lC]"     "}"     -> "\\[rC]"+    "\8722" -> "-"  -- minus sign, see #200+    "\8943" -> "cdots" -- centered ellipses, see #200     "\8805" -> ">="     "\8804" -> "<="     "\8801" -> "=="

@@ -297,7 +297,8 @@  isBarChar :: Char -> Bool isBarChar c = c == '\x203E' || c == '\x00AF' ||-              c == '\x0304' || c == '\x0333'+              c == '\x0304' || c == '\x0333' ||+              c == '_'  -- | Checks whether an expression marks the start of an nary operator -- expression. These are different integrals, sums, products, and

@@ -276,16 +276,22 @@   txtcmd <- (flip S.getLaTeXTextCommand ttype) <$> asks mathEnv   tell [ControlSeq txtcmd]   tellGroup (mapM_ writeExp $ everywhere (mkT (fromUnicode ttype)) es)-writeExp (EArray [AlignRight, AlignLeft] rows) = do+writeExp (EArray as rows)+  | isRLSequence as = do   env <- asks mathEnv   if "amsmath" `elem` env      then table "aligned" [] rows-     else table "array" [AlignRight, AlignLeft] rows+     else table "array" as rows writeExp (EArray aligns rows) = do   env <- asks mathEnv   if "amsmath" `elem` env && all (== AlignCenter) aligns      then table "matrix" [] rows      else table "array" aligns rows++isRLSequence :: [Alignment] -> Bool+isRLSequence [AlignRight, AlignLeft] = True+isRLSequence (AlignRight : AlignLeft : as) = isRLSequence as+isRLSequence _ = False  table :: T.Text -> [Alignment] -> [ArrayLine] -> Math () table name aligns rows = do

@@ -0,0 +1,96 @@+<<< omml+<m:oMathPara>+  <m:oMath>+    <m:r>+      <w:rPr>+        <w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"+        w:cs="Times New Roman" />+      </w:rPr>+      <m:t>f</m:t>+    </m:r>+    <m:d>+      <m:dPr>+        <m:ctrlPr>+          <w:rPr>+            <w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"+            w:cs="Times New Roman" />+            <w:i />+          </w:rPr>+        </m:ctrlPr>+      </m:dPr>+      <m:e>+        <m:r>+          <w:rPr>+            <w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"+            w:cs="Times New Roman" />+          </w:rPr>+          <m:t>x</m:t>+        </m:r>+      </m:e>+    </m:d>+    <m:r>+      <w:rPr>+        <w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"+        w:cs="Times New Roman" />+      </w:rPr>+      <m:t>=</m:t>+    </m:r>+    <m:d>+      <m:dPr>+        <m:begChr m:val="{" />+        <m:endChr m:val="" />+        <m:ctrlPr>+          <w:rPr>+            <w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"+            w:cs="Times New Roman" />+            <w:i />+          </w:rPr>+        </m:ctrlPr>+      </m:dPr>+      <m:e>+        <m:eqArr>+          <m:eqArrPr>+            <m:ctrlPr>+              <w:rPr>+                <w:rFonts w:ascii="Cambria Math"+                w:hAnsi="Cambria Math" w:cs="Times New Roman" />+                <w:i />+              </w:rPr>+            </m:ctrlPr>+          </m:eqArrPr>+          <m:e>+            <m:r>+              <w:rPr>+                <w:rFonts w:ascii="Cambria Math"+                w:hAnsi="Cambria Math" w:cs="Times New Roman" />+              </w:rPr>+              <m:t>x&amp;=1 &amp; y&amp;=2</m:t>+            </m:r>+            <m:ctrlPr>+              <w:rPr>+                <w:rFonts w:ascii="Cambria Math"+                w:eastAsia="Cambria Math" w:hAnsi="Cambria Math"+                w:cs="Cambria Math" />+                <w:i />+              </w:rPr>+            </m:ctrlPr>+          </m:e>+          <m:e>+            <m:r>+              <w:rPr>+                <w:rFonts w:ascii="Cambria Math"+                w:hAnsi="Cambria Math" w:cs="Times New Roman" />+              </w:rPr>+              <m:t>xxx&amp;=111 &amp; yyy&amp;=222</m:t>+            </m:r>+          </m:e>+        </m:eqArr>+      </m:e>+    </m:d>+  </m:oMath>+</m:oMathPara>+>>> tex+f(x) = \left\{ \begin{aligned}+x & = 1\  & \ y & = 2 \\+xxx & = 111\  & \ yyy & = 222 \\+\end{aligned} \right.\ 

@@ -19,4 +19,4 @@     (EGrouped [ ENumber "2" , EIdentifier "a" ]) ] >>> eqn-x = {\[u2212] b +- sqrt {b sup 2 \[u2212] 4 a c}} over {2 a}+x = {- b +- sqrt {b sup 2 - 4 a c}} over {2 a}

@@ -22,4 +22,4 @@     ] ] >>> eqn-2 = left ( {left ( 3 \[u2212] x right ) times 2} over {3 \[u2212] x} right )+2 = left ( {left ( 3 - x right ) times 2} over {3 - x} right )

@@ -330,7 +330,7 @@ matrix{ ccol{ {""} above {roman "0"} above {roman "1"} above {roman "2"} above {roman "3"} above {roman "4"} above {roman "5"} above {roman "6"} above {roman "7"} above {roman "8"} above {roman "9"} above {roman "A"} above {roman "B"} above {roman "C"} above {roman "D"} above {roman "E"} above {roman "F"} } ccol{ {roman "220"} above \[u2200] above \[u2201] above partial above \[u2203] above \[u2204] above \[u2205] above \[u2206] above grad above \[u2208] above \[u2209] above \[u220A] above \[u220B] above \[u220C] above \[u220D] above \[u220E] above prod }-ccol{ {roman "221"} above \[u2210] above sum above \[u2212] above \[u2213] above \[u2214] above \[u2215] above \[u2216] above \[u2217] above \[u2218] above \[u2219] above \[u221A] above \[u221B] above \[u221C] above \[u221D] above inf above \[u221F] }+ccol{ {roman "221"} above \[u2210] above sum above - above \[u2213] above \[u2214] above \[u2215] above \[u2216] above \[u2217] above \[u2218] above \[u2219] above \[u221A] above \[u221B] above \[u221C] above \[u221D] above inf above \[u221F] } ccol{ {roman "222"} above \[u2220] above \[u2221] above \[u2222] above \[u2223] above \[u2224] above \[u2225] above \[u2226] above \[u2227] above \[u2228] above \[u2229] above \[u222A] above int above \[u222C] above \[u222D] above \[u222E] above \[u222F] } ccol{ {roman "223"} above \[u2230] above \[u2231] above \[u2232] above \[u2233] above \[u2234] above \[u2235] above \[u2236] above \[u2237] above \[u2238] above \[u2239] above \[u223A] above \[u223B] above \[u223C] above \[u223D] above \[u223E] above \[u223F] } ccol{ {roman "224"} above \[u2240] above \[u2241] above \[u2242] above \[u2243] above \[u2244] above \[u2245] above \[u2246] above \[u2247] above approx above \[u2249] above \[u224A] above \[u224B] above \[u224C] above \[u224D] above \[u224E] above \[u224F] }@@ -343,6 +343,6 @@ ccol{ {roman "22B"} above \[u22B0] above \[u22B1] above \[u22B2] above \[u22B3] above \[u22B4] above \[u22B5] above \[u22B6] above \[u22B7] above \[u22B8] above \[u22B9] above \[u22BA] above \[u22BB] above \[u22BC] above \[u22BD] above \[u22BE] above \[u22BF] } ccol{ {roman "22C"} above \[u22C0] above \[u22C1] above union above inter above \[u22C4] above \[u22C5] above \[u22C6] above \[u22C7] above \[u22C8] above \[u22C9] above \[u22CA] above \[u22CB] above \[u22CC] above \[u22CD] above \[u22CE] above \[u22CF] } ccol{ {roman "22D"} above \[u22D0] above \[u22D1] above \[u22D2] above \[u22D3] above \[u22D4] above \[u22D5] above \[u22D6] above \[u22D7] above \[u22D8] above \[u22D9] above \[u22DA] above \[u22DB] above \[u22DC] above \[u22DD] above \[u22DE] above \[u22DF] }-ccol{ {roman "22E"} above \[u22E0] above \[u22E1] above \[u22E2] above \[u22E3] above \[u22E4] above \[u22E5] above \[u22E6] above \[u22E7] above \[u22E8] above \[u22E9] above \[u22EA] above \[u22EB] above \[u22EC] above \[u22ED] above \[u22EE] above \[u22EF] }+ccol{ {roman "22E"} above \[u22E0] above \[u22E1] above \[u22E2] above \[u22E3] above \[u22E4] above \[u22E5] above \[u22E6] above \[u22E7] above \[u22E8] above \[u22E9] above \[u22EA] above \[u22EB] above \[u22EC] above \[u22ED] above \[u22EE] above cdots } ccol{ {roman "22F"} above \[u22F0] above \[u22F1] above \[u22F2] above \[u22F3] above \[u22F4] above \[u22F5] above \[u22F6] above \[u22F7] above \[u22F8] above \[u22F9] above \[u22FA] above \[u22FB] above \[u22FC] above \[u22FD] above \[u22FE] above \[u22FF] } }

@@ -17,4 +17,4 @@     (ENumber "2") ] >>> eqn-S sub {roman "new"} = S sub {roman "old"} \[u2212] {{left ( 5 \[u2212] T right )} sup 2} over 2+S sub {roman "new"} = S sub {roman "old"} - {{left ( 5 - T right )} sup 2} over 2

@@ -28,4 +28,4 @@ , EIdentifier "y" ] >>> eqn-int sub a sup x back 16 back 16 back 16 int sub a sup s f left ( y right ) ^ d y ^ d s = int sub a sup x f left ( y right ) left ( x \[u2212] y right ) ^ d y+int sub a sup x back 16 back 16 back 16 int sub a sup s f left ( y right ) ^ d y ^ d s = int sub a sup x f left ( y right ) left ( x - y right ) ^ d y

@@ -23,4 +23,4 @@     NormalFrac (ENumber "1") (ESub (EIdentifier "l") (ENumber "0")) ] >>> eqn-phi sub n left ( kappa right ) = 0.033 C sub n sup 2 kappa sup {\[u2212] 11 / 3} , fwd 100 1 over {L sub 0} << kappa << 1 over {l sub 0}+phi sub n left ( kappa right ) = 0.033 C sub n sup 2 kappa sup {- 11 / 3} , fwd 100 1 over {L sub 0} << kappa << 1 over {l sub 0}

@@ -31,6 +31,6 @@ ] >>> eqn f left ( x right ) = left { matrix{-lcol{ 1 above {1 over 2} above {1 \[u2212] x sup 2} }-lcol{ {\[u2212] 1 <= x < 0} above {x = 0} above {roman "otherwise"} }+lcol{ 1 above {1 over 2} above {1 - x sup 2} }+lcol{ {- 1 <= x < 0} above {x = 0} above {roman "otherwise"} } } right ""

@@ -54,4 +54,4 @@     (EGrouped [ EIdentifier "n" , ESymbol Ord "!" ]) ] >>> eqn-{""} sub p F sub q left ( a sub 1 , ... , a sub p ; c sub 1 , ... , c sub q ; z right ) = sum from {n = 0} to inf {{left ( a sub 1 right )} sub n \[u22EF] {left ( a sub p right )} sub n} over {{left ( c sub 1 right )} sub n \[u22EF] {left ( c sub q right )} sub n} {z sup n} over {n !}+{""} sub p F sub q left ( a sub 1 , ... , a sub p ; c sub 1 , ... , c sub q ; z right ) = sum from {n = 0} to inf {{left ( a sub 1 right )} sub n cdots {left ( a sub p right )} sub n} over {{left ( c sub 1 right )} sub n cdots {left ( c sub q right )} sub n} {z sup n} over {n !}

@@ -40,4 +40,4 @@        ]) ] >>> eqn-bold {C} left ( n , k right ) = {bold {C}} sub k sup n = {""} sub n {bold {C}} sub k = left ( n / k right ) = {n !} over {k ! ^ left ( n \[u2212] k right ) !}+bold {C} left ( n , k right ) = {bold {C}} sub k sup n = {""} sub n {bold {C}} sub k = left ( n / k right ) = {n !} over {k ! ^ left ( n - k right ) !}

@@ -151,5 +151,5 @@ >>> eqn matrix{ ccol{ {roman "cacute"} above {roman "Cacute"} above {roman "cap"} above {roman "Cap"} above {roman "capand"} above {roman "capbrcup"} above {roman "capcap"} above {roman "capcup"} above {roman "capdot"} above {roman "CapitalDifferentialD"} above {roman "caps"} above {roman "caret"} above {roman "caron"} above {roman "Cayleys"} above {roman "ccaps"} above {roman "ccaron"} above {roman "Ccaron"} above {roman "ccedil"} above {roman "Ccedil"} above {roman "ccirc"} above {roman "Ccirc"} above {roman "Cconint"} above {roman "ccups"} above {roman "ccupssm"} above {roman "cdot"} above {roman "Cdot"} above {roman "cedil"} above {roman "Cedilla"} above {roman "cemptyv"} above {roman "cent"} above {roman "centerdot"} above {roman "CenterDot"} above {roman "cfr"} above {roman "Cfr"} above {roman "chcy"} above {roman "CHcy"} above {roman "check"} above {roman "checkmark"} above {roman "chi"} above {roman "cir"} above {roman "circ"} above {roman "circeq"} above {roman "circlearrowleft"} above {roman "circlearrowright"} above {roman "circledast"} above {roman "circledcirc"} above {roman "circleddash"} above {roman "CircleDot"} above {roman "circledR"} above {roman "circledS"} above {roman "CircleMinus"} above {roman "CirclePlus"} above {roman "CircleTimes"} above {roman "cire"} above {roman "cirE"} above {roman "cirfnint"} above {roman "cirmid"} above {roman "cirscir"} above {roman "ClockwiseContourIntegral"} above {roman "CloseCurlyDoubleQuote"} above {roman "CloseCurlyQuote"} above {roman "clubs"} above {roman "clubsuit"} above {roman "colon"} above {roman "Colon"} above {roman "colone"} above {roman "Colone"} above {roman "coloneq"} above {roman "comma"} above {roman "commat"} above {roman "comp"} above {roman "compfn"} above {roman "complement"} above {roman "complexes"} above {roman "cong"} above {roman "congdot"} above {roman "Congruent"} above {roman "conint"} above {roman "Conint"} above {roman "ContourIntegral"} above {roman "copf"} above {roman "Copf"} above {roman "coprod"} above {roman "Coproduct"} above {roman "copy"} above {roman "copysr"} above {roman "CounterClockwiseContourIntegral"} above {roman "cross"} above {roman "Cross"} above {roman "cscr"} above {roman "Cscr"} above {roman "csub"} above {roman "csube"} above {roman "csup"} above {roman "csupe"} above {roman "ctdot"} above {roman "cudarrl"} above {roman "cudarrr"} above {roman "cuepr"} above {roman "cuesc"} above {roman "cularr"} above {roman "cularrp"} above {roman "cup"} above {roman "Cup"} above {roman "cupbrcap"} above {roman "cupcap"} above {roman "CupCap"} above {roman "cupcup"} above {roman "cupdot"} above {roman "cupor"} above {roman "cups"} above {roman "curarr"} above {roman "curarrm"} above {roman "curlyeqprec"} above {roman "curlyeqsucc"} above {roman "curlyvee"} above {roman "curlywedge"} above {roman "curren"} above {roman "curvearrowleft"} above {roman "curvearrowright"} above {roman "cuvee"} above {roman "cuwed"} above {roman "cwconint"} above {roman "cwint"} above {roman "cylcty"} }-ccol{ \[u0107] above \[u0106] above \[u2229] above \[u22D2] above \[u2A44] above \[u2A49] above \[u2A4B] above \[u2A47] above \[u2A40] above \[u2145] above "∩︀" above \[u2041] above \[u02C7] above \[u212D] above \[u2A4D] above \[u010D] above \[u010C] above \[u00E7] above \[u00C7] above \[u0109] above \[u0108] above \[u2230] above \[u2A4C] above \[u2A50] above \[u010B] above \[u010A] above \[u00B8] above \[u00B8] above \[u29B2] above \[u00A2] above cdot above cdot above \[u1D520] above \[u212D] above \[u0447] above \[u0427] above \[u2713] above \[u2713] above chi above \[u25CB] above \[u02C6] above \[u2257] above \[u21BA] above \[u21BB] above \[u229B] above \[u229A] above \[u229D] above \[u2299] above \[u00AE] above \[u24C8] above \[u2296] above \[u2295] above \[u2297] above \[u2257] above \[u29C3] above \[u2A10] above \[u2AEF] above \[u29C2] above \[u2232] above \[u201D] above \[u2019] above \[u2663] above \[u2663] above : above \[u2237] above \[u2254] above \[u2A74] above \[u2254] above , above @ above \[u2201] above \[u2218] above \[u2201] above \[u2102] above \[u2245] above \[u2A6D] above == above \[u222E] above \[u222F] above \[u222E] above \[u1D554] above \[u2102] above \[u2210] above \[u2210] above \[u00A9] above \[u2117] above \[u2233] above \[u2717] above \[u2A2F] above \[u1D4B8] above \[u1D49E] above \[u2ACF] above \[u2AD1] above \[u2AD0] above \[u2AD2] above \[u22EF] above \[u2938] above \[u2935] above \[u22DE] above \[u22DF] above \[u21B6] above \[u293D] above \[u222A] above \[u22D3] above \[u2A48] above \[u2A46] above \[u224D] above \[u2A4A] above \[u228D] above \[u2A45] above "∪︀" above \[u21B7] above \[u293C] above \[u22DE] above \[u22DF] above \[u22CE] above \[u22CF] above \[u00A4] above \[u21B6] above \[u21B7] above \[u22CE] above \[u22CF] above \[u2232] above \[u2231] above \[u232D] }+ccol{ \[u0107] above \[u0106] above \[u2229] above \[u22D2] above \[u2A44] above \[u2A49] above \[u2A4B] above \[u2A47] above \[u2A40] above \[u2145] above "∩︀" above \[u2041] above \[u02C7] above \[u212D] above \[u2A4D] above \[u010D] above \[u010C] above \[u00E7] above \[u00C7] above \[u0109] above \[u0108] above \[u2230] above \[u2A4C] above \[u2A50] above \[u010B] above \[u010A] above \[u00B8] above \[u00B8] above \[u29B2] above \[u00A2] above cdot above cdot above \[u1D520] above \[u212D] above \[u0447] above \[u0427] above \[u2713] above \[u2713] above chi above \[u25CB] above \[u02C6] above \[u2257] above \[u21BA] above \[u21BB] above \[u229B] above \[u229A] above \[u229D] above \[u2299] above \[u00AE] above \[u24C8] above \[u2296] above \[u2295] above \[u2297] above \[u2257] above \[u29C3] above \[u2A10] above \[u2AEF] above \[u29C2] above \[u2232] above \[u201D] above \[u2019] above \[u2663] above \[u2663] above : above \[u2237] above \[u2254] above \[u2A74] above \[u2254] above , above @ above \[u2201] above \[u2218] above \[u2201] above \[u2102] above \[u2245] above \[u2A6D] above == above \[u222E] above \[u222F] above \[u222E] above \[u1D554] above \[u2102] above \[u2210] above \[u2210] above \[u00A9] above \[u2117] above \[u2233] above \[u2717] above \[u2A2F] above \[u1D4B8] above \[u1D49E] above \[u2ACF] above \[u2AD1] above \[u2AD0] above \[u2AD2] above cdots above \[u2938] above \[u2935] above \[u22DE] above \[u22DF] above \[u21B6] above \[u293D] above \[u222A] above \[u22D3] above \[u2A48] above \[u2A46] above \[u224D] above \[u2A4A] above \[u228D] above \[u2A45] above "∪︀" above \[u21B7] above \[u293C] above \[u22DE] above \[u22DF] above \[u22CE] above \[u22CF] above \[u00A4] above \[u21B6] above \[u21B7] above \[u22CE] above \[u22CF] above \[u2232] above \[u2231] above \[u232D] } }

@@ -610,7 +610,7 @@ } right |} above {left | matrix{ ccol{ 1 above {v sub 1 sup {""}} above {v sub 1 sup 2} above \[u22EE] above {v sub 1 sup {n - 1}} } ccol{ 1 above {v sub 2 sup {""}} above {v sub 2 sup 2} above \[u22EE] above {v sub 2 sup {n - 1}} }-ccol{ \[u22EF] above \[u22EF] above \[u22EF] above \[u22F1] above \[u22EF] }+ccol{ cdots above cdots above cdots above \[u22F1] above cdots } ccol{ 1 above {v sub n sup {""}} above {v sub n sup 2} above \[u22EE] above {v sub n sup {n - 1}} } } right | = prod from {1 <= i < j <= n} to {""} ( v sub j sup {""} - v sub i sup {""} )} above {matrix{ ccol{ {{x from {""}} to \[u02D9]} above {{y from {""}} to \[u02D9]} above {{z from {""}} to \[u02D9]} }@@ -620,7 +620,7 @@ ccol{ {grad fwd 0 times {B from {""}} to \[u21BC] - ^ 1 over c ^ {partial fwd 0 {E from {""}} to \[u21BC]} over {partial fwd 0 t}} above {grad fwd 0 cdot {E from {""}} to \[u21BC]} above {grad fwd 0 times {E from {""}} to \[u21BC] ^ + ^ 1 over c ^ {partial fwd 0 {B from {""}} to \[u21BC]} over {partial fwd 0 t}} above {grad fwd 0 cdot {B from {""}} to \[u21BC]} } ccol{ = above = above = above = } ccol{ {{4 pi} over c ^ {j from {""}} to \[u21BC]} above {4 pi rho} above {{0 from {""}} to \[u21BC]} above 0 }-} right ""} above {R sub {mu nu} sup {""} - 1 over 2 ^ g sub {mu nu} sup {""} ^ R = {8 pi G} over {c sub {""} sup 4} ^ T sub {mu nu} sup {""}} above {1 over {( sqrt {varphi sqrt 5} - varphi ) e sub {""} sup {25 over pi}} = 1 + {e sub {""} sup {- 2 pi}} over {1 + {e sub {""} sup {- 4 pi}} over {1 + {e sub {""} sup {- 6 pi}} over {1 + {e sub {""} sup {- 8 pi}} over {1 + ...}}}}} above {sum from {k = 1} to inf 1 over {2 sub {""} sup {\[u230A] k cdot fwd 0 varphi \[u230B]}} = 1 over {2 sub {""} sup 0 + 1 over {2 sub {""} sup 1 + \[u22EF]}}} above {1 + {sum from {k = 1} to inf {q sub {""} sup {k sub {""} sup 2 + k}} over {( 1 - q ) ( 1 - q sub {""} sup 2 ) \[u22EF] ( 1 - q sub {""} sup k )}} = {prod from {j = 0} to inf 1 over {( 1 - q sub {""} sup {5 j + 2} ) ( 1 - q sub {""} sup {5 j + 3} )}} , roman "  " roman "  " {f o r} ~ | q | < 1 .} above {matrix{+} right ""} above {R sub {mu nu} sup {""} - 1 over 2 ^ g sub {mu nu} sup {""} ^ R = {8 pi G} over {c sub {""} sup 4} ^ T sub {mu nu} sup {""}} above {1 over {( sqrt {varphi sqrt 5} - varphi ) e sub {""} sup {25 over pi}} = 1 + {e sub {""} sup {- 2 pi}} over {1 + {e sub {""} sup {- 4 pi}} over {1 + {e sub {""} sup {- 6 pi}} over {1 + {e sub {""} sup {- 8 pi}} over {1 + ...}}}}} above {sum from {k = 1} to inf 1 over {2 sub {""} sup {\[u230A] k cdot fwd 0 varphi \[u230B]}} = 1 over {2 sub {""} sup 0 + 1 over {2 sub {""} sup 1 + cdots}}} above {1 + {sum from {k = 1} to inf {q sub {""} sup {k sub {""} sup 2 + k}} over {( 1 - q ) ( 1 - q sub {""} sup 2 ) cdots ( 1 - q sub {""} sup k )}} = {prod from {j = 0} to inf 1 over {( 1 - q sub {""} sup {5 j + 2} ) ( 1 - q sub {""} sup {5 j + 3} )}} , roman "  " roman "  " {f o r} ~ | q | < 1 .} above {matrix{ ccol{ H above \[u2193] above H } ccol{ <- above {fwd 0} above -> } ccol{ K above \[u2191] above K }

@@ -7684,14 +7684,14 @@ ] >>> eqn matrix{-ccol{ {2  {sum {a  b}}} above {x sup {prime 3}} above {{{f sup prime  {( x )}} + {sin  cos  theta}} = 1} above {{{f  {( z )}} = {sum from {n = 0} to inf {a sub n  z sup n}}} roman ", " {{left | z right | < R} \[u200B] {( {R != 0} )}}} above {left ∫ {""} sub C {left ( {sum from {n = 0} to inf {a sub n  z sup n}} right )  {\[u2146] z}} right "" = {sum from {n = 0} to inf {a sub n  left ∫ {""} sub C {z sup n  {\[u2146] z}} right ""}}} above {{lim from {n -> inf} left | left ∫ {""} sub C {left [ {{f  {( z )}} \[u2212] {sum from {k = 0} to n {a sub k  z sup k}}} right ]  {\[u2146] z}} right "" right |} = 0} above {left "" {n >= {N  {( \[u03B5] )}}} "⇒" {left | {{f  {( z )}} \[u2212] {sum from {k = 0} to n {a sub k  z sup k}}} right | < \[u03B5]} right ""} above {{10 roman " Bq"} + {10 roman " Ci"}} above {{10 roman " amol"} + {10 roman " Emol"} \[u2212] {10 roman " fmol"} + {10 roman " Gmol"} \[u2212] {10 roman " kmol"} + {10 roman " Mmol"}} above {{10 roman " μmol"} + {10 roman " mmol"} \[u2212] {10 roman " mol"} + {10 roman " nmol"} \[u2212] {10 roman " Pmol"} + {10 roman " pmol"} \[u2212] {10 roman " Tmol"}} above {{10 roman " acre"} + {10 roman " hectare"} \[u2212] {10 {roman " ft"} sup 2} + {10 {roman " in"} sup 2} \[u2212] {10 {roman " m"} sup 2}} above {{10 roman " A"} + {10 roman " kA"} \[u2212] {10 roman " μA"} + {10 roman " mA"} \[u2212] {10 roman " nA"}} above {{10 roman " F"} + {10 roman " μF"} \[u2212] {10 roman " mF"} + {10 roman " nF"} \[u2212] {10 roman " pF"}} above {{10 roman " C"} + {1.0 roman " m/s/s"} \[u2212] {0.1 {roman " m" / {roman "s"} sup 2}}} above {{10 roman " kS"} + {10 roman " μS"} \[u2212] {10 roman " mS"} + {10 roman " S"}} above {{10 roman " kV"} + {10 roman " MV"} \[u2212] {10 roman " μV"} + {10 roman " mV"} \[u2212] {10 roman " nV"} + {10 roman " pV"} \[u2212] {10 roman " V"}} above {{10 roman " GΩ"} + {10 roman " kΩ"} \[u2212] {10 roman " MΩ"} + {10 roman " mΩ"} \[u2212] {10 roman " Ω"}} above {{10 roman " Btu"} + {10 roman " cal"} \[u2212] {10 roman " eV"} + {10 roman " erg"} \[u2212] {10 roman " GeV"} + {10 roman " GJ"}} above {{10 roman " J"} + {10 roman " kcal"} \[u2212] {10 roman " kJ"} + {10 roman " MeV"} \[u2212] {10 roman " MJ"} + {10 roman " μJ"} \[u2212] {10 roman " mJ"} + {10 roman " nJ"}} above {{10 roman " dyn"} + {10 roman " kN"} \[u2212] {10 roman " MN"} + {10 roman " μN"} \[u2212] {10 roman " mN"} + {10 roman " N"} \[u2212] {10 roman " ozf"} + {10 roman " lbf"}} above {{10 roman " EHz"} + {10 roman " GHz"} \[u2212] {10 roman " Hz"} + {10 roman " kHz"} \[u2212] {10 roman " MHz"} + {10 roman " PHz"} \[u2212] {10 roman " THz"}} above {{10 roman " fc"} + {10 roman " lx"} \[u2212] {10 roman " phot"}} above {{10 roman " Å"} + {10 roman " am"} \[u2212] {10 roman " cm"} + {10 roman " dm"} \[u2212] {10 roman " fm"} + {10 roman " ft"} \[u2212] {10 roman " in"}} above {{10 roman " km"} + {10 roman " m"} \[u2212] {10 roman " μm"} + {10 roman " mi"} \[u2212] {10 roman " mm"} + {10 roman " nm"} \[u2212] {10 roman " pm"}} above {10 roman " sb"} above {10 roman " lm"} above {10 roman " cd"} above {{10 roman " Mx"} + {10 roman " μWb"} \[u2212] {10 roman " mWb"} + {10 roman " nWb"} \[u2212] {10 roman " Wb"}} above {{10 roman " G"} + {10 roman " μT"} \[u2212] {10 roman " mT"} + {10 roman " nT"} \[u2212] {10 roman " pT"} + {10 roman " T"}} above {{10 roman " H"} + {10 roman " μH"} \[u2212] {10 roman " mH"}} above {{10 roman " u"} + {10 roman " cg"} \[u2212] {10 roman " dg"} + {10 roman " g"} \[u2212] {10 roman " kg"} + {10 roman " μg"} \[u2212] {10 roman " mg"} + {10 roman " lb"} \[u2212] {10 roman " slug"}} above {{10 roman " °"} + {10 roman " μrad"} \[u2212] {10 roman " mrad"} + {10 {fwd 0} sup {roman "′"}} \[u2212] {10 roman " rad"} + {10 {fwd 0} sup {roman "′′"}}} above {{10 roman " GW"} + {10 roman " hp"} \[u2212] {10 roman " kW"} + {10 roman " MW"} \[u2212] {10 roman " μW"} + {10 roman " mW"} \[u2212] {10 roman " nW"} + {10 roman " W"}} above {{10 roman " atm"} + {10 roman " bar"} \[u2212] {10 roman " kbar"} + {10 roman " kPa"} \[u2212] {10 roman " MPa"} + {10 roman " μPa"} \[u2212] {10 roman " mbar"} + {10 roman " mmHg"} \[u2212] {10 roman " Pa"} + {10 roman " torr"}} above {10 roman " sr"} above {{10 roman " °C"} + {10 roman " °F"} \[u2212] {10 roman " K"}} above {{10 roman " as"} + {10 roman " d"} \[u2212] {10 roman " fs"} + {10 roman " h"} \[u2212] {10 roman " μs"} + {10 roman " ms"} \[u2212] {10 roman " min"} + {10 roman " ns"} \[u2212] {10 roman " ps"} + {10 roman " s"} \[u2212] {10 roman " y"}} above {{10 {roman " ft"} sup 3} + {10 {roman " in"} sup 3} \[u2212] {10 {roman " m"} sup 3} + {10 roman " gal"} \[u2212] {10 roman " l"}} above {{10 roman " ml"} + {10 roman " pint"} \[u2212] {10 roman " qt"}} above {1 over {x  left ( y right )} = {left ( {{\[u2212] {int {e sup {{\[u2212] 1 over 2}  y sup 2}  {sin  y}  {\[u2146] y}}}} + C sub 1} right )  e sup {1 over 2  y sup 2}}} above {{{\[u2145] sub x y} \[u2212] y} = {sin  x}} above {left ( 1 over 2 right )  left ( 1 over 2 right )  left ( 1 over 2 right )} above {left [ 1 over 2 right ]  left ( 1 over 2 right )  left { 1 over 2 right }} above {left 〈 1 over 2 right 〉  left ⌊ 1 over 2 right ⌋  left ⌈ 1 over 2 right ⌉} above {left "" "↑" 1 over 2 "↑" right ""  left "" "↓" 1 over 2 "↓" right ""  left "" "↕" 1 over 2 "↕" right ""} above {1 over 2  1 over 2  1 over 2} above {1 over 2  1 over 2  1 over 2} above {1 over 2  1 over 2  1 over 2} above {{\[u2212] {( {a \[u2212] b} )}} = {b \[u2212] a}} above {{2 over 5 + 3 over 7} = {{2 \[u22C5] 7} + {3 \[u22C5] 5}} over 35 = 29 over 35} above {left | a right | = left { matrix{-ccol{ a above {\[u2212] a} }+ccol{ {2  {sum {a  b}}} above {x sup {prime 3}} above {{{f sup prime  {( x )}} + {sin  cos  theta}} = 1} above {{{f  {( z )}} = {sum from {n = 0} to inf {a sub n  z sup n}}} roman ", " {{left | z right | < R} \[u200B] {( {R != 0} )}}} above {left ∫ {""} sub C {left ( {sum from {n = 0} to inf {a sub n  z sup n}} right )  {\[u2146] z}} right "" = {sum from {n = 0} to inf {a sub n  left ∫ {""} sub C {z sup n  {\[u2146] z}} right ""}}} above {{lim from {n -> inf} left | left ∫ {""} sub C {left [ {{f  {( z )}} - {sum from {k = 0} to n {a sub k  z sup k}}} right ]  {\[u2146] z}} right "" right |} = 0} above {left "" {n >= {N  {( \[u03B5] )}}} "⇒" {left | {{f  {( z )}} - {sum from {k = 0} to n {a sub k  z sup k}}} right | < \[u03B5]} right ""} above {{10 roman " Bq"} + {10 roman " Ci"}} above {{10 roman " amol"} + {10 roman " Emol"} - {10 roman " fmol"} + {10 roman " Gmol"} - {10 roman " kmol"} + {10 roman " Mmol"}} above {{10 roman " μmol"} + {10 roman " mmol"} - {10 roman " mol"} + {10 roman " nmol"} - {10 roman " Pmol"} + {10 roman " pmol"} - {10 roman " Tmol"}} above {{10 roman " acre"} + {10 roman " hectare"} - {10 {roman " ft"} sup 2} + {10 {roman " in"} sup 2} - {10 {roman " m"} sup 2}} above {{10 roman " A"} + {10 roman " kA"} - {10 roman " μA"} + {10 roman " mA"} - {10 roman " nA"}} above {{10 roman " F"} + {10 roman " μF"} - {10 roman " mF"} + {10 roman " nF"} - {10 roman " pF"}} above {{10 roman " C"} + {1.0 roman " m/s/s"} - {0.1 {roman " m" / {roman "s"} sup 2}}} above {{10 roman " kS"} + {10 roman " μS"} - {10 roman " mS"} + {10 roman " S"}} above {{10 roman " kV"} + {10 roman " MV"} - {10 roman " μV"} + {10 roman " mV"} - {10 roman " nV"} + {10 roman " pV"} - {10 roman " V"}} above {{10 roman " GΩ"} + {10 roman " kΩ"} - {10 roman " MΩ"} + {10 roman " mΩ"} - {10 roman " Ω"}} above {{10 roman " Btu"} + {10 roman " cal"} - {10 roman " eV"} + {10 roman " erg"} - {10 roman " GeV"} + {10 roman " GJ"}} above {{10 roman " J"} + {10 roman " kcal"} - {10 roman " kJ"} + {10 roman " MeV"} - {10 roman " MJ"} + {10 roman " μJ"} - {10 roman " mJ"} + {10 roman " nJ"}} above {{10 roman " dyn"} + {10 roman " kN"} - {10 roman " MN"} + {10 roman " μN"} - {10 roman " mN"} + {10 roman " N"} - {10 roman " ozf"} + {10 roman " lbf"}} above {{10 roman " EHz"} + {10 roman " GHz"} - {10 roman " Hz"} + {10 roman " kHz"} - {10 roman " MHz"} + {10 roman " PHz"} - {10 roman " THz"}} above {{10 roman " fc"} + {10 roman " lx"} - {10 roman " phot"}} above {{10 roman " Å"} + {10 roman " am"} - {10 roman " cm"} + {10 roman " dm"} - {10 roman " fm"} + {10 roman " ft"} - {10 roman " in"}} above {{10 roman " km"} + {10 roman " m"} - {10 roman " μm"} + {10 roman " mi"} - {10 roman " mm"} + {10 roman " nm"} - {10 roman " pm"}} above {10 roman " sb"} above {10 roman " lm"} above {10 roman " cd"} above {{10 roman " Mx"} + {10 roman " μWb"} - {10 roman " mWb"} + {10 roman " nWb"} - {10 roman " Wb"}} above {{10 roman " G"} + {10 roman " μT"} - {10 roman " mT"} + {10 roman " nT"} - {10 roman " pT"} + {10 roman " T"}} above {{10 roman " H"} + {10 roman " μH"} - {10 roman " mH"}} above {{10 roman " u"} + {10 roman " cg"} - {10 roman " dg"} + {10 roman " g"} - {10 roman " kg"} + {10 roman " μg"} - {10 roman " mg"} + {10 roman " lb"} - {10 roman " slug"}} above {{10 roman " °"} + {10 roman " μrad"} - {10 roman " mrad"} + {10 {fwd 0} sup {roman "′"}} - {10 roman " rad"} + {10 {fwd 0} sup {roman "′′"}}} above {{10 roman " GW"} + {10 roman " hp"} - {10 roman " kW"} + {10 roman " MW"} - {10 roman " μW"} + {10 roman " mW"} - {10 roman " nW"} + {10 roman " W"}} above {{10 roman " atm"} + {10 roman " bar"} - {10 roman " kbar"} + {10 roman " kPa"} - {10 roman " MPa"} + {10 roman " μPa"} - {10 roman " mbar"} + {10 roman " mmHg"} - {10 roman " Pa"} + {10 roman " torr"}} above {10 roman " sr"} above {{10 roman " °C"} + {10 roman " °F"} - {10 roman " K"}} above {{10 roman " as"} + {10 roman " d"} - {10 roman " fs"} + {10 roman " h"} - {10 roman " μs"} + {10 roman " ms"} - {10 roman " min"} + {10 roman " ns"} - {10 roman " ps"} + {10 roman " s"} - {10 roman " y"}} above {{10 {roman " ft"} sup 3} + {10 {roman " in"} sup 3} - {10 {roman " m"} sup 3} + {10 roman " gal"} - {10 roman " l"}} above {{10 roman " ml"} + {10 roman " pint"} - {10 roman " qt"}} above {1 over {x  left ( y right )} = {left ( {{- {int {e sup {{- 1 over 2}  y sup 2}  {sin  y}  {\[u2146] y}}}} + C sub 1} right )  e sup {1 over 2  y sup 2}}} above {{{\[u2145] sub x y} - y} = {sin  x}} above {left ( 1 over 2 right )  left ( 1 over 2 right )  left ( 1 over 2 right )} above {left [ 1 over 2 right ]  left ( 1 over 2 right )  left { 1 over 2 right }} above {left 〈 1 over 2 right 〉  left ⌊ 1 over 2 right ⌋  left ⌈ 1 over 2 right ⌉} above {left "" "↑" 1 over 2 "↑" right ""  left "" "↓" 1 over 2 "↓" right ""  left "" "↕" 1 over 2 "↕" right ""} above {1 over 2  1 over 2  1 over 2} above {1 over 2  1 over 2  1 over 2} above {1 over 2  1 over 2  1 over 2} above {{- {( {a - b} )}} = {b - a}} above {{2 over 5 + 3 over 7} = {{2 \[u22C5] 7} + {3 \[u22C5] 5}} over 35 = 29 over 35} above {left | a right | = left { matrix{+ccol{ a above {- a} } ccol{ {roman "if"} above {roman "if"} } ccol{ {a >= 0} above {a < 0} }-} right ""} above {a sup n = {{a \[u22C5] a \[u22C5] \[u22EF] \[u22C5] a} from \[uFE38]} from {n roman " factors"}} above {{left ( a over b right )} sup {\[u2212] n} = {left ( b over a right )} sup n} above {{"" sup n sqrt a = b} roman "  means " {b sup n = a} roman "."} above {"" sup 4 sqrt {16 over 81} = {"" sup 4 sqrt 16} over {"" sup 4 sqrt 81} = 2 over 3} above {left { {x \[u2223] {{x != 0} , {x != 1}}} right }} above {{a sub n  x sup n} + {a sub {n \[u2212] 1}  x sup {n \[u2212] 1}} + \[u22EF] + {a sub 1  x} + a sub 0} above {{a sup 3 \[u2212] b sup 3} = {left ( {a \[u2212] b} right )  left ( {a sup 2 + {a  b} + b sup 2} right )}} above {{( {x + y} )} sup 2} above {H = left { {{left ( matrix{+} right ""} above {a sup n = {{a \[u22C5] a \[u22C5] cdots \[u22C5] a} from \[uFE38]} from {n roman " factors"}} above {{left ( a over b right )} sup {- n} = {left ( b over a right )} sup n} above {{"" sup n sqrt a = b} roman "  means " {b sup n = a} roman "."} above {"" sup 4 sqrt {16 over 81} = {"" sup 4 sqrt 16} over {"" sup 4 sqrt 81} = 2 over 3} above {left { {x \[u2223] {{x != 0} , {x != 1}}} right }} above {{a sub n  x sup n} + {a sub {n - 1}  x sup {n - 1}} + cdots + {a sub 1  x} + a sub 0} above {{a sup 3 - b sup 3} = {left ( {a - b} right )  left ( {a sup 2 + {a  b} + b sup 2} right )}} above {{( {x + y} )} sup 2} above {H = left { {{left ( matrix{ ccol{ a above c } ccol{ b above d }-} right ) \[u2208] G} \[u2223] {{{a  d} \[u2212] {b  c}} = 1}} right }} above {{{| x |} + {|| y ||} + {\[lC] z \[rC]} \[u2212] {[ {a  c} ]} + {( b )}} = {[ {a , b} ]}} above {x = 1} above {x = 1} above {x = 1} above {x = 1} above {left [ {{\[u2212] 10 over 3} , {\[u2212] 7 over 3}} right ) \[u222A] left ( {{\[u2212] 7 over 3} , {\[u2212] 4 over 3}} right ]} above {{{A  {partial u} over {partial x}} + {B  {partial u} over {partial y}} + {C  u}} = E} above {sum from {fwd 0} to {fwd 0} x} above {sum from {matrix{+} right ) \[u2208] G} \[u2223] {{{a  d} - {b  c}} = 1}} right }} above {{{| x |} + {|| y ||} + {\[lC] z \[rC]} - {[ {a  c} ]} + {( b )}} = {[ {a , b} ]}} above {x = 1} above {x = 1} above {x = 1} above {x = 1} above {left [ {{- 10 over 3} , {- 7 over 3}} right ) \[u222A] left ( {{- 7 over 3} , {- 4 over 3}} right ]} above {{{A  {partial u} over {partial x}} + {B  {partial u} over {partial y}} + {C  u}} = E} above {sum from {fwd 0} to {fwd 0} x} above {sum from {matrix{ ccol{ {1 < i < 10} above {1 < j < 10} } }} to {fwd 0} 2 sup {i + j}} above {GAMMA sub {1 sub {^ sup {matrix{ ccol{ {2 sub {^ sup {matrix{@@ -7705,20 +7705,20 @@ }}} above {2 sup {matrix{ ccol{ 4 above 3 } }}} }-}}}} above {{y  left ( x right )} = {{x  e sup x} \[u2212] e sup x + 2} over {e sup x} = {x \[u2212] 1 + 2 over {e sup x}}} above {matrix{-rcol{ {{{\[u2145] sub {x \[u200B] x} y} \[u2212] y} = 0} above {{y  {( 0 )}} = 1} above {{y sup prime  left ( 0 right )} = 0} }-}} above {{y  left ( x right )} = {{1 over 3  e sup {{\[u2212] "" sup 3 sqrt {( {\[u2212] 1} )}}  x}} + {2 over 3  e sup {1 over 2  "" sup 3 sqrt {( {\[u2212] 1} )}  x}  {cos  {1 over 2  sqrt 3  "" sup 3 sqrt {left ( {\[u2212] 1} right )}  x}}}}} above {{y  left ( t right )} = {2  {tan  left ( {{2  t} \[u2212] {1 over 4  pi}} right )}}} above {{\[u2131]  left ( {matrix{-ccol{ {e sup {2  pi  i  x}} above {2  pi  {Dirac  left ( {x \[u2212] {2  pi}} right )}} }+}}}} above {{y  left ( x right )} = {{x  e sup x} - e sup x + 2} over {e sup x} = {x - 1 + 2 over {e sup x}}} above {matrix{+rcol{ {{{\[u2145] sub {x \[u200B] x} y} - y} = 0} above {{y  {( 0 )}} = 1} above {{y sup prime  left ( 0 right )} = 0} }+}} above {{y  left ( x right )} = {{1 over 3  e sup {{- "" sup 3 sqrt {( {- 1} )}}  x}} + {2 over 3  e sup {1 over 2  "" sup 3 sqrt {( {- 1} )}  x}  {cos  {1 over 2  sqrt 3  "" sup 3 sqrt {left ( {- 1} right )}  x}}}}} above {{y  left ( t right )} = {2  {tan  left ( {{2  t} - {1 over 4  pi}} right )}}} above {{\[u2131]  left ( {matrix{+ccol{ {e sup {2  pi  i  x}} above {2  pi  {Dirac  left ( {x - {2  pi}} right )}} } } , x , s} right )} = left ( matrix{-ccol{ {2  pi  {Dirac  left ( {s \[u2212] {2  pi}} right )}} above {2  pi  e sup {{\[u2212] 2}  i  pi  s}} }+ccol{ {2  pi  {Dirac  left ( {s - {2  pi}} right )}} above {2  pi  e sup {{- 2}  i  pi  s}} } } right )} above {matrix{ ccol{ {x = 1} above {{x + 3} = 123} } }} above {matrix{ ccol{ t above 0 above .1 above .2 above .3 above .4 above .5 above .6 above .7 above .8 above .9 above 1.0 } ccol{ x above 1.0000 above 1.1158 above 1.2668 above 1.4582 above 1.6953 above 1.9830 above 2.3256 above 2.7265 above 3.1873 above 3.7077 above 4.2842 }-ccol{ y above 1.0000 above 1.0938 above 1.1695 above 1.2173 above 1.2253 above 1.1791 above 1.0619 above .8542 above .5344 above .0777 above {\[u2212] .5424} }-ccol{ z above 1.0000 above .8842 above .7332 above .5418 above .3047 above .0170 above {\[u2212] .3256} above {\[u2212] .7265} above {\[u2212] 1.1873} above {\[u2212] 1.7077} above {\[u2212] 2.2842} }-}} above {{K sub v  {( z )}} = {BesselK sub v  left ( z right )}} above {{{z sup 2  {\[u2146] sup 2 w} over {\[u2146] z sup 2}} + {z  {\[u2146] w} over {\[u2146] z}} \[u2212] {left ( {z sup 2 + v sup 2} right )  w}} = 0} above {{{partial sup 2 {u  {( {x , y} )}}} over {partial x sup 2} \[u2212] {partial sup 2 {u  {( {x , y} )}}} over {partial y sup 2}} = 0} above {{y  left ( {t , x} right )} = {{F sub 1  left ( {{\[u2212] x} \[u2212] {a  t}} right )} + {F sub 2  left ( {x \[u2212] {a  t}} right )}}} above {matrix{+ccol{ y above 1.0000 above 1.0938 above 1.1695 above 1.2173 above 1.2253 above 1.1791 above 1.0619 above .8542 above .5344 above .0777 above {- .5424} }+ccol{ z above 1.0000 above .8842 above .7332 above .5418 above .3047 above .0170 above {- .3256} above {- .7265} above {- 1.1873} above {- 1.7077} above {- 2.2842} }+}} above {{K sub v  {( z )}} = {BesselK sub v  left ( z right )}} above {{{z sup 2  {\[u2146] sup 2 w} over {\[u2146] z sup 2}} + {z  {\[u2146] w} over {\[u2146] z}} - {left ( {z sup 2 + v sup 2} right )  w}} = 0} above {{{partial sup 2 {u  {( {x , y} )}}} over {partial x sup 2} - {partial sup 2 {u  {( {x , y} )}}} over {partial y sup 2}} = 0} above {{y  left ( {t , x} right )} = {{F sub 1  left ( {{- x} - {a  t}} right )} + {F sub 2  left ( {x - {a  t}} right )}}} above {matrix{ ccol{ 1 above 4 } ccol{ 2 above 5 } ccol{ 3 above 6 }@@ -7727,46 +7727,46 @@ }} above {matrix{ ccol{ {a  b} above {c  d} above {e  f} } }} above {matrix{-ccol{ {{x + {2  y} \[u2212] 3} = 5} above {{{4  x} \[u2212] y \[u2212] 5} = 98} }+ccol{ {{x + {2  y} - 3} = 5} above {{{4  x} - y - 5} = 98} } }} above {matrix{ ccol{ {x = z} above {1 = 3} } }} above {matrix{-ccol{ {{A sub 1 = {{N sub 0  {( {lambda ; OMEGA sup prime} )}} \[u2212] {varphi  {( {lambda ; OMEGA sup prime} )}}}} roman ","} above {{A sub 2 = {{varphi  {( {lambda ; OMEGA sup prime} )}} \[u2212] {varphi  {( {lambda ; OMEGA} )}}}} roman ","} above {{A sub 3 = {{N}  {( {lambda ; omega} )}}} roman "."} }+ccol{ {{A sub 1 = {{N sub 0  {( {lambda ; OMEGA sup prime} )}} - {varphi  {( {lambda ; OMEGA sup prime} )}}}} roman ","} above {{A sub 2 = {{varphi  {( {lambda ; OMEGA sup prime} )}} - {varphi  {( {lambda ; OMEGA} )}}}} roman ","} above {{A sub 3 = {{N}  {( {lambda ; omega} )}}} roman "."} } }} above {matrix{ ccol{ {sin  theta} above {cos  gamma} } }} above {x = left { matrix{-lcol{ x above {\[u2212] x} }+lcol{ x above {- x} } lcol{ {roman "if " {x < 0}} above {roman "if " {x >= 0}} } } right ""} above {matrix{ ccol{ {L  M  R  M} above {L  M  R  M} } }} above {matrix{ ccol{ {M  A  T  H} above {M  A  T  H} } }} above {roman "⋮"} above {{"∇×" F} = 0} above {"∇·" F} above {{"∇·∇" F} = {{grad sup 2 F} + 7} = A} above {{"∇×" {( {{x  y} , {y  z} , {z  x}} )}} = left [ matrix{-ccol{ {\[u2212] y} above {\[u2212] z} above {\[u2212] x} }-} right ]} above {{"∇×" {( {y , z , x} )}} = left ( {{\[u2212] 1} , {\[u2212] 1} , {\[u2212] 1}} right ) != 0} above {{x + y + alpha} = 102} above {{bold {a} + bold {b}} = bold {c}} above {x + 1} above {{x + {f  {( bold {x} )}} \[u2212] 1} = 123} above {{italic {T}  italic {h}  italic {e}  italic {q}  italic {u}  italic {i}  italic {c}  italic {k}  b  r  o  w  n  f  o  x  j  u  m  p  s  bold {o}  bold {v}  bold {e}  bold {r}  t  h  e  {l}  {a}  {z}  {y}  {d}  {o}  {g}} roman "." {T  h  e  e  n  d} roman "."} above {left ( {{{partial f} over {partial x sub 1}  left ( {c sub 1 , c sub 2 , ... , c sub n} right )} , {{partial f} over {partial x sub 2}  left ( {c sub 1 , c sub 2 , ... , c sub n} right )} , ... , {{partial f} over {partial x sub {n \[u200B] 1}}  left ( {c sub 1 , c sub 2 , ... , c sub n} right )}} right )} above {{grad left ( {{c  u  v} + {v sup 2  w}} right )} = left ( {{u  v} , {c  v} , {{c  u} + {2  v  w}} , v sup 2} right )} above {matrix{+ccol{ {- y} above {- z} above {- x} }+} right ]} above {{"∇×" {( {y , z , x} )}} = left ( {{- 1} , {- 1} , {- 1}} right ) != 0} above {{x + y + alpha} = 102} above {{bold {a} + bold {b}} = bold {c}} above {x + 1} above {{x + {f  {( bold {x} )}} - 1} = 123} above {{italic {T}  italic {h}  italic {e}  italic {q}  italic {u}  italic {i}  italic {c}  italic {k}  b  r  o  w  n  f  o  x  j  u  m  p  s  bold {o}  bold {v}  bold {e}  bold {r}  t  h  e  {l}  {a}  {z}  {y}  {d}  {o}  {g}} roman "." {T  h  e  e  n  d} roman "."} above {left ( {{{partial f} over {partial x sub 1}  left ( {c sub 1 , c sub 2 , ... , c sub n} right )} , {{partial f} over {partial x sub 2}  left ( {c sub 1 , c sub 2 , ... , c sub n} right )} , ... , {{partial f} over {partial x sub {n \[u200B] 1}}  left ( {c sub 1 , c sub 2 , ... , c sub n} right )}} right )} above {{grad left ( {{c  u  v} + {v sup 2  w}} right )} = left ( {{u  v} , {c  v} , {{c  u} + {2  v  w}} , v sup 2} right )} above {matrix{ ccol{ {{D sub u  {f  left ( {a , b , c} right )}} = {{grad {f  left ( {a , b , c} right )}} \[u22C5] bold {u}}} above {= {{{{partial f} over {partial x}  left ( {a , b , c} right )}  u sub 1} + {{{partial f} over {partial y}  left ( {a , b , c} right )}  u sub 2} + {{{partial f} over {partial z}  left ( {a , b , c} right )}  u sub 3}}} }-}} above {{theta \[u2208] left { {pi + {2  X sub 3  pi} \[u2212] left ( {"arccos"  {1 over 7  sqrt 14}} right )} "|" {X sub 3 \[u2208] \[u2124]} right }} , {theta \[u2208] left { {{2  X sub 4  pi} \[u2212] pi + left ( {"arccos"  {1 over 7  sqrt 14}} right )} "|" {X sub 4 \[u2208] \[u2124]} right }}} above {P = {A  {left ( {A sup T  A} right )} sup {\[u2212] 1}  A sup T}} above {{"det" left ( matrix{+}} above {{theta \[u2208] left { {pi + {2  X sub 3  pi} - left ( {"arccos"  {1 over 7  sqrt 14}} right )} "|" {X sub 3 \[u2208] \[u2124]} right }} , {theta \[u2208] left { {{2  X sub 4  pi} - pi + left ( {"arccos"  {1 over 7  sqrt 14}} right )} "|" {X sub 4 \[u2208] \[u2124]} right }}} above {P = {A  {left ( {A sup T  A} right )} sup {- 1}  A sup T}} above {{"det" left ( matrix{ ccol{ x above a above a } ccol{ y above b above d } ccol{ 1 above 1 above 1 }-} right )} = {{x  b} \[u2212] {x  d} + {a  d} \[u2212] {a  b}} = 0} above {{{A  left ( theta right )}  {A  left ( {\[u2212] theta} right )}} = {left [ matrix{+} right )} = {{x  b} - {x  d} + {a  d} - {a  b}} = 0} above {{{A  left ( theta right )}  {A  left ( {- theta} right )}} = {left [ matrix{ ccol{ {cos  theta} above {sin  theta} }-ccol{ {\[u2212] {sin  theta}} above {cos  theta} }+ccol{ {- {sin  theta}} above {cos  theta} } } right ]  left [ matrix{-ccol{ {cos  theta} above {\[u2212] {sin  theta}} }+ccol{ {cos  theta} above {- {sin  theta}} } ccol{ {sin  theta} above {cos  theta} } } right ]}} above {{J  {( A )}} = left [ matrix{ ccol{ {J sub {n sub 1}  left ( lambda sub 1 right )} above 0 above {roman "⋮"} above 0 } ccol{ 0 above {J sub {n sub 2}  left ( lambda sub 2 right )} above {roman "⋮"} above 0 }-ccol{ \[u22EF] above \[u22EF] above {roman "⋱"} above \[u22EF] }+ccol{ cdots above cdots above {roman "⋱"} above cdots } ccol{ 0 above 0 above {roman "⋮"} above {J sub {n sub k}  left ( lambda sub k right )} } } right ]} above {{"det" left ( matrix{-ccol{ {{\[u2212] 4} + X} above 0 above 0 }-ccol{ {\[u2212] 1} above {{\[u2212] 4} + X} above 0 }-ccol{ 0 above 0 above {{\[u2212] 4} + X} }-} right )} = {left ( {X \[u2212] 4} right )} sup 3} above {left "" left { left ( matrix{-ccol{ {{\[u2212] 1 over 2} \[u2212] {1 over 6  sqrt 33}} above 1 }-} right ) right } "↔" {5 over 2 \[u2212] {1 over 2  sqrt 33}} right ""} above {left "" "∥" A "∥" right "" = {max from {x != 0} {left "" "∥" {A  x} "∥" right ""} over {left "" "∥" x "∥" right ""}}} above {{left ( matrix{+ccol{ {{- 4} + X} above 0 above 0 }+ccol{ {- 1} above {{- 4} + X} above 0 }+ccol{ 0 above 0 above {{- 4} + X} }+} right )} = {left ( {X - 4} right )} sup 3} above {left "" left { left ( matrix{+ccol{ {{- 1 over 2} - {1 over 6  sqrt 33}} above 1 }+} right ) right } "↔" {5 over 2 - {1 over 2  sqrt 33}} right ""} above {left "" "∥" A "∥" right "" = {max from {x != 0} {left "" "∥" {A  x} "∥" right ""} over {left "" "∥" x "∥" right ""}}} above {{left ( matrix{ ccol{ {a sub {1 \[u200B] 1}} above {a sub {2 \[u200B] 1}} } ccol{ {a sub {1 \[u200B] 2}} above {a sub {2 \[u200B] 2}} } } right ) + left ( matrix{@@ -7781,19 +7781,19 @@ } right ] right )} = {{left [ matrix{ ccol{ 1 above 4 } ccol{ 2 above 3 }-} right ]} sup 2 \[u2212] {5  left [ matrix{+} right ]} sup 2 - {5  left [ matrix{ ccol{ 1 above 4 } ccol{ 2 above 3 }-} right ]} \[u2212] 2} = left [ matrix{-ccol{ 2 above {\[u2212] 4} }-ccol{ {\[u2212] 2} above 0 }-} right ]} above {x = {lim from {x = 1} {sum from 1 to 2 a}}} above {{int sub a sup b {{f  {( x )}}  {\[u2146] x}}} = {lim from {{\[u2225] P \[u2225]} -> 0} {sum from {i = 1} to n {{f  left ( {x to \[u00AF]} sub i right )}  {DELTA x sub i}}}}} above {{int sub a sup b {{f  {( x )}}  {\[u2146] x}}} = {lim from {n -> inf} {{b \[u2212] a} over n  {sum from {i = 1} to n {f  left ( {a + {i  {b \[u2212] a} over n}} right )}}}}} above {{int sub 0 sup 2 {x sup 5  sqrt {x sup 3 + 1}  {\[u2146] x}}} = {int sub 1 sup 3 {2 over 3  u  {sqrt {left ( u sup 2 right )}} over {{left ( {u sup 2 \[u2212] 1} right )} sup {2 over 3}}  left ( {{u sup 2  {left ( {u sup 2 \[u2212] 1} right )} sup {2 over 3}} \[u2212] {left ( {u sup 2 \[u2212] 1} right )} sup {2 over 3}} right )  {\[u2146] u}}}} above {left ∫ {{f  {( {g  {( x )}} )}}  {g sup prime  {( x )}}  {\[u2146] x}} right "" = left ∫ {{f  {( u )}}  {\[u2146] u}} right ""} above {x = {2  {sum from {n = 1} to 100 {n  {( {n \[u2212] 1} )}}}}} above {{lim from {x -> 0} {sin  left ( 1 over x right )}} = {{\[u2212] 1} .. 1}} above {{h  {( {i , j} )}} = {{{( {2 \[u2212] j} )}  {g  {( i )}}} + {{( {j \[u2212] 1} )}  {f  {( {g  {( i )}} )}}}}} above {\[u25B3] : left "" left [ {0 , 1} right ] "→" left [ {0 , 1} right ] right ""} above {{0 \[u25BD] x} = x} above {{x \[u25B3] y} = {h sup {\[u2212] 1}  left ( {{h  left ( x right )}  {h  left ( y right )}} right )}} above {{x \[u25B3] y} = {f sup {\[u2212] 1}  left ( {max left { {{{f  left ( x right )} + {f  left ( y right )} \[u2212] 1} , 0} right }} right )}} above {{x \[u25BD] y} = {eta  left ( {{eta  left ( x right )} \[u25B3] {eta  left ( y right )}} right )}} above {{x  {\[u25B3] sub 0 y}} = left { matrix{+} right ]} - 2} = left [ matrix{+ccol{ 2 above {- 4} }+ccol{ {- 2} above 0 }+} right ]} above {x = {lim from {x = 1} {sum from 1 to 2 a}}} above {{int sub a sup b {{f  {( x )}}  {\[u2146] x}}} = {lim from {{\[u2225] P \[u2225]} -> 0} {sum from {i = 1} to n {{f  left ( {x to \[u00AF]} sub i right )}  {DELTA x sub i}}}}} above {{int sub a sup b {{f  {( x )}}  {\[u2146] x}}} = {lim from {n -> inf} {{b - a} over n  {sum from {i = 1} to n {f  left ( {a + {i  {b - a} over n}} right )}}}}} above {{int sub 0 sup 2 {x sup 5  sqrt {x sup 3 + 1}  {\[u2146] x}}} = {int sub 1 sup 3 {2 over 3  u  {sqrt {left ( u sup 2 right )}} over {{left ( {u sup 2 - 1} right )} sup {2 over 3}}  left ( {{u sup 2  {left ( {u sup 2 - 1} right )} sup {2 over 3}} - {left ( {u sup 2 - 1} right )} sup {2 over 3}} right )  {\[u2146] u}}}} above {left ∫ {{f  {( {g  {( x )}} )}}  {g sup prime  {( x )}}  {\[u2146] x}} right "" = left ∫ {{f  {( u )}}  {\[u2146] u}} right ""} above {x = {2  {sum from {n = 1} to 100 {n  {( {n - 1} )}}}}} above {{lim from {x -> 0} {sin  left ( 1 over x right )}} = {{- 1} .. 1}} above {{h  {( {i , j} )}} = {{{( {2 - j} )}  {g  {( i )}}} + {{( {j - 1} )}  {f  {( {g  {( i )}} )}}}}} above {\[u25B3] : left "" left [ {0 , 1} right ] "→" left [ {0 , 1} right ] right ""} above {{0 \[u25BD] x} = x} above {{x \[u25B3] y} = {h sup {- 1}  left ( {{h  left ( x right )}  {h  left ( y right )}} right )}} above {{x \[u25B3] y} = {f sup {- 1}  left ( {max left { {{{f  left ( x right )} + {f  left ( y right )} - 1} , 0} right }} right )}} above {{x \[u25BD] y} = {eta  left ( {{eta  left ( x right )} \[u25B3] {eta  left ( y right )}} right )}} above {{x  {\[u25B3] sub 0 y}} = left { matrix{ ccol{ {x \[u2227] y} above 0 } ccol{ {roman "if"} above {roman "if"} } ccol{ {x \[u2228] {y = 1}} above {x \[u2228] {y < 1}} }-} right ""} above {{lim from {a -> 1 sup +} {log sub a  left [ {1 + {left ( {a sup x \[u2212] 1} right )  left ( {a sup y \[u2212] 1} right )} over {a \[u2212] 1}} right ]}} = {lim from {a -> 1 sup \[u2212]} {log sub a  left [ {1 + {left ( {a sup x \[u2212] 1} right )  left ( {a sup y \[u2212] 1} right )} over {a \[u2212] 1}} right ]}} = {x  y}} above {{g  {( x )}} = {exp  left ( {\[u2212] {1 \[u2212] {left ( {1 \[u2212] x} right )} sup a} over {left ( {2 sup a \[u2212] 1} right )  {left ( {1 \[u2212] x} right )} sup a}} right )}} above {{"Aut" {( bold {I} )}} = left { {f : left "" left [ {0 , 1} right ] "→" left [ {0 , 1} right ] right ""} ~ left | matrix{+} right ""} above {{lim from {a -> 1 sup +} {log sub a  left [ {1 + {left ( {a sup x - 1} right )  left ( {a sup y - 1} right )} over {a - 1}} right ]}} = {lim from {a -> 1 sup -} {log sub a  left [ {1 + {left ( {a sup x - 1} right )  left ( {a sup y - 1} right )} over {a - 1}} right ]}} = {x  y}} above {{g  {( x )}} = {exp  left ( {- {1 - {left ( {1 - x} right )} sup a} over {left ( {2 sup a - 1} right )  {left ( {1 - x} right )} sup a}} right )}} above {{"Aut" {( bold {I} )}} = left { {f : left "" left [ {0 , 1} right ] "→" left [ {0 , 1} right ] right ""} ~ left | matrix{ lcol{ {f roman " is one-to-one and onto, and"} above {{x <= y} roman " implies " {{f  left ( x right )} <= {f  left ( y right )}}} }-} right "" right }} above {{{x sup 2 + y sup 2} = r sup 2} , roman "  " {{tan  theta} = y over x}} above {sqrt 2  sqrt {1 \[u2212] t sup 2}} above {left [ {{{( {2 + {sin  t}} )}  10  {cos  t}} , {{( {2 + {cos  t}} )}  10  {sin  t}} , {3  {sin  {3  t}}}} right ]} above {left { {{t = 0} , {s = 0}} right } , left { {{t = pi} , {s = pi}} right }} above {matrix{+} right "" right }} above {{{x sup 2 + y sup 2} = r sup 2} , roman "  " {{tan  theta} = y over x}} above {sqrt 2  sqrt {1 - t sup 2}} above {left [ {{{( {2 + {sin  t}} )}  10  {cos  t}} , {{( {2 + {cos  t}} )}  10  {sin  t}} , {3  {sin  {3  t}}}} right ]} above {left { {{t = 0} , {s = 0}} right } , left { {{t = pi} , {s = pi}} right }} above {matrix{ ccol{ {matrix{ ccol{ 1 above 2 above 3 above 4 above 5 above 6 above 7 above 8 above 9 above 10 } ccol{ 2 above 4 above 6 above 8 above 10 above 1 above 3 above 5 above 7 above 9 }@@ -7816,23 +7816,23 @@ ccol{ {roman "x"} } }} above {matrix{ ccol{ x }-}} above {{{\[u2146] f} over {\[u2146] x}  {( x sub 1 )}} = 5} above {{int {x  {\[u2146] x}}} = {\[u222C] {x  y  {\[u2146] x}  {\[u2146] y}}} = {\[u222D] {x  y  z  {\[u2146] x}  {\[u2146] y}  {\[u2146] z}}} = {\[u2A0C] {x  y  z  t  {\[u2146] x}  {\[u2146] y}  {\[u2146] z}  {\[u2146] t}}}} above {"mod" a} above {{5 "mod" 3} = 2} above {{{f  {( 0 )}} "mod" 3} = 1} above {{{{5  x} + 4} == 8} \[u200B] left ( {"mod" 13} right )} above {a = {{{( {5 \[u2212] 3} )} / 5} "mod" 7} = 6} above {{{left ( {{2  x sup 2} + x + 2} right ) + left ( {{2  x} + 1} right )} "mod" 3} = {2  x sup 2}} above {matrix{+}} above {{{\[u2146] f} over {\[u2146] x}  {( x sub 1 )}} = 5} above {{int {x  {\[u2146] x}}} = {\[u222C] {x  y  {\[u2146] x}  {\[u2146] y}}} = {\[u222D] {x  y  z  {\[u2146] x}  {\[u2146] y}  {\[u2146] z}}} = {\[u2A0C] {x  y  z  t  {\[u2146] x}  {\[u2146] y}  {\[u2146] z}  {\[u2146] t}}}} above {"mod" a} above {{5 "mod" 3} = 2} above {{{f  {( 0 )}} "mod" 3} = 1} above {{{{5  x} + 4} == 8} \[u200B] left ( {"mod" 13} right )} above {a = {{{( {5 - 3} )} / 5} "mod" 7} = 6} above {{{left ( {{2  x sup 2} + x + 2} right ) + left ( {{2  x} + 1} right )} "mod" 3} = {2  x sup 2}} above {matrix{ ccol{ + above 000 above 1 } ccol{ 0 above 000 above 1 } ccol{ 1 above 111 above 0 }-}} above 4. 974 9 above {\[u2146] over {\[u2146] x} {F  {( x )}}} above {left [ {86.333 , 146.33 , 129.33} right ]} above {{BinomialDist  {( {x ; {n , p}} )}} = {sum from {k = 0} to x {left ( n over k right )  p sup k  q sup {n \[u2212] k}}}} above {{"Pr" {( {X <= 54} )}} = {BinomialDist  {( {54 ; {100 , .55}} )}} = .45846} above {{k = {max left { {left | {{partial f} over {partial y}  {( {x , y} )}} right | : {{( {x , y} )} \[u2208] D}} right }}} roman "."} above {m = {lim from {x -> to {""} a} {{f  {( x )}} \[u2212] {f  {( a )}}} over {x \[u2212] a}}} above {left | A right | = left | matrix{+}} above 4. 974 9 above {\[u2146] over {\[u2146] x} {F  {( x )}}} above {left [ {86.333 , 146.33 , 129.33} right ]} above {{BinomialDist  {( {x ; {n , p}} )}} = {sum from {k = 0} to x {left ( n over k right )  p sup k  q sup {n - k}}}} above {{"Pr" {( {X <= 54} )}} = {BinomialDist  {( {54 ; {100 , .55}} )}} = .45846} above {{k = {max left { {left | {{partial f} over {partial y}  {( {x , y} )}} right | : {{( {x , y} )} \[u2208] D}} right }}} roman "."} above {m = {lim from {x -> to {""} a} {{f  {( x )}} - {f  {( a )}}} over {x - a}}} above {left | A right | = left | matrix{ ccol{ {a sub {1 \[u200B] 1}} above {a sub {2 \[u200B] 1}} above \[u22C5] above \[u22C5] above \[u22C5] above {a sub {n \[u200B] 1}} } ccol{ {a sub {1 \[u200B] 2}} above {a sub {2 \[u200B] 2}} above \[u22C5] above \[u22C5] above \[u22C5] above {a sub {n \[u200B] 2}} } ccol{ \[u22C5] above \[u22C5] above \[u22C5] above ^ above ^ above \[u22C5] } ccol{ \[u22C5] above \[u22C5] above ^ above \[u22C5] above ^ above \[u22C5] } ccol{ \[u22C5] above \[u22C5] above ^ above ^ above \[u22C5] above \[u22C5] } ccol{ {a sub {1 \[u200B] n}} above {a sub {2 \[u200B] n}} above \[u22C5] above \[u22C5] above \[u22C5] above {a sub {n \[u200B] n}} }-} right | = {{a sub {1 \[u200B] 1}  A sub {1 \[u200B] 1}} + {a sub {1 \[u200B] 2}  A sub {1 \[u200B] 2}} + \[u22EF] + {a sub {1 \[u200B] n}  A sub {1 \[u200B] n}}}} above {{x = 1} {( roman "hl text " x roman " end." )}} above {{x = 1} {( roman "hl to URI " x roman " end" )}} above {{x = 1} {( roman "sex" )}} above {{x = 1} {( roman "jbm" )}} above {""} above {{{f  {( x )}}  g  {[ y ]}  h  {\[lC] z \[rC]}} + {{\[u230A] a \[u230B]}  {\[u2308] b \[u2309]}  {\[u2329] c \[u232A]}}} above {left "" 123 over {456 over A} right | left "" "∥" A over {B over A} right "" {left "" "/" 1 over {2 over A} "/" right ""  left ( 3 over {4 over A} right )} left "" "↕" 5 over {6 over A} "↕" right "" 7 over {8 over A} left "" "⇕" {9 over 20} over {10 over A} "⇕" right "" {left "" "↑" 11 over {12 over A} "↑" right ""  left "" "⇑" 13 over {14 over A} "⇑" right ""} left "" "↓" 15 over {16 over A} "↓" right "" left "" "⇓" 17 over {18 over A} "⇓" right ""} above {x  matrix{+} right | = {{a sub {1 \[u200B] 1}  A sub {1 \[u200B] 1}} + {a sub {1 \[u200B] 2}  A sub {1 \[u200B] 2}} + cdots + {a sub {1 \[u200B] n}  A sub {1 \[u200B] n}}}} above {{x = 1} {( roman "hl text " x roman " end." )}} above {{x = 1} {( roman "hl to URI " x roman " end" )}} above {{x = 1} {( roman "sex" )}} above {{x = 1} {( roman "jbm" )}} above {""} above {{{f  {( x )}}  g  {[ y ]}  h  {\[lC] z \[rC]}} + {{\[u230A] a \[u230B]}  {\[u2308] b \[u2309]}  {\[u2329] c \[u232A]}}} above {left "" 123 over {456 over A} right | left "" "∥" A over {B over A} right "" {left "" "/" 1 over {2 over A} "/" right ""  left ( 3 over {4 over A} right )} left "" "↕" 5 over {6 over A} "↕" right "" 7 over {8 over A} left "" "⇕" {9 over 20} over {10 over A} "⇕" right "" {left "" "↑" 11 over {12 over A} "↑" right ""  left "" "⇑" 13 over {14 over A} "⇑" right ""} left "" "↓" 15 over {16 over A} "↓" right "" left "" "⇓" 17 over {18 over A} "⇓" right ""} above {x  matrix{ ccol{ x above x } ccol{ x above x }-}  x} above {{left ( {a sub 1 , a sub 2 , ... , a sub n} right ) \[u22C5] left ( {b sub 1 , b sub 2 , ... , b sub n} right )} = {{a sub 1  b sub 1 sup *} + {a sub 2  b sub 2 sup *} + \[u22EF] + {a sub n  b sub n sup *}}} above {left ⌊ n over 5 right ⌋ + left ⌊ n over {5 sup 2} right ⌋ + left ⌊ n over {5 sup 3} right ⌋ + left ⌊ n over {5 sup 4} right ⌋ + \[u22EF]} above {x sub 1 + \[u22EF] + x sub n} above {{{x + \[u22EF] + x} from \[uFE38]} from {k roman " times"}} above {"" sup n sqrt {x sub 1  x sub 2  \[u22EF]  x sub n}} above {{n !} = {1 times 2 times 3 times 4 times \[u22EF] times n}} above {P : {a = x sub 0 < x sub 1 < x sub 2 < \[u22EF] < x sub n = b}} above {{f  {( x )}} = {30 over {13  {cos  x}} + {10 over 3  sqrt {left ( {100 + 9 over {cos sup 2  x} \[u2212] {60 over {cos  x}  {sin  left ( {x + {29 over 90  pi}} right )}}} right )}}}} above {{left ∫ {{cos  {( {A  x} )}}  {sin  {( {B  x} )}}  {\[u2146] x}} right "" = {{\[u2212] {cos  {{( {B \[u2212] A} )}  x}}} over {2  {( {B \[u2212] A} )}} + {\[u2212] {cos  {{( {B + A} )}  x}}} over {2  {( {B + A} )}} + C}} roman " ."} above {{235.3 + 813} = 1048. 3} above {{max from {{\[u2212] 2} <= x <= 2} left ( {x sup 3 \[u2212] {6  x} + 3} right )} = 8.0} above {{x  decade} = {2  century}} above {{\[u2146] sup 5 left ( {x sup 7 \[u2212] {3  x sup 6}} right )} over {\[u2146] x sup 5} roman "  " {\[u2146] sup n {sin  x}} over {\[u2146] x sup n} roman "  " {{\[u2146] sup 3} over {\[u2146] x sup 3} {f  {( x )}}} roman "  " {{\[u2146] sup 2} over {\[u2146] t sup 2} left ( {{4  t sup 5} \[u2212] {3  t}} right )}} above {{f  {( x )}} = {30 over {13  {cos  x}} + {10 over 3  sqrt {left ( {100 + 9 over {cos sup 2  x} \[u2212] {60 over {cos  x}  {sin  left ( {x + {29 over 90  pi}} right )}}} right )}}}} above {left ∫ {""} sub {{bold {R}} sup 3} {left ( {{{left | u sub 1 right |} sup 2 + {left | {grad u sub 0} right |} sup 2} over 2 + {{left | u sub 0 right |} sup 6} over 6} right )  {\[u2146] x}} right "" < inf} above {{left ( {"∇×" bold {F}} right ) \[u22C5] bold {k}} = {z + 1}} above {M  {M sup {M over M}} over M} above {{\[u2145] sub x x sup 2} roman "  " {\[u2145] sub x left ( x sup 2 right )} roman "  " {\[u2145] sub {x \[u200B] x} left ( x sup 2 right )} roman "  " {\[u2145] sub {x sup 2} left ( x sup 2 right )} roman "  " {\[u2145] sub {x \[u200B] y} left ( {x sup 2  y sup 3} right )} roman "  " {\[u2145] sub {x sup s \[u200B] y sup t} left ( {x sup 2  y sup 3} right )}} above {5 ^ {24 !} ^ x sup 6} above {matrix{+}  x} above {{left ( {a sub 1 , a sub 2 , ... , a sub n} right ) \[u22C5] left ( {b sub 1 , b sub 2 , ... , b sub n} right )} = {{a sub 1  b sub 1 sup *} + {a sub 2  b sub 2 sup *} + cdots + {a sub n  b sub n sup *}}} above {left ⌊ n over 5 right ⌋ + left ⌊ n over {5 sup 2} right ⌋ + left ⌊ n over {5 sup 3} right ⌋ + left ⌊ n over {5 sup 4} right ⌋ + cdots} above {x sub 1 + cdots + x sub n} above {{{x + cdots + x} from \[uFE38]} from {k roman " times"}} above {"" sup n sqrt {x sub 1  x sub 2  cdots  x sub n}} above {{n !} = {1 times 2 times 3 times 4 times cdots times n}} above {P : {a = x sub 0 < x sub 1 < x sub 2 < cdots < x sub n = b}} above {{f  {( x )}} = {30 over {13  {cos  x}} + {10 over 3  sqrt {left ( {100 + 9 over {cos sup 2  x} - {60 over {cos  x}  {sin  left ( {x + {29 over 90  pi}} right )}}} right )}}}} above {{left ∫ {{cos  {( {A  x} )}}  {sin  {( {B  x} )}}  {\[u2146] x}} right "" = {{- {cos  {{( {B - A} )}  x}}} over {2  {( {B - A} )}} + {- {cos  {{( {B + A} )}  x}}} over {2  {( {B + A} )}} + C}} roman " ."} above {{235.3 + 813} = 1048. 3} above {{max from {{- 2} <= x <= 2} left ( {x sup 3 - {6  x} + 3} right )} = 8.0} above {{x  decade} = {2  century}} above {{\[u2146] sup 5 left ( {x sup 7 - {3  x sup 6}} right )} over {\[u2146] x sup 5} roman "  " {\[u2146] sup n {sin  x}} over {\[u2146] x sup n} roman "  " {{\[u2146] sup 3} over {\[u2146] x sup 3} {f  {( x )}}} roman "  " {{\[u2146] sup 2} over {\[u2146] t sup 2} left ( {{4  t sup 5} - {3  t}} right )}} above {{f  {( x )}} = {30 over {13  {cos  x}} + {10 over 3  sqrt {left ( {100 + 9 over {cos sup 2  x} - {60 over {cos  x}  {sin  left ( {x + {29 over 90  pi}} right )}}} right )}}}} above {left ∫ {""} sub {{bold {R}} sup 3} {left ( {{{left | u sub 1 right |} sup 2 + {left | {grad u sub 0} right |} sup 2} over 2 + {{left | u sub 0 right |} sup 6} over 6} right )  {\[u2146] x}} right "" < inf} above {{left ( {"∇×" bold {F}} right ) \[u22C5] bold {k}} = {z + 1}} above {M  {M sup {M over M}} over M} above {{\[u2145] sub x x sup 2} roman "  " {\[u2145] sub x left ( x sup 2 right )} roman "  " {\[u2145] sub {x \[u200B] x} left ( x sup 2 right )} roman "  " {\[u2145] sub {x sup 2} left ( x sup 2 right )} roman "  " {\[u2145] sub {x \[u200B] y} left ( {x sup 2  y sup 3} right )} roman "  " {\[u2145] sub {x sup s \[u200B] y sup t} left ( {x sup 2  y sup 3} right )}} above {5 ^ {24 !} ^ x sup 6} above {matrix{ ccol{ {matrix{-ccol{ {x + "" sup 2 sqrt {{a sup {y \[u2212] 1}} over 12.34}} above ^ }+ccol{ {x + "" sup 2 sqrt {{a sup {y - 1}} over 12.34}} above ^ } ccol{ {sin  theta} above 1 } }} } }} above {matrix{@@ -7840,10 +7840,10 @@ ccol{ 1 above 0 } }} above {left ( matrix{ ccol{ 0 above i }-ccol{ {\[u2212] i} above 0 }+ccol{ {- i} above 0 } } right )} above {left [ matrix{ ccol{ 1 above 0 }-ccol{ 0 above {\[u2212] 1} }+ccol{ 0 above {- 1} } } right ]} above {left | matrix{ ccol{ a above c } ccol{ b above d }@@ -7861,14 +7861,14 @@ ccol{ {x = 1} above {x sup 2} above {roman "jbm"} } ccol{ {roman "not"} above {roman "merged"} above {roman "lowlife"} } ccol{ {roman "here"} above {y sub 1} above {roman "The end."} }-}} above {{x sup 2 + y sup 2} = {z sup 2 \[u2212] 1}} above {matrix{-ccol{ {{x sup 2 + y sup 2} = {z sup 2 \[u2212] 1}} above {{x + y sup 3} = z sup 3} }+}} above {{x sup 2 + y sup 2} = {z sup 2 - 1}} above {matrix{+ccol{ {{x sup 2 + y sup 2} = {z sup 2 - 1}} above {{x + y sup 3} = z sup 3} } }} above {matrix{-ccol{ {{x sup 2 + y sup 2} = {z sup 2 \[u2212] 1}} above {{x + y sup 3} = z sup 3} }+ccol{ {{x sup 2 + y sup 2} = {z sup 2 - 1}} above {{x + y sup 3} = z sup 3} } }} above {matrix{-ccol{ {{x sup 2 + y sup 2} = 1} above {x = sqrt {1 \[u2212] y sup 2}} }+ccol{ {{x sup 2 + y sup 2} = 1} above {x = sqrt {1 - y sup 2}} } }} above {matrix{-ccol{ {{( {a + b} )} sup 2 = {a sup 2 + {2  a  b} + b sup 2}} above {{{( {a + b} )} \[u22C5] {( {a \[u2212] b} )}} = {a sup 2 \[u2212] b sup 2}} }+ccol{ {{( {a + b} )} sup 2 = {a sup 2 + {2  a  b} + b sup 2}} above {{{( {a + b} )} \[u22C5] {( {a - b} )}} = {a sup 2 - b sup 2}} } }} above {matrix{ ccol{ {roman "First line of equation"} above {roman "Middle line of equation"} above {roman "Other middle line of equation"} above {roman "Last line of equation"} } }} above {matrix{@@ -7876,14 +7876,14 @@ }} above {matrix{ ccol{ {{( {a + b} )} sup 4 = {{( {a + b} )} sup 2  {( {a + b} )} sup 2}} above {= {{( {a sup 2 + {2  a  b} + b sup 2} )}  {( {a sup 2 + {2  a  b} + b sup 2} )}}} above {= {a sup 4 + {4  a sup 3  b} + {6  a sup 2  b sup 2} + {4  a  b sup 3} + b sup 4}} } }} above {matrix{-ccol{ {{x sup 2 + y sup 2} = 1} above {x = sqrt {1 \[u2212] y sup 2}} }+ccol{ {{x sup 2 + y sup 2} = 1} above {x = sqrt {1 - y sup 2}} } } roman "  " matrix{-ccol{ {{( {a + b} )} sup 2 = {a sup 2 + {2  a  b} + b sup 2}} above {{{( {a + b} )} \[u22C5] {( {a \[u2212] b} )}} = {a sup 2 \[u2212] b sup 2}} }+ccol{ {{( {a + b} )} sup 2 = {a sup 2 + {2  a  b} + b sup 2}} above {{{( {a + b} )} \[u22C5] {( {a - b} )}} = {a sup 2 - b sup 2}} } }} above {matrix{ ccol{ {roman "Vertex"} above {roman "Focus"} above {roman "Directrix"} }-ccol{ {V  {( {0 , 0} )}} above {F  {( {0 , p} )}} above {y = {\[u2212] p}} }-}} above {{\[u2146] over {\[u2146] x} roman "  " {( {"csc" sup {\[u2212] 1}  x} )}} = {\[u2212] 1 over {left | x right |  sqrt {x sup 2 \[u2212] 1}}}} above {{{tanh sup {\[u2212] 1}  x} = {1 over 2  {ln  left ( {1 + x} over {1 \[u2212] x} right )}}} roman "  " {{\[u2212] 1} < x < 1}} above {{{\[u2220] alpha} + {\[u2220] A B C} + {\[u2220] 1}} = {\[u25B5] a b c}} above {y = {e sup {\[u2212] {int {P  {\[u2146] x}}}}  left [ {{int {e sup {int {P  {\[u2146] x}}}  Q  {\[u2146] x}}} + c} right ]}} above {x = {1 + y sup 3}} above {{$ 1.00} + {25 \[u00A2]} \[u2212] {3 \[u00A3]} + {2.45 \[u00A4]} \[u2212] {0.7 \[u00A5]} \[u2212] {a \[u20A0]} + {20 \[u20A3]} + {30 \[u20A4]} \[u2212] {4.56 \[u20A7]}} above {matrix{-ccol{ {{{2  x} + y} = 3} above {{{3  x} \[u2212] {4  y}} = 5} above {{a + b} = {c + 12345}} }+ccol{ {V  {( {0 , 0} )}} above {F  {( {0 , p} )}} above {y = {- p}} }+}} above {{\[u2146] over {\[u2146] x} roman "  " {( {"csc" sup {- 1}  x} )}} = {- 1 over {left | x right |  sqrt {x sup 2 - 1}}}} above {{{tanh sup {- 1}  x} = {1 over 2  {ln  left ( {1 + x} over {1 - x} right )}}} roman "  " {{- 1} < x < 1}} above {{{\[u2220] alpha} + {\[u2220] A B C} + {\[u2220] 1}} = {\[u25B5] a b c}} above {y = {e sup {- {int {P  {\[u2146] x}}}}  left [ {{int {e sup {int {P  {\[u2146] x}}}  Q  {\[u2146] x}}} + c} right ]}} above {x = {1 + y sup 3}} above {{$ 1.00} + {25 \[u00A2]} - {3 \[u00A3]} + {2.45 \[u00A4]} - {0.7 \[u00A5]} - {a \[u20A0]} + {20 \[u20A3]} + {30 \[u20A4]} - {4.56 \[u20A7]}} above {matrix{+ccol{ {{{2  x} + y} = 3} above {{{3  x} - {4  y}} = 5} above {{a + b} = {c + 12345}} } }} above {matrix{ ccol{ {roman "Unrestricted"} } ccol{ {roman "   "} }@@ -7896,6 +7896,6 @@ ccol{ {x = {y + z}} above {= {k + m}} } }} above {matrix{ lcol{ {roman "College Algebra " roman "Second Edition"} above {roman "James Stewart " roman "McMaster Universitiy"} above {roman "Lothar Redlin" roman " Pennsylvania State University"} above {roman "Saleem Watson" roman " California State University, Long Beach"} above {roman "Copyright 1996, ISBN 0 534-33983-2"} above {roman "Brooks/Cole Publishing Company"} above {roman "An International Thomson Publishing Company"} }-} ~} above {left { {1 over 2} over {1 over 2} "↑" sum from 1 to 2 right }} above {left 〈 {1 over 2} over {1 over 2} "|" sum from 1 to 2 right 〉} above {left ⌈ {1 over 2} over {1 over 2} "|" sum from 1 to 2 right ⌉} above {left "" "⇓" left "" {1 over 2} over {1 over 2} "↕" sum from 1 to 2 right "" "⇓" right ""} above {left [ {1 over 2} over {1 over 2} right ]} above {left ( {1 over 2} over {1 over 2} right )} above {left { {1 over 2} over {1 over 2} right }} above {left 〈 {1 over 2} over {1 over 2} right 〉} above {left ⌊ {1 over 2} over {1 over 2} right ⌋} above {left ⌈ {1 over 2} over {1 over 2} right ⌉} above {left "" "↑" {1 over 2} over {1 over 2} "↑" right ""} above {left "" "↓" {1 over 2} over {1 over 2} "↓" right ""} above {left "" "↕" {1 over 2} over {1 over 2} "↕" right ""} above {left "" "⇑" {1 over 2} over {1 over 2} "⇑" right ""} above {left "" "⇓" {1 over 2} over {1 over 2} "⇓" right ""} above {left "" "⇕" {1 over 2} over {1 over 2} "⇕" right ""} above {{1 over 2} over {1 over 2}} above {left \arrowvert {1 over 2} over {1 over 2} right \arrowvert} above {left \Arrowvert {1 over 2} over {1 over 2} right \Arrowvert} above {left \bracevert {1 over 2} over {1 over 2} right \bracevert} above {left | {1 over 2} over {1 over 2} right |} above {left | {1 over 2} over {1 over 2} right |} above {left | {1 over 2} over {1 over 2} right |} above {left "" "∥" {1 over 2} over {1 over 2} "∥" right ""} above {left "" "∥" {1 over 2} over {1 over 2} "∥" right ""} above {left "" "/" {1 over 2} over {1 over 2} "/" right ""} above {left "" "\" {1 over 2} over {1 over 2} "\" right ""} above {left ⎱ {1 over 2} over {1 over 2} right ⎰} above {left \lgroup {1 over 2} over {1 over 2} right \rgroup} above {left ⌞ {1 over 2} over {1 over 2} right ⌟} above {left ⌜ {1 over 2} over {1 over 2} right ⌝} above {A <- from ^ to {n + mu \[u2212] 1} B -> from T to {n +- i \[u2212] 1} C} above {1 over {sqrt 2 + 1 over {sqrt 3 + 1 over {sqrt 4 + 1 over {sqrt 5 + 1 over {sqrt 6 + ...}}}}}} above {1 over {sqrt 2 + 1 over {sqrt 3 + 1 over {sqrt 4 + 1 over {sqrt 5 + 1 over {sqrt 6 + ...}}}}}} above {left ( {sin  theta} over M right ⌋} above {left ( {sin  theta} over M right ⌋} above {left ( {sin  theta} over M right ⌋} above {left ( {sin  theta} over M right ⌋} above {left ( {sin  theta} over M right ⌋} above {left ( {sin  theta} over M right ⌋} above {left ( {sin  theta} over M right ⌋} above {left ( {sin  theta} over M right ⌋} above {left ( {sin  theta} over M right ⌋} above {{sin  theta} over M} above {{sin  theta} over M} above {{sin  theta} over M} above {{sin  theta} over M} above {{sin  theta} over M} above {{sin  theta} over M} above {{sin  theta} over M} above {{sin  theta} over M} above {{sin  theta} over M} }+} ~} above {left { {1 over 2} over {1 over 2} "↑" sum from 1 to 2 right }} above {left 〈 {1 over 2} over {1 over 2} "|" sum from 1 to 2 right 〉} above {left ⌈ {1 over 2} over {1 over 2} "|" sum from 1 to 2 right ⌉} above {left "" "⇓" left "" {1 over 2} over {1 over 2} "↕" sum from 1 to 2 right "" "⇓" right ""} above {left [ {1 over 2} over {1 over 2} right ]} above {left ( {1 over 2} over {1 over 2} right )} above {left { {1 over 2} over {1 over 2} right }} above {left 〈 {1 over 2} over {1 over 2} right 〉} above {left ⌊ {1 over 2} over {1 over 2} right ⌋} above {left ⌈ {1 over 2} over {1 over 2} right ⌉} above {left "" "↑" {1 over 2} over {1 over 2} "↑" right ""} above {left "" "↓" {1 over 2} over {1 over 2} "↓" right ""} above {left "" "↕" {1 over 2} over {1 over 2} "↕" right ""} above {left "" "⇑" {1 over 2} over {1 over 2} "⇑" right ""} above {left "" "⇓" {1 over 2} over {1 over 2} "⇓" right ""} above {left "" "⇕" {1 over 2} over {1 over 2} "⇕" right ""} above {{1 over 2} over {1 over 2}} above {left \arrowvert {1 over 2} over {1 over 2} right \arrowvert} above {left \Arrowvert {1 over 2} over {1 over 2} right \Arrowvert} above {left \bracevert {1 over 2} over {1 over 2} right \bracevert} above {left | {1 over 2} over {1 over 2} right |} above {left | {1 over 2} over {1 over 2} right |} above {left | {1 over 2} over {1 over 2} right |} above {left "" "∥" {1 over 2} over {1 over 2} "∥" right ""} above {left "" "∥" {1 over 2} over {1 over 2} "∥" right ""} above {left "" "/" {1 over 2} over {1 over 2} "/" right ""} above {left "" "\" {1 over 2} over {1 over 2} "\" right ""} above {left ⎱ {1 over 2} over {1 over 2} right ⎰} above {left \lgroup {1 over 2} over {1 over 2} right \rgroup} above {left ⌞ {1 over 2} over {1 over 2} right ⌟} above {left ⌜ {1 over 2} over {1 over 2} right ⌝} above {A <- from ^ to {n + mu - 1} B -> from T to {n +- i - 1} C} above {1 over {sqrt 2 + 1 over {sqrt 3 + 1 over {sqrt 4 + 1 over {sqrt 5 + 1 over {sqrt 6 + ...}}}}}} above {1 over {sqrt 2 + 1 over {sqrt 3 + 1 over {sqrt 4 + 1 over {sqrt 5 + 1 over {sqrt 6 + ...}}}}}} above {left ( {sin  theta} over M right ⌋} above {left ( {sin  theta} over M right ⌋} above {left ( {sin  theta} over M right ⌋} above {left ( {sin  theta} over M right ⌋} above {left ( {sin  theta} over M right ⌋} above {left ( {sin  theta} over M right ⌋} above {left ( {sin  theta} over M right ⌋} above {left ( {sin  theta} over M right ⌋} above {left ( {sin  theta} over M right ⌋} above {{sin  theta} over M} above {{sin  theta} over M} above {{sin  theta} over M} above {{sin  theta} over M} above {{sin  theta} over M} above {{sin  theta} over M} above {{sin  theta} over M} above {{sin  theta} over M} above {{sin  theta} over M} } ccol{ {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {x = {1 + y}} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} above {""} } }

@@ -19,4 +19,4 @@     (EGrouped [ ENumber "2" , EIdentifier "a" ]) ] >>> eqn-x = {\[u2212] b +- sqrt {b sup 2 \[u2212] 4 a c}} over {2 a}+x = {- b +- sqrt {b sup 2 - 4 a c}} over {2 a}

@@ -55,5 +55,5 @@ >>> eqn matrix{ ccol{ {roman "macr"} above {roman "male"} above {roman "malt"} above {roman "maltese"} above {roman "map"} above {roman "Map"} above {roman "mapsto"} above {roman "mapstodown"} above {roman "mapstoleft"} above {roman "mapstoup"} above {roman "marker"} above {roman "mcomma"} above {roman "mcy"} above {roman "Mcy"} above {roman "mdash"} above {roman "mDDot"} above {roman "measuredangle"} above {roman "MediumSpace"} above {roman "Mellintrf"} above {roman "mfr"} above {roman "Mfr"} above {roman "mho"} above {roman "micro"} above {roman "mid"} above {roman "midast"} above {roman "midcir"} above {roman "middot"} above {roman "minus"} above {roman "minusb"} above {roman "minusd"} above {roman "minusdu"} above {roman "MinusPlus"} above {roman "mlcp"} above {roman "mldr"} above {roman "mnplus"} above {roman "models"} above {roman "mopf"} above {roman "Mopf"} above {roman "mp"} above {roman "mscr"} above {roman "Mscr"} above {roman "mstpos"} above {roman "mu"} above {roman "multimap"} above {roman "mumap"} }-ccol{ \[u00AF] above \[u2642] above \[u2720] above \[u2720] above \[u21A6] above \[u2905] above \[u21A6] above \[u21A7] above \[u21A4] above \[u21A5] above \[u25AE] above \[u2A29] above \[u043C] above \[u041C] above \[u2014] above \[u223A] above \[u2221] above \[u205F] above \[u2133] above \[u1D52A] above \[u1D510] above \[u2127] above \[u00B5] above \[u2223] above * above \[u2AF0] above cdot above \[u2212] above \[u229F] above \[u2238] above \[u2A2A] above \[u2213] above \[u2ADB] above ... above \[u2213] above \[u22A7] above \[u1D55E] above \[u1D544] above \[u2213] above \[u1D4C2] above \[u2133] above \[u223E] above mu above \[u22B8] above \[u22B8] }+ccol{ \[u00AF] above \[u2642] above \[u2720] above \[u2720] above \[u21A6] above \[u2905] above \[u21A6] above \[u21A7] above \[u21A4] above \[u21A5] above \[u25AE] above \[u2A29] above \[u043C] above \[u041C] above \[u2014] above \[u223A] above \[u2221] above \[u205F] above \[u2133] above \[u1D52A] above \[u1D510] above \[u2127] above \[u00B5] above \[u2223] above * above \[u2AF0] above cdot above - above \[u229F] above \[u2238] above \[u2A2A] above \[u2213] above \[u2ADB] above ... above \[u2213] above \[u22A7] above \[u1D55E] above \[u1D544] above \[u2213] above \[u1D4C2] above \[u2133] above \[u223E] above mu above \[u22B8] above \[u22B8] } }

@@ -6,4 +6,4 @@ , ENumber "0" ] >>> eqn-x sup 2 \[u2212] 1 = 0+x sup 2 - 1 = 0

@@ -54,6 +54,6 @@ M = left [ matrix{ ccol{ {alpha sub 1} above {alpha sub 2} above \[u22EE] above {alpha sub m} } ccol{ {alpha sub 1 sup q} above {alpha sub 2 sup q} above \[u22EE] above {alpha sub m sup q} }-ccol{ \[u22EF] above \[u22EF] above \[u22F1] above \[u22EF] }-ccol{ {alpha sub 1 sup {q sup {n \[u2212] 1}}} above {alpha sub 2 sup {q sup {n \[u2212] 1}}} above \[u22EE] above {alpha sub m sup {q sup {n \[u2212] 1}}} }+ccol{ cdots above cdots above \[u22F1] above cdots }+ccol{ {alpha sub 1 sup {q sup {n - 1}}} above {alpha sub 2 sup {q sup {n - 1}}} above \[u22EE] above {alpha sub m sup {q sup {n - 1}}} } } right ]

@@ -54,4 +54,4 @@     ] ] >>> eqn-left ⟨ psi left | {T} left { delta over {delta phi} F left [ phi right ] right } right | psi right ⟩ = \[u2212] roman {i} left ⟨ psi left | {T} left { F left [ phi right ] delta over {delta phi} S left [ phi right ] right } right | psi right ⟩+left ⟨ psi left | {T} left { delta over {delta phi} F left [ phi right ] right } right | psi right ⟩ = - roman {i} left ⟨ psi left | {T} left { F left [ phi right ] delta over {delta phi} S left [ phi right ] right } right | psi right ⟩

@@ -22,4 +22,4 @@     ] ] >>> eqn-int sub 0 sup 1 x sup x ^ roman {d} x = sum from {n = 1} to inf {{left ( \[u2212] 1 right )} sup {n + 1} ^ n sup {\[u2212] n}}+int sub 0 sup 1 x sup x ^ roman {d} x = sum from {n = 1} to inf {{left ( - 1 right )} sup {n + 1} ^ n sup {- n}}

@@ -128,5 +128,5 @@ >>> eqn S = \[lC] 0 <= phi <= 2 pi , ~ 0 <= theta <= pi , ~ 0 <= rho <= R \[rC] matrix{ rcol{ {roman {V o l u m e}} above {""} above {""} above {""} above {""} }-lcol{ {= \[u222D] from S back 16 rho sup 2 sin theta ^ roman {d} rho ^ roman {d} theta ^ roman {d} phi} above {= int sub 0 sup {2 pi} back 16 roman {d} phi ^ int sub 0 sup pi back 16 sin theta ^ roman {d} theta ^ int sub 0 sup R back 16 rho sup 2 roman {d} rho} above {= phi | sub 0 sup {2 pi} ~ left ( \[u2212] cos theta right ) | sub 0 sup pi ~ 1 over 3 rho sup 3 | sub 0 sup R} above {= 2 pi times 2 times 1 over 3 R sup 3} above {= 4 over 3 pi R sup 3} }+lcol{ {= \[u222D] from S back 16 rho sup 2 sin theta ^ roman {d} rho ^ roman {d} theta ^ roman {d} phi} above {= int sub 0 sup {2 pi} back 16 roman {d} phi ^ int sub 0 sup pi back 16 sin theta ^ roman {d} theta ^ int sub 0 sup R back 16 rho sup 2 roman {d} rho} above {= phi | sub 0 sup {2 pi} ~ left ( - cos theta right ) | sub 0 sup pi ~ 1 over 3 rho sup 3 | sub 0 sup R} above {= 2 pi times 2 times 1 over 3 R sup 3} above {= 4 over 3 pi R sup 3} } }

@@ -247,21 +247,16 @@     </m:r>     <m:sSubSup>       <m:e>-        <m:limLow>+        <m:bar>+          <m:barPr>+            <m:pos m:val="bot" />+          </m:barPr>           <m:e>             <m:r>               <m:t>u</m:t>             </m:r>           </m:e>-          <m:lim>-            <m:r>-              <m:rPr>-                <m:sty m:val="p" />-              </m:rPr>-              <m:t>_</m:t>-            </m:r>-          </m:lim>-        </m:limLow>+        </m:bar>       </m:e>       <m:sub>         <m:r>

@@ -1,5 +1,5 @@ Name:                texmath-Version:             0.12.5.3+Version:             0.12.5.4 Cabal-Version:       >= 1.10 Build-type:          Simple Synopsis:            Conversion between math formats.