$\newenvironment {prompt}{}{} \newcommand {\DeclareMathOperator }[2]{\@OldDeclareMathOperator {##1}{##2}\immediate \write \myfile {\unexpanded {\DeclareMathOperator }{\unexpanded {##1}}{\unexpanded {##2}}}} \newcommand {\ungraded }[0]{} \newcommand {\todo }[0]{} \newcommand {\oiint }[0]{{\large \bigcirc }\kern -1.56em\iint } \newcommand {\mooculus }[0]{\textsf {\textbf {MOOC}\textnormal {\textsf {ULUS}}}} \newcommand {\npfourdigitsep }[0]{\nprt@numsepfourtrue } \newcommand {\npfourdigitnosep }[0]{\nprt@numsepfourfalse } \newcommand {\npaddmissingzero }[0]{\nprt@addmissingzerotrue } \newcommand {\npnoaddmissingzero }[0]{\nprt@addmissingzerofalse } \newcommand {\npaddplus }[0]{\nprt@addplus@mantissatrue } \newcommand {\npnoaddplus }[0]{\nprt@addplus@mantissafalse } \newcommand {\npaddplusexponent }[0]{\nprt@addplus@exponenttrue } \newcommand {\npnoaddplusexponent }[0]{\nprt@addplus@exponentfalse } \newcommand {\nprt@debug }[1]{} \newcommand {\npdecimalsign }[1]{\def \nprt@decimal {{##1}}} \newcommand {\npthousandsep }[1]{\def \nprt@separator@before {{##1}}\def \nprt@separator@after {{##1}}} \newcommand {\npthousandthpartsep }[1]{\def \nprt@separator@after {{##1}}} \newcommand {\npproductsign }[1]{\def \nprt@prod {\ensuremath {{}##1{}}}} \newcommand {\npunitseparator }[1]{\def \nprt@unitsep {{##1}}} \newcommand {\npdegreeseparator }[1]{\def \nprt@degreesep {{##1}}} \newcommand {\npcelsiusseparator }[1]{\def \nprt@celsiussep {{##1}}} \newcommand {\nppercentseparator }[1]{\def \nprt@percentsep {{##1}}} \newcommand {\nprounddigits }[1]{\def \nprt@rounddigits {##1}\def \nprt@roundnull {}\nprt@fillnull {\nprt@roundnull }{##1}} \newcommand {\npnoround }[0]{\nprounddigits {-1}} \newcommand {\nproundexpdigits }[1]{\def \nprt@roundexpdigits {##1}\def \nprt@roundexpnull {}\nprt@fillnull {\nprt@roundexpnull }{##1}} \newcommand {\npnoroundexp }[0]{\nproundexpdigits {-1}} \newcommand {\npnolpadding }[0]{\nplpadding [\@empty ]{-1}} \newcommand {\npreplacenull }[1]{\def \nprt@replacenull {##1}} \newcommand {\npprintnull }[0]{\let \nprt@replacenull =\@empty } \newcommand {\npunitcommand }[1]{\ensuremath {\mathrm {##1}}} \newcommand {\npdigits }[2]{\edef \nprt@mantissa@fixeddigits@before {##1}\edef \nprt@mantissa@fixeddigits@after {##2}\nprt@mantissa@fixeddigitstrue } \newcommand {\npnodigits }[0]{\nprt@mantissa@fixeddigitsfalse } \newcommand {\npnoexponentdigits }[0]{\nprt@exponent@fixeddigitsfalse } \newcommand {\nprt@error }[2]{\ifnprt@errormessage \PackageError {numprint}{##1}{##2}\else \PackageWarning {numprint}{##1}\fi \nprt@argumenterrortrue } \newcommand {\nprt@IfCharInString }[2]{\nprt@charfoundfalse \begingroup \def \nprt@searchfor {##1}\edef \nprt@argtwo {##2}\expandafter \nprt@@IfCharInString \nprt@argtwo \@empty \@empty \endgroup \ifnprt@charfound \expandafter \@firstoftwo \else \expandafter \@secondoftwo \fi } \newcommand {\nprt@plus@test }[0]{+} \newcommand {\nprt@minus@test }[0]{-} \newcommand {\nprt@plusminus@test }[0]{\pm } \newcommand {\nprt@numberlist }[0]{0123456789} \newcommand {\nprt@dotlist }[0]{.,} \newcommand {\nprt@explist }[0]{eEdD} \newcommand {\nprt@signlist }[0]{+-\pm } \newcommand {\nprt@ignorelist }[0]{} \newcommand {\nprt@testsign }[2]{\edef \nprt@commandname {##1}\edef \nprt@tmp {##2}\expandafter \nprt@@testsign \expandafter {\expandafter \nprt@commandname \expandafter }\nprt@tmp \@empty \@empty \@empty \@empty } \newcommand {\nprt@calcblockwidth }[3]{\edef \nprt@argone {##1}\edef \nprt@argtwo {##2}\edef \nprt@argthree {##3}\edef \nprt@mantissaname {mantissa}\edef \nprt@aftername {after}\ifx \nprt@argone \nprt@mantissaname \ifmmode \settowidth {\nprt@digitwidth }{$##30$}\settowidth {\nprt@sepwidth }{$##3\csname nprt@separator@##2\endcsname $}\settowidth {\nprt@decimalwidth }{$##3\nprt@decimal $}\else \settowidth {\nprt@digitwidth }{0}\settowidth {\nprt@sepwidth }{\csname nprt@separator@##2\endcsname }\settowidth {\nprt@decimalwidth }{\nprt@decimal }\fi \else \ifmmode \settowidth {\nprt@digitwidth }{$##3{}^{0}$}\settowidth {\nprt@sepwidth }{$##3{}^{\csname nprt@separator@##2\endcsname }$}\settowidth {\nprt@decimalwidth }{$##3{}^{\nprt@decimal }$}\else \settowidth {\nprt@digitwidth }{\textsuperscript {0}}\settowidth {\nprt@sepwidth }{\textsuperscript {\csname nprt@separator@##2\endcsname }}\settowidth {\nprt@decimalwidth }{\textsuperscript {\nprt@decimal }}\fi \fi \nprt@debug {Widths for ##1 ##2 decimal sign (\ifx \nprt@argthree \@empty text mode\else math mode ##3\fi ):\MessageBreak digits \the \nprt@digitwidth ,separators \the \nprt@sepwidth ,\MessageBreak decimal sign \the \nprt@decimalwidth }\ifnum \csname nprt@##1@fixeddigits@##2\endcsname <\csname thenprt@##1@digits##2\endcsname \PackageWarning {numprint}{##1 exceeds reserved space ##2\MessageBreak decimal sign}\fi \setlength {\nprt@blockwidth }{\csname nprt@##1@fixeddigits@##2\endcsname \nprt@digitwidth }\setcounter {nprt@blockcnt}{\csname nprt@##1@fixeddigits@##2\endcsname }\advance \c@nprt@blockcnt by -1\relax \divide \c@nprt@blockcnt 3\ifnprt@numsepfour \else \ifnum \csname nprt@##1@fixeddigits@before\endcsname <5 \ifnum \csname nprt@##1@fixeddigits@after\endcsname <5 \setcounter {nprt@blockcnt}{0}\fi \fi \fi \addtolength {\nprt@blockwidth }{\thenprt@blockcnt \nprt@sepwidth }\ifx \nprt@argtwo \nprt@aftername \expandafter \ifnum \csname nprt@##1@fixeddigits@after\endcsname >0 \addtolength {\nprt@blockwidth }{\the \nprt@decimalwidth }\fi \fi } \newcommand {\npunit }[1]{\def \nprt@unit {##1}} \newcommand {\npafternum }[1]{\def \nprt@afternum {##1}} \newcommand {\npmakebox }[0]{\@ifnextchar [{\nprt@makebox }{\makebox }} \newcommand {\nprt@makebox }[0]{} \newcommand {\nprt@round }[2]{\begingroup \edef \nprt@numname {##1}\ifnum ##2<0 \else \nprt@debug {\string \nprt@round : Round after ##2 digits for ##1}\setcounter {nprt@##1@digitsafter}{##2}\expandafter \g@addto@macro \csname nprt@##1@after\endcsname {\nprt@roundnull }\nprt@rndpos =##2 \nprt@roundupfalse \edef \nprt@tmpnum {\csname nprt@##1@after\endcsname }\edef \nprt@newnum {}\expandafter \nprt@round@after \nprt@tmpnum \@empty \@empty \expandafter \xdef \csname nprt@##1@after\endcsname {\nprt@newnum }\ifnprt@roundup \edef \nprt@tmpnum {\csname nprt@##1@before\endcsname }\edef \nprt@newnum {}\expandafter \nprt@round@before \nprt@tmpnum \@empty \@empty \ifnprt@roundup \expandafter \xdef \expandafter \nprt@newnum {1\nprt@newnum }\advance \csname c@nprt@##1@digitsbefore\endcsname by 1\relax \fi \expandafter \xdef \csname nprt@##1@before\endcsname {\nprt@newnum }\fi \fi \endgroup \ifnum ##2<0 \else \ifnum ##2=0 \csname nprt@##1@decimalfoundfalse\endcsname \else \csname nprt@##1@decimalfoundtrue\endcsname \fi \fi } \newcommand {\nprt@lpad }[3]{\ifnum ##2<0 \else \nprt@debug {\string \nprt@lpad : Padding ##1 with ##3 to a length of ##2}\ifnum \csname thenprt@##1@digitsbefore\endcsname <##2 \expandafter \xdef \csname nprt@##1@before\endcsname {##3\csname nprt@##1@before\endcsname }\advance \csname c@nprt@##1@digitsbefore\endcsname by 1\relax \nprt@lpad {##1}{##2}{##3}\fi \fi } \newcommand {\nprt@sign@+ }[0]{{\ensuremath {+}}} \newcommand {\nprt@sign@-}[0]{{\ensuremath {-}}} \newcommand {\nprt@sign@+-}[0]{{\ensuremath {\pm }}} \newcommand {\nprt@printsign }[2]{\nprt@debug {\string \nprt@printsign : ‘##2’}\edef \nprt@marg {##2}\csname ifnprt@addplus@##1\endcsname \ifx \nprt@marg \@empty \edef \nprt@marg {+}\fi \fi \ifx \nprt@marg \@empty \else \@ifundefined {nprt@sign@\nprt@marg }{\PackageWarning {numprint}{Unknown sign ‘\nprt@marg ’. Print as typed in}\nprt@marg }{\csname nprt@sign@\nprt@marg \endcsname }\fi } \newcommand {\nprt@printbefore }[1]{\ifnprt@addmissingzero \ifnum \csname thenprt@##1@digitsbefore\endcsname =0 \expandafter \edef \csname nprt@##1@before\endcsname {0}\advance \csname c@nprt@##1@digitsbefore\endcsname by 1\relax \fi \fi \begingroup \edef \nprt@numbertoprint {\csname nprt@##1@before\endcsname }\ifnprt@numsepfour \else \ifnum \csname thenprt@##1@digitsbefore\endcsname <5 \ifnum \csname thenprt@##1@digitsafter\endcsname <5 \nprt@shortnumbertrue \fi \fi \fi \ifnprt@shortnumber \nprt@numbertoprint \else \setcounter {nprt@blockcnt}{\csname thenprt@##1@digitsbefore\endcsname }\advance \c@nprt@blockcnt by -1\relax \divide \c@nprt@blockcnt 3\setcounter {nprt@digitsfirstblock}{\csname thenprt@##1@digitsbefore\endcsname }\setcounter {nprt@cntprint}{\thenprt@blockcnt }\multiply \c@nprt@cntprint 3\advance \c@nprt@digitsfirstblock by -\thenprt@cntprint \relax \ifnum \thenprt@digitsfirstblock =1 \expandafter \nprt@printone \nprt@numbertoprint \@empty \else \ifnum \thenprt@digitsfirstblock =2 \expandafter \nprt@printtwo \nprt@numbertoprint \@empty \else \ifnum \thenprt@digitsfirstblock =3 \expandafter \nprt@printthree \nprt@numbertoprint \@empty \else \ifnum \thenprt@digitsfirstblock =0 \else \PackageError {numprint}{internal error}{}\fi \fi \fi \fi \fi \endgroup } \newcommand {\nprt@printafter }[1]{\csname ifnprt@##1@decimalfound\endcsname \ifnprt@addmissingzero \ifnum \csname thenprt@##1@digitsafter\endcsname =0 \expandafter \edef \csname nprt@##1@after\endcsname {0}\advance \csname c@nprt@##1@digitsafter\endcsname by 1\relax \fi \fi \ifx \nprt@replacenull \@empty \else \ifnum \csname thenprt@##1@digitsafter\endcsname =0 \expandafter \edef \csname nprt@##1@after\endcsname {0}\advance \csname c@nprt@##1@digitsafter\endcsname by 1\relax \fi \fi \fi \begingroup \edef \nprt@numbertoprint {\csname nprt@##1@after\endcsname }\ifx \nprt@numbertoprint \@empty \else \ifnprt@numsepfour \else \ifnum \csname thenprt@##1@digitsbefore\endcsname <5 \ifnum \csname thenprt@##1@digitsafter\endcsname <5 \nprt@shortnumbertrue \fi \fi \fi \ifx \nprt@replacenull \@empty \else \ifnum \nprt@numbertoprint =0 \nprt@shortnumbertrue \edef \nprt@numbertoprint {\nprt@replacenull }\fi \fi \ifnprt@shortnumber \nprt@numbertoprint \else \expandafter \nprt@printthree@after \nprt@numbertoprint \@empty \@empty \@empty \fi \fi \endgroup } \newcommand {\npdefunit }[3]{\if ##3* \else \expandafter \def \csname nprt@factor@##1\endcsname {##3}\fi \expandafter \def \csname nprt@unit@##1\endcsname {##2}} \newcommand {\nprt@ifundefined }[1]{\begingroup \expandafter \expandafter \expandafter \endgroup \expandafter \ifx \csname ##1\endcsname \relax \expandafter \@firstoftwo \else \expandafter \@secondoftwo \fi } \newcommand {\nprt@addto }[2]{\expandafter \nprt@ifundefined {##1}{}{\expandafter \addto \expandafter {\csname ##1\endcsname }{##2}}} \newcommand {\npaddtolanguage }[2]{\nprt@addto {extras##1}{\csname npstyle##2\endcsname }\nprt@addto {noextras##1}{\npstyledefault }} \newcommand {\npstyledefault }[0]{\npthousandsep {\,}\npdecimalsign {,}\npproductsign {\cdot }\npunitseparator {\,}\npdegreeseparator {}\npcelsiusseparator {\nprt@unitsep }\nppercentseparator {\nprt@unitsep }} \newcommand {\npstylegerman }[0]{\npthousandsep {\,}\npdecimalsign {,}\npproductsign {\cdot }\npunitseparator {\,}\npdegreeseparator {}\npcelsiusseparator {\nprt@unitsep }\nppercentseparator {\nprt@unitsep }} \newcommand {\npstyleenglish }[0]{\npthousandsep {,}\npdecimalsign {.}\npproductsign {\times }\npunitseparator {\,}\npdegreeseparator {}\npcelsiusseparator {\nprt@unitsep }\nppercentseparator {\nprt@unitsep }} \newcommand {\npstyleportuguese }[0]{\npthousandsep {.}\npdecimalsign {,}\npproductsign {\cdot }\npunitseparator {\,}\npdegreeseparator {}\npcelsiusseparator {\nprt@unitsep }\nppercentseparator {\nprt@unitsep }} \newcommand {\npstyledutch }[0]{\npthousandsep {\,}\npdecimalsign {,}\npproductsign {\cdot }\npunitseparator {\,}\npdegreeseparator {}\npcelsiusseparator {\nprt@unitsep }\nppercentseparator {}} \newcommand {\npstylefrench }[0]{\npthousandsep {~}\npdecimalsign {,}\npproductsign {\cdot }\npunitseparator {\,}\npdegreeseparator {}\npcelsiusseparator {\nprt@unitsep }\nppercentseparator {\nprt@unitsep }} \newcommand {\nprt@renameerror }[1]{\expandafter \def \csname ##1\endcsname {\PackageError {numprint}{This command has been renamed to\MessageBreak \string \np ##1}{In order to avoid problems with other packages and for consistency,this\MessageBreak command has been renamed in this version.}}} \newcommand {\tkz@getdecimal }[1]{\expandafter \@getdecimal ##1.\@nil } \newcommand {\CountToken }[1]{\c@pgfmath@countb 0 \expandafter \C@untToken ##1\@nil } \newcommand {\C@untToken }[0]{\afterassignment \C@untT@ken \let \CurrT@ken = } \newcommand {\C@untT@ken }[0]{\ifx \CurrT@ken \@nil \else \advance \c@pgfmath@countb by1 \expandafter \C@untToken \fi } \newcommand {\sagemath }[0]{\textsf {SageMath}} \newcommand {\inftyOverInfty }[0]{\ensuremath {\boldsymbol {\tfrac {\infty }{\infty }}}} \newcommand {\zeroOverInfty }[0]{\ensuremath {\boldsymbol {\tfrac {0}{\infty }}}} \newcommand {\zeroTimesInfty }[0]{\ensuremath {\small \boldsymbol {0\cdot \infty }}} \newcommand {\inftyMinusInfty }[0]{\ensuremath {\small \boldsymbol {\infty -\infty }}} \newcommand {\oneToInfty }[0]{\ensuremath {\boldsymbol {1^\infty }}} \newcommand {\zeroToZero }[0]{\ensuremath {\boldsymbol {0^0}}} \newcommand {\inftyToZero }[0]{\ensuremath {\boldsymbol {\infty ^0}}} \newcommand {\surfaceColor }[0]{violet} \newcommand {\surfaceColorTwo }[0]{redyellow} \newcommand {\sliceColor }[0]{greenyellow} \newcommand {\vector }[1]{\left \langle ##1\right \rangle } \newcommand {\sectionOutcomes }[0]{} \newcommand {\reserved@a }[2]{} \newcommand {\HyperFirstAtBeginDocument }[0]{\AtBeginDocument } \newcommand {\reserved@a }[1]{} \newcommand {\reserved@a }[2]{} \newcommand {\vnameref }[1]{\unskip ~\nameref {##1}\@vpageref [\unskip ]{##1}} \newcommand {\ref }[0]{\@ifstar \@refstar \T@ref } \newcommand {\pageref }[0]{\@ifstar \@pagerefstar \T@pageref } \newcommand {\nameref }[0]{\@ifstar \@namerefstar \T@nameref } \newcommand {\descriptionlabel }[1]{\hspace {\labelsep }\textbf {##1:}} \newcommand {\reserved@a }[2]{} \newcommand {\reserved@a }[0]{\AtBeginDocument } \newcommand {\reserved@a }[1]{} \newcommand {\reserved@a }[2]{}$