Sindbad~EG File Manager

Current Path : /home/beeson/public_html/WebMathXpert/documentation/
Upload File :
Current File : //home/beeson/public_html/WebMathXpert/documentation/Spec.dvi

����;� TeX output 2025.03.21:1730�������7
�����V�������۽��"V

cmbx10�WEB���MA��
�THXPER�T����)����s6�cmss8�1������k)�|{Ycmr8�MICHAEL��XBEESON����)���2���9�����e�K�`y

cmr10�1.���H�� �-�

cmcsc10�Intr��oduction����)���3�����BलW��*�eb�!�MathXp�Gert�!�is�a�W��*�eb-based�v���ersion�of�MathXp�Gert.�`�It�allo���ws�users�to�access����)���4�����6लMathXp�Gert�٬from�their�w���eb�bro�wser,���without�an�y�additional�٭soft�w�are.���This�do�Gcu-����)���5�����6लmen���t��#is�a��"tec�hnical�description�of�its��"arc�hitecture�and�implemen�tation,��in�tended�for����)���6�����6लin���terested�UUsoft�w�are�designers�and�programmers.����)���7�����BलW��*�eb�I>MathXp�Gert�is�I=comp�osed�of�t���w�o�I>parts:��The��!�':

cmti10�MathXp��}'ert��DEngine�,�~�whic���h�runs�on����)���8�����6लa��serv���er�and�do�Ges�not�in�teract�directly��with�users,��and�the�\clien�t",��whic�h�in�teracts����)���9�����6लwith�y�users.��The�Engine�do�Ges�all�the�mathematical�computations,���t���yp�esetting,���and����&���10�����6लpro�Gduces�߷(instructions�to�dra���w�߶the)�graphs.�	�All�in�teractions�߶with�the�user�are����&���11�����6लhandled���b���y���the�clien�t,��whic�h�is���an�ordinary�\fron���t-end",��in�v�olving�no���mathematical����&���12�����6लcomputations,�UUbut�simply�in���terface�programming�(in�PHP�and�Ja�v��q�ascript).����&���13�����BलAs�s`the�original�saauthor�of�MathXp�Gert,�z�I�sYha���v�e�s`prepared�b�oth�the�saEngine�and�the����&���14�����6लclien���t.��oIn���the�future�b�Goth�will�b�ecome�op�en-source�pro��8jects.��nI��van���ticipate�that�the����&���15�����6लEngine��can�b�Gecome�the�core�of�sev���eral�dieren�t�pro��8jects,��whic�h�are�not�discussed����&���16�����6लin���this�do�Gcumen���t.�J[MathXp�ert's���stated���purp�ose�is�to�\help���studen���ts�learn�algebra,����&���17�����6लtrigonometry��*�,��and��calculus."�D�It�will��b�Ge�natural�to�incorp�orate��MathXp�ert�as�one����&���18�����6लcomp�Gonen���t�UUof�w�ebsites�that�complemen�t�MathXp�Gert�with�other�learning�to�ols.����&���19�����BलOnly���if���someone�wishes�to�add�to�the�mathematical�capabilities�of�MathXp�Gert����&���20�����6लw���ould�qSit�b�Ge�qRnecessary�to�mo�dify�the�Engine.��I�qLthink�most�pro��8jects�qRthat�w���ould�use����&���21�����6लMathXp�Gert���w���ould���simply�comm�unicate�with�the���existing�Engine.�ADCompare�to�T���U>�'E���xX,����&���22�����6लwhic���h�Pis�a�complicated�program�that�needs�little�mo�Gdication,�Qwbut�there�are�man�y����&���23�����6लdieren���t�U�clien�t�U�programs�that�pro���vide�an�en���vironmen�t�making�U�it�con�v�enien�t�U�to�use����&���24�����6लT���U>�'E���xX.����&���25����������2�2.���OP�Ar��chitecture��O��Uver��rview����&���26�����BलW��*�eb�UUMathXp�Gert�is�based�on�a�clien���t-serv�er�UUarc�hitecture�as�follo�ws:����&���27���!J�����O���
!",�

cmsy10�����Y�IJThe�UU�MathXp��}'ert���Engine�,�or�for�short�just�the��Engine��runs�on�a�serv���er.����&���28��������O�ø����Y�IJThe�%�Engine�%�con���tains�that�part�of�MathXp�Gert's�co�de�%�that�p�erforms�%�calcula-����&���29�����Y�IJtions�UUand�mak���es�graphs.����&���30��������O�ø����Y�IJThe�UUEngine�do�Ges�not�directly�in���teract�with�a�user.����&���31��������O�ø����Y�IJThe�UUEngine�runs�un���til�purp�Gosefully�stopp�ed�or�restarted.����&���32��������O�ø����Y�IJThe�UUEngine�is�written�in�C�and�is�based�on�the�MathXp�Gert�source�co�de.����&���33��������O�ø����Y�IJThe�عEngine�غcan�handle�man���y�clien�ts�غsim�ultaneously�and/or�غsequen�tially��*�.�H>It����&���34�����Y�IJcomm���unicates�UUwith�the�clien�ts�via�TCP�so�Gc�k�ets,�as�describ�Ged�b�elo���w.����&���35���6ट<̉ff<�O[���#�f�cmti8�Date����:��XMarc�Îh�21,�2025.�������k�ٓ�Rcmr7�1����*��7
��������6ऱ2���,'MICHAEL���BEESON���V���������O�ø����Y�IJEac���h�":�client��of�the�";engine�is�a�w�a�y�for�the�user�";to�in�teract�with�MathXp�Gert.����&���36�����Y�IJIn�4fW��*�eb�MathXp�Gert,�:�the�4eclien���t�is�a�w�eb�bro�wser�4ewindo�w�(lo�Gcated�an�ywhere����&���37�����Y�IJon�UUthe�In���ternet).��� �1�����&���38��������O�ø����Y�IJThe��
clien���t�will�presen�t��do��}'cument�^windows��allo�wing�the�user�to�in�teract�with����&���39�����Y�IJMathXp�Gert��do�cumen���ts.��The��do�cumen�t��windo�ws��will�b�Ge�either��symb��}'olic��or����&���40�����Y���gr��}'aphic�al�,�K=corresp�Gonding�H�to�t���w�o�H�w�a�ys�H�of�viewing�do�Gcumen���ts�in�MathXp�Gert.����&���41��������O�ø����Y�IJBefore�k�a�k�do�Gcumen���t�is�initialized,�q�the�clien�t�will�k�use�\en�try�pages"�k�to�assist����&���42�����Y�IJthe��user��to�select�or�en���ter�an�appropriate�problem,�"�so�that�a�do�Gcumen���t�can����&���43�����Y�IJb�Ge�Y�initialized.�~�Th���us�eac�h�Y�session�has�a�pre-do�Gcumen���t�phase,���and�then�a����&���44�����Y�IJphase�q�of�q�in���teracting�with�the�do�Gcumen���t,�x�in�whic�h�q�the�problem�is�solv���ed�or����&���45�����Y�IJthe��graph��is�made�and�manipulated.�O4Then�that�session�is�o���v�er;�0for�the��next����&���46�����Y�IJproblem,�UUone�starts�o���v�er.����&���47��������O�ø����Y�IJThe���engine�and�the���clien���t�will�comm�unicate�via��messages�,�)=whic�h�are�dis-����&���48�����Y�IJcussed�UUb�Gelo���w.����&���49��������O�ø����Y�IJRendering���in�the�do�Gcumen���t�windo�ws�is�to���b�Ge�done�b�y�SV�G��graphics.� AAll����&���50�����Y�IJbro���wsers�UUare�able�to�render�SV�G.����&���51��������O�ø����Y�IJThe�UUSV���G�co�Gde�is�generated�b�y�C�co�Gde�in�the�Engine.��� �2�����&���52���.3�������3.�����Fur��UTther��fea�tures�of�the�ar��chitecture����&���53�����BलIn��this��section�w���e�sp�Gecify�some�MathXp�Gert-sp�ecic��features�of�the�Engine/clien���t����&���54�����6लrelations.����&���55���������O�ø����Y�IJA��single�.running�instance�of�-the��Engine��can�serv���e�man�y�clien�ts.��QThat�is����&���56�����Y�IJb�Gecause�ԑMathXp�ert�can�Ԓcreate�and�manage�man���y�do�cumen���ts;��0eac�h�one����&���57�����Y�IJcan��b�Ge�tagged�with��a��SessionId�.�}AEac���h�clien�t��(bro�wser�session)�op�Gens�one����&���58�����Y�IJdo�Gcumen���t.�7Eac�h��do�cumen�t��can��b�e�op�ened�(view���ed��and�manipulated)�as�a����&���59�����Y�IJsym���b�Golic��do�cumen�t��or��as�a�graphic�do�Gcumen�t.�Z�When��a�sym�b�Golic�do�cumen���t����&���60�����Y�IJis�v�op�Gen,�~�a�press�v�of�the��Gr��}'aph��button�will�op�Gen�another�bro���wser�windo�w�v�in����&���61�����Y�IJwhic���h�>�a�>�graph�of�the�curren���t�line�of�the�sym���b�Golic�do�cumen���t�will�>�b�e�displa���y�ed.����&���62�����Y�IJBut�e�actually��*�,�i�it�is�another�e�view�of�the�same�do�Gcumen���t.���The�user�can�op�Gen����&���63�����Y�IJanother�UUdo�Gcumen���t,�but�that�will�b�e�a�dieren���t�session.����&���64��������O�ø����Y�IJMathXp�Gert�lxhas�the�ly�Do��}'cument��data�structure.��0Eac���h�do�Gcumen�t�lxis�managed����&���65�����Y�IJb���y���the���Engine�on�b�Gehalf�of�a�particular�clien���t.��uThe�do�Gcumen�t���data�struc-����&���66�����Y�IJture�g�is�g�not�a���v��q�ailable�directly�to�the�clien���t.��$Instead,��fthe�clien�t�g�views�the����&���67�����Y�IJdo�Gcumen���t,�/�either�&}via�a�&|graphical�view,�or�via�&|a�sym���b�Golic�view.�b)The�Engine����&���68�����Y�IJresp�Gonds�1to�man���y�1messages�b�y�making�c�hanges�to�the�1do�Gcumen�t,�8Yand�then����&���69�����Y�IJcalling����SendSymb��}'olDo�cument��or����SendGr�aphDo�cument��to�send�a���resp�Gonse�to����&���70�����Y�IJthe��clien���t.���Eac�h�resp�Gonse��consists�of�SV���G�jgraphics�elemen�ts��sucien�t�to����&���71�����Y�IJdispla���y�i!the�whole�calculation�i"or�graph.��+The�exact�manner�of�displa���y�is�up����&���72�����Y�IJto�UUthe�clien���t.����&���73���6ट���ff<��͍�����h�1���s�In�Мprinciple,�яthe�clien�Ît�Нcould�b�<re�an�application�program�on�a�computer�or�phone;��1that�w�Îould��
�b�<re��Xthe�easy�w�Îa�y��J�,��Xfor�example,�to�mak�Îe�a�Mac�OS�v�ersion�of�MathXp�<rert.��
�r������h�2���s�The��reasons�for��c�Îho�<rosing�SV�G���graphics�are�as�follo�ws:�PwThe�clien�t�m�ust�ha�v�e��some�w�a�y�to���displa�Îy��=math�form�ulas�and�graphics.���SV�G��9co�<rde�is�device-indep�enden�Ît,��consists�of�text,��is�device-���indep�<renden�Ît,��Xand�supp�orted�b�Îy�all�mo�dern�bro�Îwsers.��������7
����������WEB���MA��Z�THXPER�T�����3����V���������O�ø����Y�IJThe��parser��is�part�of�the�Engine.��No�parsing�will�b�Ge�done�b���y�the�clien���t,����&���74�����Y�IJeither�&in�'PHP�or�the�bro���wser.�X
Only�strings�are�passed�b�Get���w�een�'Engine�and����&���75�����Y�IJClien���t.�q�(These�UUare�UTF-8�strings.)��� �3�����&���76��������O�ø����Y�IJIn���Windo���ws���MathXp�Gert,��5a�user�can�dene�a�function,��5whic���h�is�then�a���v��q�ail-����&���77�����Y�IJable��eto��dall�do�Gcumen���ts.��User-dened�functions�will�not�b�Ge�supp�orted��ein����&���78�����Y�IJW��*�ebMathXp�Gert.����&���79��������O�ø����Y�IJThe��JEngine�will�not�b�Ge�able�to�sa���v�e��Jor�op�en�MathXp�ert�do�cumen���ts.�K�F��*�or����&���80�����Y�IJbrevit���y��*�,�UUw�e�omit�discussion�of�the�reasons�for�this�decision.����&���81��������O�ø����Y�IJStrings��Wthat�are�displa���y�ed��Win�the�bro���wser�come�from�the��L��}'o�c�alizer�,�'Wwhic�h����&���82�����Y�IJis�_part�`of�the�Engine.���This�deliv���ers�natural-language�text�in�the��sele��}'cte�d����&���83�����Y���language�.�44The��zLo�Gcalizer��yis�describ�ed��ymore�fully��zb�elo���w.�44These�strings��yare����&���84�����Y�IJUTF-8�penco�Gded,�v�so�that�should�pb�e�the�default�penco�ding�used�b���y�pthe�in�ter-����&���85�����Y�IJface.�q�The�UULo�Gcalizer�is�discussed�more�fully�b�elo���w.����&���86��������O�ø����Y�IJThe�ÊEngine�Ëis�not�a�m���ulti-threaded�program.��fAlthough�it�can�sim���ultane-����&���87�����Y�IJously�mb�Ge�connected�to�m���ultiple�clien�ts,��it�can�therefore�resp�Gond�to�only�one����&���88�����Y�IJmessage�UUat�a�time.�q�Therefore�the�resp�Gonse�to�messages�m���ust�b�e�sp�eedy��*�.����&���89��������O�ø����Y�IJThe�n5Engine�is�in���tended�to�run�for�n4long�p�Gerio�ds�n5of�time�without�restarting.����&���90�����Y�IJIf���a�do�Gcumen���t�is���left�unattended�b�y�its�o�wner�for���long�enough�(presen�tly�an����&���91�����Y�IJhour),��"it�{�will�b�Ge�destro���y�ed,��#so�{�as�{�to�no�longer�o�ccup���y�memory�and�a�place����&���92�����Y�IJin�UUthe�hash�table.��� �4�����&���93���l\����Gܲ4.�����SV��UG��graphics�and�documents����&���94�����BलThe���purp�Gose���of�this�section�is�to�in���tro�Gduce�and�explain�the�division�of�resp�Gonsibil-����&���95�����6लities�d"b�Get���w�een�Engine�d#and�clien�t�with�regard�to�the�d#displa�y�of�sym�b�Golic�do�cumen���ts.����&���96�����6लIn�`particular,���some�`
(but�not�all)�of�the�messages�that�are�used�to�comm���unicate����&���97�����6लab�Gout�œdo�cumen���ts�are�discussed.�‚Some�of�the�p�oin���ts�in�Ŕthis�section�are�illustrated����&���98�����6लin�UUthe��ParseA���ndDisplay��demo,�whic���h�is�a�v��q�ailable�at����&���99�������6��'��<x

cmtt10�https://www.mathxpert.org/ParseAndDisplay.php�.����#P��100����,��6ल4.1.��Co�Q�ordinates.��The���Engine�main���tains�a���xed�co�Gordinate�system�for�sym�b�Golic����#P��101�����6लdo�Gcumen���ts,���called���\pap�yrus���co�ordinates",���and���uses�just�t���w�o���fon�t���sizes,�\tenp�Goin�t"����#P��102�����6लand�HA\eigh���tp�Goin�t",�J�in�accordance�with�H@the�usual�con�v�en�tions�for�H@t�yp�Gesetting�mathe-����#P��103�����6लmatics.�g�The��Vactual�fon���t�size�used��Wfor�displa�y�is�the�resp�Gonsibilit�y��Wof�the�in�terface,����#P��104�����6लwhic���h�_qcon�trols�it�b�y�setting�or�resetting�the�SV�G�_nViewBo�x.��The�P�arseAndDispla�y����#P��105�����6लdemo�v9illustrates�v:this�with�buttons�for��L��}'ar�ger��*T��;�yp�e�v9�and��Smal���ler�T��;�yp��}'e�.��tP���ap�yrus�v9co-����#P��106�����6लordinates��#are��$\square",��`i.e.,��a16�units�horizon���tal�and�v���ertical�is�the�same�distance�on����#P��107�����6लthe�$�pap���yrus,�.Wand�hence�should�$�b�Ge�on�the�user's�screen�also.�a�These�\units"�are�CSS����#P��108�����6लpixels,�UUwhic���h�are�in�tended�b�y�CSS�to�b�Ge�ab�out�the�same�size�on�ev���ery�device.����#P��109�����BलAs��an��example,�hwhen�the�user�selects�a�rectangle,�hthe�in���terface�m�ust��con�v�ert�the����#P��110�����6लrectangle��0to��1pap���yrus�co�Gordinates�b�efore��1sending�a��Sele��}'cte�dR�e�ctangle��0�message�to�the����#P��111�����6लEngine.�Y]It���is���the�resp�Gonsibilit���y�of�the�in�terface�to���handle�the�con�v�ersions�b�Get�w�een����#P��112���6ट
���ff<��͍�����h�3���s�SV�ÎG�l�graphics�l�elemen�ts�l�can�b�<re�treated�as�one�string,���con�Îtaining�newline�c�Îharacters;��^suc�h�l�a��
�string�\�lo�<roks�lik�Îe�an�arra�y�of�\�strings�to�the�h�uman�ey�e,�t�but�it�is�just�a�string.���P�assing�SV�G�\�graphics���this��Xw�Îa�y�through�a�so�<rc�k�et�demonstrated�in�the�P�olygonDemo�pro�<rof-of-concept�program.��
�r������h�4���s�There�H�is�a�H��destr���oyDo�cument�H޹message�that�a�clien�Ît�could�send�the�Engine,�e�but�the�in�Îterface���nev�Îer�(�sends�it.���There�is�no�go�<ro�d�(�w�a�y�to�tell�on�the�clien�t�side�(�when�the�PHP�(psession�is�closing.���Sending��Xit��Ywhen�the�bro�Îwser�windo�w��Xcloses�is�not�righ�Ît,��since��Symb���olDo�c.php��X�closes�ev�Îery�time�a���message��Xneeds�to�b�<re�sen�Ît,�b�y�p�<rosting�a�hidden�form;�then�it�is�reop�ened�to�pro�cess�that�form.�����!٠�7
��������6ऱ4���,'MICHAEL���BEESON���V������6लthe��w\pap���yrus��xco�Gordinates"�used�b���y�the�Engine�and�lo�Gcal�co�ordinates��win�the�user's����#P��113�����6लwindo���w.�q�The�UUEngine�kno�ws�nothing�ab�Gout�lo�cal�co�ordinates.����#P��114�������6ल4.2.��F��
�on��9ts.��The�8�Engine�do�Ges�not�sp�ecify�the�fon���ts�8�to�b�e�used�for�displa���y�of�form�ulas;����#P��115�����6लthis���should���tec���hnically�b�Ge�an�in���terface�matter.�S5Ho�w�ev�er,��the�c�hoice���is�limited,��since����#P��116�����6लthe�l�fon���ts�m�ust�l�b�Ge�a�v��q�ailable�on�all�l�bro�wsers�and�m�ust�b�Ge�l�suitable�for�mathematics.����#P��117�����6लIn�_0particular,���the�UTF-8�c���haracters�for�parts�of�large�_1in�tegral�signs�v��q�ary�widely����#P��118�����6लin�)�size�)�and�shap�Ge�from�one�fon���t�to�another.��W��*�e�ha���v�e�tested�)�the�generated�SV���G����#P��119�����6लco�Gde�e�with�Times�New�Roman�and�e�Cam���bria�Math,���whic�h�are�not�v�ery�dieren�t.����#P��120�����6लW��*�e���used���Times�New�Roman.��ZSee�the�P���arseAndDispla�y���demo�co�Gde,�(=whic�h���can����#P��121�����6लeasily��b�Ge��edited�to�use�sev���eral�dieren�t��fon�ts�listed��there,�*�so�the�curious�can�see�for����#P��122�����6लthemselv���es.�Q�Of���course,�9the�in�terface�is�free���to�use�other�fon�ts�for���text�not�generated����#P��123�����6लb���y�UUthe�Engine.����#P��124���?��B��Changing�܈typ��}'e�܉size�.�^�The��GEngine�uses��Honly�t���w�o��Gfon�ts�(12��Hp�Goin�t�and�8��Hp�Goin�t;��the����#P��125�����6लlatter�v�is�used�v�in�exp�Gonen���ts�and�subscripts).��MChanging�the�visible�t�yp�Ge�v�size�is�done����#P��126�����6लb���y��pthe�in�terface,��kusing��qa�concept�of�SV�G��Ucalled�the�ViewBo�x.�M&This�is�demonstrated����#P��127�����6लb�Goth��Uin��ParseA���ndDisplay.php��V�and�in��Symb��}'olicDo�c.php�.���Changing�the��Ut���yp�Ge�size�b�y����#P��128�����6लc���hanging���the�ViewBo�x�of���the��<svg>��elemen�ts�do�Ges�not�c�hange�their�lo�Gcation,��e.g.,����#P��129�����6लthe��reason�strings�will�still��b�Gegin�in�the�same�place.��kThat�is�dieren���t�than�what����#P��130�����6लhapp�Gens��xif�y���ou�just�use�the��yusual�k�eys�to�increase�size�in�the�bro�wser;��
then�if�size����#P��131�����6लis�Iincreased,�Kzthe�Ireasons�mo���v�e�to�Ithe�righ�t�Iand�p�Gerhaps�o-screen.�m�There�are�some����#P��132�����6लfurther��subtleties�to��c���hanging�t�yp�Ge�size�that��are�not�discussed�here,�.eas�this�is�an����#P��133�����6लin���terface��issue.���Our�p�Goin�t��
here�is�mainly�that�it��is��an�in���terface�issue:�g8the�Engine����#P��134�����6लdo�Ges��not�kno���w�what��the�curren�t�t�yp�Ge�size�is,�4�although�it��do�es�kno���w�where�ev�ery����#P��135�����6लform���ula�UUw�ould�b�Ge�if�the�t�yp�Ge�size�w�ere�the�default.����#P��136�������6ल4.3.��The��7do�Q�cumen��9t�as�the�in�terface�sees��8it.��F��*�rom��sthe��tin���terface's�viewp�Goin�t,����#P��137�����6लthe��do�Gcumen���t�(at��an�y�giv�en�time)�consists�of��a�n�um�b�Ger�of��<svg>��elemen�ts.�[These����#P��138�����6लare�Rlab�Geled�with��class�Q�and��id�.���F��*�or�example,�=�class��line��and�id��line0��w���ould�b�Ge����#P��139�����6लthe��sSV���G��dgraphics��tfor�the�displa�y�of��tthe�form�ula�in�line��t0,��:i.e.,��;the�problem.�#"Class����#P��140�����6��reason��G�is�for�the�justications�(or�reasons)�for��Fthe�steps.�4�The�p�Gossible�classes�are����#P��141�����6लgiv���en�Q(precisely�Q)and�completely�in�a�table�far�b�Gelo���w;�R�for�no�w�Q(w�e�are�Q)just�explaining����#P��142�����6लgeneral�Wprinciples.�v�But�Wfor�example,�Wpthere�are�classes��assumption�,�Wp�comment�,��hint�,����#P��143�����6��menuitem�,�UU�matherror�,�and�others.����#P��144�����BलWhen���a���do�Gcumen���t�is�b�Geing�view���ed�graphically��*�,��-it�will�ha���v�e���other��<svg>��elemen���ts,����#P��145�����6लcon���taining��Gco�Gde��Hto�dra�w�the��Haxes,�A�the�title,�A�the�tic�ks,�A�the�axis�lab�Gels,�the�tic���k����#P��146�����6लlab�Gels,�'�and�ythe�zgraph�pap�er.�^�The��<svg>�y�elemen���ts�generated�b���y�the�Engine�all�ha���v�e����#P��147�����6लabsolute�'p�Gositioning,��meaning�that�they�will�b�e�placed�at�the�lo�cations�sp�ecied�b���y����#P��148�����6लthe�3MEngine�relativ���e�to�least�ancestor�with�3Nrelativ�e�or�absolute�p�Gositioning.�foIt�is�the����#P��149�����6लin���terface's��.resp�Gonsibilit�y��-to�place�these��<svg>��elemen���ts�prop�Gerly��*�.��PThey�can�easily����#P��150�����6लb�Ge��manipulated��b���y�Ja�v��q�ascript�using��the�DOM��mo�Gdel.��HF��*�or�example,�?�assumptions����#P��151�����6लand�(dhin���ts�(eare�generated�with��display:none�;���when�it�is�desired�to�displa���y�them,����#P��152�����6लthey�UUare�cloned�and�the�clone�is�giv���en��display:block�.����#P��153�����6ल4.4.��Do�Q�cumen��9t��vcreation.��A���do�Gcumen���t���is���created�at�the�rst�comm���unication�from����#P��154�����6लthe���in���terface.��cThat�allo�ws�the���Engine�to�allo�Gcate�a�heap�for�that�do�Gcumen���t�(eac�h����#P��155�����6लdo�Gcumen���t���has�its�o�wn�heap),��so�memory�is�a�v��q�ailable.���That�heap�can�b�Ge�used�im-����#P��156�����6लmediately��*�,�>=but��b�Gefore�the��do�cumen���t�can��b�e�used�to��mak���e�graphs�or�calculations,����#P��157�����6लthe��Ein���terface�or�Engine�m�ust�sp�Gecify�a��topic��and�a��pr��}'oblem�;��the�problem�m�ust�parse����#P��158�����6लand���b�Ge���\c���hec�k�ed"�as�appropriate�for���the�topic.�i7Eac�h�topic�is�either���a�graphics����#P��159������6���7
����������WEB���MA��Z�THXPER�T�����5����V������6लtopic�+2or�+1a�sym���b�Golic�topic;�9=in�Windo���ws�MathXp�Gert,�3�there�w���ere�corresp�Gondingly�t���w�o����#P��160�����6लkinds��xof��wdo�Gcumen���ts.�5/In�W��*�eb�MathXp�ert,���there��wis�only�one�kind�of�do�Gcumen���t,���but����#P��161�����6लa�6�do�Gcumen���t�can�b�e��viewe��}'d��sym���b�olically�or�graphically��*�.�g�The�in���terface�has�t�w�o�main����#P��162�����6लles,�+S�SymbolicDoc.php� Ҳand��GraphDoc.php�,�to�pro���vide�these�t�w�o� �views.�`FBefore�the����#P��163�����6लtopic�@5and�@6problem�are�selected�and�c���hec�k�ed,�Dothe�do�Gcumen�t�@5is�said�to�b�Ge�\uninitial-����#P��164�����6लized."�_vAfter�dan�cinitial�in���teraction�with�the�in�terface,�)aduring�whic�h�the�do�Gcumen�t�is����#P��165�����6लinitialized,�}the��AEngine��Bwill�nally�call�either��sendGr��}'aphDo�cument��or��B�sendSymb�ol-����#P��166�����6��Do��}'cument�,�/and�%rthe�%sresulting�cascade�of��<svg>��elemen���ts�will�b�Ge�sen�t�%sto�the�bro�wser����#P��167�����6लfor�UUdispla���y��*�.����#P��168���Q썑6ल4.5.��Up�Q�dating���a���do�cumen��9t.��F��*�rom��rthe�in���terface's�p�Goin�t�of�view,�U�these��<svg>����#P��169�����6लelemen���ts��are�\blobs"�with�a�kno�wn�size��and�p�Gosition�(relativ�e�to�their�paren�t),�'�and����#P��170�����6लlab�Geled���with�class���and�id�and�other�CSS���and�SV���G�prop�Gerties�suc���h���as��display�.����#P��171�����6लWhile���it���is�certainly�p�Gossible�for�skilled�Ja���v��q�ascript�programmers�to�manipulate����#P��172�����6लthem�Lin�Mmore�detail,�Nthe�plan�w���e�follo�w�ed�is�Mthat�the�Engine�creates�these�elemen���ts����#P��173�����6ल(including�� colors,���etc.)�^)and��!the�in���terface�just�displa���ys�them�at�the�righ���t�time�and����#P��174�����6लplace.�o�If�O�the�user�w���an�ts�O�to�c���hange�the�graph�line�color�to�purple,�P�for�example,�just����#P��175�����6लtell�F)the�F(Engine�to�do�it,�I2and�the�whole�do�Gcumen���t�will�b�Ge�redra���wn.�l�More�explicitly��*�,����#P��176�����6लthe��Engine��will�send�SV���G���co�Gde�for�the�whole�do�Gcumen���t�to�the�clien���t�PHP���le,���whic�h����#P��177�����6लwill�UUsend�the�SV���G,�as�w�ell�as�a�few�lines�of�Ja�v��q�ascript,�to�the�bro�wser.����#P��178�����BलA�UUsym���b�Golic�do�cumen���t�is�up�dated����#P��179���������O�ø����Y�IJafter�UUtaking�the�next�step�of�a�computation.����#P��180��������O�ø����Y�IJin�UUresp�Gonse�to�the��Undo��command.����#P��181��������O�ø����Y�IJwhen�UUthe�user's�windo���w�c�hanges�width.����#P��182�����6लThe��*do�Gcumen���t�do�es�not�need�to�b�e�up�dated��)to�increase�or�decrease�the�t���yp�e�size,����#P��183�����6लsince���the�Engine���do�Ges�not�ev���en�kno�w���ab�Gout�the�t�yp�Ge�size.�'�It�do�es���not�need�to����#P��184�����6लb�Ge��;up�dated��<to�displa���y�a�hin���t�or�the�assumptions,���since�those�elemen���ts�are�already����#P��185�����6लpresen���t���(with����display:none�),���so�Ja�v��q�ascript���can�displa�y���them�on�demand�without����#P��186�����6लcomm���unicating�UUwith�the�Engine.����#P��187�����BलWhen��the�Engine�up�Gdates�a�graphical�do�cumen���t,��similarly�SV�G��graphics�will�b�Ge����#P��188�����6लsen���t�IJto�the�clien�t.�M�SV�G�Igraphics�IKto�redra�w�the�whole�graph�will�b�Ge�sen�t.�M�That����#P��189�����6लwill��uhapp�Gen,��~for�example,�if�the��vuser�clic���ks�buttons�to�double�or�halv���e�the�v���ertical����#P��190�����6लor��horizon���tal�range�of�the��graph,�1�or�they�select�a�rectangle�and�then�clic���k��Dr��}'aw�;����#P��191�����6लor��Gthey��Fc���hange�the�v��q�alue�of�a�parameter;��?or�if�they�c���ho�Gose�to�adjust�the�colors�or����#P��192�����6लgraph�UUpap�Ger.����#P��193�����BलIn�w�Windo���ws�MathXp�Gert,��"there�is�a�w��Hand��to�ol�that�p�ermits�w�dragging�the�graph.����#P��194�����6लThe��2graph�is�redra���wn�on�ev�ery�mouse-mo�v�e.�9^That�w�on't�w�ork�o�v�er�the�In�ternet.����#P��195�����6लInstead,�>�the�9graph�is�actually�three�times�the�visible�linear�dimensions,�so�the�user����#P��196�����6लcan���drag�the���graph�without�calling�the�serv���er.��lThen,��Zon�mouse-up,�the���Engine�is����#P��197�����6लnotied��of�the�new�p�Gosition,��=and�at�that�p�oin���t�recalculates�the�three-times-larger����#P��198�����6लgraph.����#P��199���Q썑6ल4.6.��Line�	�breaking.��Windo���ws��MathXp�Gert�could�break�lines�that��
w�on't�t�in�the����#P��200�����6लwindo���w.�q�But�UQthis�UPfeature�is�not�implemen�ted�in�W��*�eb�MathExp�Gert.�q�One�reason�for����#P��201�����6लthat�0�is�0�that,�7�without�line�breaks,�7�the�redispla���y�on�resizing�the�bro���wser�windo�w�0�can����#P��202�����6लb�Ge��6handled��5lo�cally��*�.��jIt�is��6only�necessary�to�adjust�the�starting��
�b>

cmmi10�x�-co�Gordinate�of�the����#P��203�����6लreason��strings.��But�if��line�breaks�w���ere�implemen�ted,��the��breaks�w�ould��c�hange�on����#P��204�����6लresize,�z+so�r�the�Engine�w���ould�ha�v�e�to�re-send�the�whole�do�Gcumen�t;���and�the�c�hanged����#P��205�����6लparts�cw���ould�c

ic�k�er.���Moreo�v�er,�f|and�I�c
think�more�c
imp�Gortan�tly��*�,�f|it's�dicult�c
to�select����#P��206������M'��7
��������6ऱ6���,'MICHAEL���BEESON���V������6लa��mathematical��expression�that�extends�across�a�line�break,��and�it's�not�dicult�to����#P��207�����6लscroll�UUthe�bro���wser�windo�w�horizon�tally�to�view�a�line�that�is�to�Go�long�to�t.����#P��208���S������5.��̖	�The��Localizer����#P��209�����BलAs�Gmof�Septem���b�Ger�2023,���Windo�ws�MathXp�Gert�ran�in�English,���F��*�renc�h,���Spanish,����#P��210�����6लItalian,�=and���German.�VZIn�No���v�em�b�Ger���2023,�I���con�v�erted���all���those�le�to�UTF-8.�VZIn����#P��211�����6लF��*�ebruary���2024,�X�I��mused���ChatGPT�to�translate���the�les�storing�natural-language����#P��212�����6लstrings���in���to�Dutc�h.�BYThis�w�as�more���time-consuming�that�I���originally�hop�Ged;���Chat-����#P��213�����6लGPT��w���ould��=then��>only�do�translations�in�c���h�unks��=of�50�to�100�strings.�@�I��sp�Geak�Dutc���h,����#P��214�����6लso���I���could���c���hec�k�the���translations.�3USometimes�it�balks�at�a�longer�input,��vsometimes�it����#P��215�����6लjust��3mak���es��4mistak�es�(with�the�format��4of�the�strings).�BgIn�April-Ma�y�2024,��ChatGPT����#P��216�����6लtranslated���MathXp�Gert�in���to���Chinese.�S�These�translations�ha�v�e���not�b�Geen�c�hec�k�ed�b�y����#P��217�����6लa�UUnativ���e�sp�Geak�er.��qǟ� �5�����#P��218���T�����R�6.��ٷp�Messa��ges����#P��219�����BलThe��comm���unication�b�Get�w�een�the��Engine�and�the�clien�ts�is�b�y��means�of�messages����#P��220�����6लsen���t��do�v�er�so�Gc�k�ets.�y�Eac�h�clien�t��cin�teracts�with�the�Engine��cab�Gout�one�MathXp�ert����#P��221�����6लdo�Gcumen���t,�%
whic�h��is���main�tained�b�y�the���Engine.�dFThe�clien�t���sends�messages�to�the����#P��222�����6लEngine,�ԛand���in�resp�Gonse���the�Engine�up�Gdates�the�do�cumen���t,�ԛand�then���sends�the����#P��223�����6लclien���t�ihSV�G�i!graphics�sucien�t�to�presen�t�the�en�tire�do�Gcumen�t�iito�the�user.��This����#P��224�����6लapproac���h���p�Germits���the�Engine�to�mak���e�short,�Ȭrapid�resp�Gonses�(th���us�remaining�free����#P��225�����6लto�1]in���teract�with�other�clien�ts),�h^and�also�enables�clien�t�pages�to�a�v�oid�needing�to����#P��226�����6लretain��information��ab�Gout�the�do�Gcumen���t.�_�(A��few�exceptions�to�this�principle�will�b�Ge����#P��227�����6लdiscussed�UUb�Gelo���w.)����#P��228���&���6ल6.1.��Ov��9erview��Tof�messages.����#P��229���cC�����O�ø����Y�IJAll�h�comm���unication�b�Get�w�een�the�Engine�and�h�clien�t�is�done�b�y�sending�UTF-8����#P��230�����Y�IJstrings�UUthrough�so�Gc���k�ets.����#P��231��������O�ø����Y�IJMessages��%from�the��$clien���t�to�the�Engine�are�either��r��}'e�quests��%�or��r�esp�onses��%�or����#P��232�����Y���notic��}'ations�.����#P��233��������O�ø����Y�IJResp�Gonses��:supply�information��;requested�b���y�the�engine,��se.g.,��tthe�argumen�t����#P��234�����Y�IJof�UUan�op�Geration,�as�in��A��}'dd���what�to�b�oth�sides�of�the�e�quation?����#P��235��������O�ø����Y�IJNotications��require�no��resp�Gonse�(other�than�a�formal�\ok").�[+F��*�or�example,����#P��236�����Y�IJthe���title���of�a�graph�has�b�Geen�mo���v�ed���to�a�new�p�Gosition,��}or�a�parameter����#P��237�����Y�IJincremen���t��Dhas��Cb�Geen�c�hanged.�U(T��*�ec�hnically�,�{these��Care��D\Ajax�messages",�zsen�t����#P��238�����Y�IJb���y�UUXHR�or�the��fetch��API�without�closing�the�bro�wser�windo�w.)����#P��239��������O�ø����Y�IJRequests��ask�the��engine�to�do�something,�G?e.g.,�apply�a��certain�op�Geration����#P��240�����Y�IJto��|the��}curren���tly�selected�form�ula,���or�tak�e��}one�autostep,���or�\undo".�J=These����#P��241�����Y�IJusually��9require�the�screen�to�b�Ge�redra���wn,��so�after�up�dating�the�do�cumen���t�in����#P��242�����Y�IJthe��4Engine's��5memory��*�,�(lthe�Engine�calls��sendGr��}'aphDo�cument��or��4�SendSym-����#P��243�����Y���b��}'olDo�cument�.����#P��244��������O�ø����Y�IJGenerally�#�men���u�#�items�in�MathXp�Gert�corresp�ond�#�to�requests,�-�but�not�ev���ery����#P��245�����Y�IJrequest�UUcorresp�Gonds�to�a�men���u�item.����#P��246��������O�ø����Y�IJEv���ery�UUmessage�has�a��name��and�a��p��}'ar�ameter�.�q�Both�UUare�UTF-8�strings.����#P��247���6ट
s��ff<��͍�����h�5���s�It�]2is�]3not�the�case�that�y�Îou�can�just�giv�Îe�ChatGPT�]ten�large�les�to�translate�and�b�<re�done�with��
�the��next�language.��RChatGPT��itself�is�quite�adaman�Ît�that��it�is�for�in�teractiv�e��use,�Afor�con�v�ersations,���not��7for��8batc�Îh�translation.��But�it�do�<resn't�remem�Îb�er��7the�past,���so�y�ou�can��8ha�v�e�a�long�series��8of�ft�y-���line��Xtranslations,�and�it�nev�Îer�complains,�hey��J�,�y�ou�are�actually�doing�batc�h�translations!�����b)��7
����������WEB���MA��Z�THXPER�T�����7����V���������O�ø����Y�IJSome���messages���are�\pre-do�Gcumen���t",��meaning�b�efore�the�do�cumen���t���is�ini-����#P��248�����Y�IJtialized��Qb���y�a�c�hoice�of�topic�and�problem,��and�c�hec�king�that�the�problem����#P��249�����Y�IJts���the���topic.��SResp�Gonses�to�suc���h�messages�should�go�to�a�PHP��jpage�that����#P��250�����Y�IJis�G�not�G�designed�to�displa���y�a�do�Gcumen���t,�J�but�to�assist�in�getting�a�do�Gcumen���t����#P��251�����Y�IJprepared.����#P��252��������O�ø����Y�IJOther�̿messages��are�\p�Gost-do�cumen���t",��meaning�̿that�the�resp�Gonse�should�go����#P��253�����Y�IJto�Ʃa�ƨpage�designed�to�displa���y�a�do�Gcumen���t,��either�graphically�(lik���e��Gr��}'aph-����#P��254�����Y���Do��}'c.php�)���or���sym���b�Golically�(lik�e��Symb��}'olDo�c.php�).�,�The���resp�Gonse�to���suc�h�a����#P��255�����Y�IJmessage��will�b�Ge��SV���G��graphics�sucien�t�to�displa�y�the��calculation�or�graph.����#P��256���w���Y�IJ6.2.��Sym��9b�Q�olic�n�and�Graphical�Views.��Eac���h�ڳsession�with�ڲW��*�eb�MathX-����#P��257�����Y�IJp�Gert��lwill�b�egin�with��ksome�pre-do�cumen���t�messages,�-�allo�wing�the�user�to����#P��258�����Y�IJselect�f�a�f�topic�and�select�or�en���ter�a�problem.��`Then�either�a�sym���b�Golic�or����#P��259�����Y�IJgraphical��}view�of��|the�do�Gcumen���t�will�b�e�initiated�b���y��|an�appropriate�message.����#P��260�����Y�IJThere�-�ma���y�b�Ge�sev�eral�w�a�ys�to�arriv�e�at�a�-�topic�and�problem,�5�dep�Gending�on����#P��261�����Y�IJwhether���the���user�had�a�problem�in�mind�to�b�Gegin�with,��>or�w���an�ts���to�use�a����#P��262�����Y�IJproblem��Vfrom��Uthe�MathXp�Gert�Problem�Library��*�,��Uor�p�ossibly�to�edit��Ua�library����#P��263�����Y�IJproblem.��5Whatev���er�j�the�sequence,�p.ev�en�tually�a�do�Gcumen�t�will�b�Ge�initiated;����#P��264�����Y�IJafter�UUthat�the�messages�sen���t�will�b�Ge�\p�ost-do�cumen���t"�messages.����#P��265�����e�IJGenerally�^�sp�Geaking,��Rfrom�^�a�sym���b�olic�view�^�one�con���tin�ues�a�^�calculation����#P��266�����Y�IJto���solv���e���a�problem,���while�from�a�graphical�view,���one�manipulates�a�graph����#P��267�����Y�IJusing��v��q�arious��to�Gols.�Z�There�is�an�imp�Gortan���t�exception�to�this�w���ork�
o�w:�N�the����#P��268�����Y���Gr��}'aph����button,���whic���h�app�Gears�in���a�sym�b�Golic�view,���but�leads�to���a�graphical����#P��269�����Y�IJview.���That���button�op�Gens�a�new���bro���wser�tab�with�a�graphical�view.��� �6��	�3�The����#P��270�����Y�IJoriginal��tab��is�still�op�Gen�and�the�sym���b�Golic�calculation�can�b�Ge�con���tin�ued��in����#P��271�����Y�IJthat�UUtab.����#P��272�����6ल6.3.��Use�TRof�Ajax�in�requesting�information�from�the�user.��Before���reading����#P��273�����6लthis���section,�
�the�user�should�ha���v�e���a�go�Go�d���understanding���of�the�basic�arc���hitecture����#P��274�����6लdescrib�Ged��&ab�o���v�e,�band�should��%ha�v�e�read�some��%of�the�PHP��co�Gde�in�Sym���b�GolicDo�c.php;����#P��275�����6लotherwise�UUthis�section�ma���y�seem�prett�y�arcane.����#P��276�����BलIt��ma���y��happ�Gen�that�the�Engine�is�unable�to�satisfy�a�request.�'�F��*�or�example,����#P��277�����6लconsider�z�the�z�request��p��}'arseA���ndDisplay�,��whic���h�pro�vides�z�a�string�in�the�parameter����#P��278�����6लand���hop�Ges���to�receiv���e�SV�G���graphics�to���displa�y�the�form�ula�in���t�w�o-dimensional�form.����#P��279�����6लP���erhaps�M?the�form�ula�pro�vided�in�the�parameter�migh�t�fail�M@to�parse.��Then�the�request����#P��280�����6लcannot��zb�Ge�satised.�;6Then�the��yEngine�sends�an�error�message,��Cwhic���h�is�an��<svg�?�>����#P��281�����6लelemen���t�UUof�class��parserError�.����#P��282�����BलAs��gmen���tioned,�"�the�Engine�ma�y��fsometimes�need�to�request�more�information����#P��283�����6लfrom���the���clien���t,���e.g.,�\Add�what���to�b�Goth�sides?"�:The�comm���unication�b�Get�w�een���the����#P��284�����6लEngine���and���the�clien���t�is�not�symmetric:��the�Engine�cannot�send�a�message�to�the����#P��285�����6लclien���t�ѯin�the�Ѱsame�w�a�y�that�the�clien�ts�Ѱsends�a�message�to�the�Engine,��since�it�is�the����#P��286�����6लEngine�dtthat�main���tains�the�do�Gcumen�t.�!|So�when�a�(mathematical)�op�Geration�needs�an����#P��287�����6लargumen���t�(from�the�user),�&�the�Engine�con�v�eys�this�request�in�the�form�of�an��<svg>����#P��288�����6लelemen���t��qof��rclass��needsargprompt�,��xwith�an�id�that�enco�Gdes�additional�information����#P��289�����6लab�Gout��Fthe��Grequest.���The�clien���t,��Bwhose�job�it�is�to�displa���y�all�the�SV���G��,co�Gde�it�has,����#P��290�����6लbut���only���when�and�as�appropriate,��Plo�Goks�for�elemen���ts�of�class��needsargprompt�,��Qand����#P��291���6ट$ىff<��͍�����h�6���s�F��J�or��-example,��5�Symb���olicDo�c.php��implemen�Îts�that��,button�in�Ja�Îv��ascript,��6b�y�submitting��,a�hidden��
�form�Z�to�Z��(�C�scmtt8�PHP�����ff�Ў�^SELF�;�the�pro�<rcessing�of�that�form�sends�a��gr���aphButton��message�to�the�Engine,�|Dbut���with��Xco�<rde�causing�the�Engine's�resp�onse�to�b�e�sen�Ît�to�a�new�tab.�����uI��7
��������6ऱ8���,'MICHAEL���BEESON���V������6लif��one�is�presen���t,��Wit�gets�the�user's��immediate�atten�tion�to�that�request�b�y�putting����#P��292�����6लup�UUa�mo�Gdal�dialog,�allo���wing�the�user�to�supply�the�requested�information.����#P��293�����BलWhen�88the�user�87submits�data�in�that�dialog,�>
the�clien���t�sends�a��che��}'ckA���r�g�88�message����#P��294�����6लto��
the��Engine.���This�message�is�sen���t�via�Ajax,��so�a�reply�can�b�Ge�receiv���ed�without����#P��295�����6लgiving�'up�&con���trol�in�the�Ja���v��q�ascript�co�Gde.��<The�Engine�can�decide�if�the�prop�Gosed����#P��296�����6लargumen���t�C-is�acceptable�or�not,�F�and�if�not,�F�supply�an�error�message.�k�The�clien�t�can����#P��297�����6लreceiv���e���this���message�and�displa���y�the�error�message�without�closing�the�dialog,��alet����#P��298�����6लalone��the��whole�page.�@�Finally�when�the�argumen���t�is�acceptable�,�߁the�clien���t�sends�an����#P��299�����6��exe��}'cOpWithA���r�g�'²message�'�to�the�Engine,�0�whose�parameter�includes�the�commandID����#P��300�����6लof�g�the�op�Geration,�lLand�the�g�text�en���tered�as�the�arg�b�y�the�user�(whic�h�w�e�no�w�kno�w����#P��301�����6लwill�{�parse�and�{�b�Ge�an�acceptable�argumen���t�to�that�op�Geration).��� �7����The�page�can�then����#P��302�����6लdie�d�in�p�Geace,�h�kno���wing�that�the�op�eration�can�d�at�least�b�e�tried,�h�and�d�new�SV���G�d�co�de����#P��303�����6लfor�Bthe�Ado�Gcumen���t�will�come�in�resp�Gonse�to�the��exe��}'cOpWithA���r�g��message.�\�If�the�Buser����#P��304�����6लcancels���out�of�the�dialog,���no�message�is�sen���t�to�the�Engine,�and�Ja���v��q�ascript�has�to����#P��305�����6लno��longer�highligh���t�the�selected��rectangle,���just�as�if�the�user�had�clic���k�ed��outside�the����#P��306�����6लmen���u.����#P��307���<a�����\�7.����z�Components��of�the�Engine����#P��308�����BलMathXp�Gert���w���as���already�w�ell-organized�in�to�comp�Gonen�ts.�Q�These�ma�y���b�Ge�group�ed����#P��309�����6लas�UUfollo���ws:����#P��310����q�����O�ø����Y�IJThe����Op��}'er�ations��²library��*�,��\whic���h�con�tains���co�Gde�for�the�mathematical�op�Ger-����#P��311�����Y�IJations�2}that�can�2~b�Ge�in���v�ok�ed�2}to�adv��q�ance�a�calculation�one�more�step,�i�th���us����#P��312�����Y�IJup�Gdating�UUSym���b�olic�do�cumen���ts.����#P��313��������O�ø����Y�IJThe�{4�A���utostepp��}'er�,���whic���h�{5con�tains�co�Gde�{5for�deciding�whic���h�op�Geration�to�apply����#P��314�����Y�IJnext�X{and�where�Xzto�apply�it.�{8This�supp�Gorts�the�Autostep,�YDAutonish,�Hin���t,����#P��315�����Y�IJand�UUSho���wstep�buttons.����#P��316��������O�ø����Y�IJThe��N�Pr��}'over�,�whic���h�con�tains��Mco�Gde�for�main�taining�a��Mlist�of�assumptions,�and����#P��317�����Y�IJimplemen���ting��Mthe��L\pro�v�e,���refute,���assume"�algorithm�for��Lc�hec�king�required����#P��318�����Y�IJassumptions�UUof�an�op�Geration.����#P��319��������O�ø����Y�IJThe�;�He��}'ap��1Manager�.��MathXp�Gert�;do�es�not�use�mallo�c�and�;free,�s~or�a�reference-����#P��320�����Y�IJcoun���t���system���of�memory�managemen�t,��Tbut�supplies���a�separate�heap�to�eac���h����#P��321�����Y�IJdo�Gcumen���t,��from��Uwhic�h�memory�is��Tmanaged�b�y�functions�that��Tb�Geha�v�e�lik�e����#P��322�����Y�IJmallo�Gc�UUand�free.����#P��323��������O�ø����Y�IJThe���Parser���tak���es�a�string�to�b�Ge�parsed,�
and�pro�Gduces�a�term.�It�needs�a����#P��324�����Y�IJheap�UUto�w���ork�with.����#P��325��������O�ø����Y�IJThe����SV���GGener��}'ator��is�giv���en�a�term,���and�pro�Gduces�SV�G��wco�Gde�to�displa�y�that����#P��326�����Y�IJterm,�UUalong�with�the�rectangle�required�to�do�so�without�line�breaks.����#P��327��������O�ø����Y�IJThe�I��Bignum�I��library��*�,�Lwhic���h�computes�with�arbitrary�precision�in���tegers�and����#P��328�����Y�IJrationals.��� �8�����#P��329��������O�ø����Y�IJThe��J�Pr��}'oblem��Libr�ary��con���tains�some�6500��Kmathematical�form�ulas,���whic�h�are����#P��330�����Y�IJaccessed�uOin�uPresp�Gonse�to��GetPr��}'oblem��messages,��Mwhose�parameters�include����#P��331���6टu�ff<��͍�����h�7���s�T��J�ec�Îhnically�,�X�it�>�is�>�Ja�v��ascript�running�>�the�dialog�b�<ro�x,�X�on�the�bro�wser;�s+but�only�PHP�>tco�<rde�on��
�the�Oserv�Îer�can�send�a�message�to�Nthe�Engine.�lSo,�
in�practice,�the�Ja�v��ascript�uses�either�XHR�Aor���the����fetch����API���to�mak�Îe�a�request�to�the�PHP���page,���whic�Îh�up�<ron�receipt�sends�the��exe���cOpWithA���r�g����message��to�the�serv�Îer.���This�tric�k�enables,�2xin��eect,�Ja�v��ascript��to�send�a�message�to�the�Engine.���See��Xthe�le��FetchMessage.js��for�the�details.��
�r������h�8���s�Floating�Q4p�<roin�Ît�n�um�b�<rers�in�MathXp�ert�are�just�doubles;��#y�Îou�can't�ask�for���2cmmi8�����to�100�decimal���places.�����	�>��7
����������WEB���MA��Z�THXPER�T�����9����V������Y�IJa����topic����and��problem���E�ff&f��ǫnumber�.���The�resp�Gonse�to�suc���h�a�message�is�SV���G����#P��332�����Y�IJgraphics���to���displa���y�the�selected�problem.��� �9��Q��Other�messages�to�comm���unicate����#P��333�����Y�IJwith�UUthe�Problem�Library�are�detailed�b�Gelo���w.����#P��334��������O�ø����Y�IJThe�ǜ�Gr��}'apher��pro�Gduces�2d�graphs,���with�careful�atten���tion�to�the�singularities����#P��335�����Y�IJand�N�jumps.�o�More�precisely��*�,�Pthe�N�Grapher�initializes�or�up�Gdates�graph�do�Gcu-����#P��336�����Y�IJmen���ts�R�in�resp�Gonse�to�messages.�p�The�graph�do�cumen���t�R�has�a�slot�for�storing����#P��337�����Y�IJthe���singularities�and�a�slot���for�the�jumps.�6�These�can�b�Ge�requested�b���y�appro-����#P��338�����Y�IJpriate��)messages��((in�MathXp�Gert�there�is�a�men���u�item��View��Singularities�).����#P��339�����Y�IJThe���Grapher�can�resp�Gond���to�a�n���um�b�er���of�dieren���t�messages,���corresp�onding����#P��340�����Y�IJto�UUmen���u�items,�button�presses,�and�mouse�op�Gerations�in�MathXp�ert.����#P��341�����e�IJWhen�*�the�*�engine�receiv���es�a�request�to�initialize�or�up�Gdate�a�graph�(do�Gc-����#P��342�����Y�IJumen���t),�7the�	�Grapher�handles�that�request.���First,�it�up�Gdates�the�in���ternal����#P��343�����Y�IJdo�Gcumen���t� data�structure.��$Then,�R�it�sends�a�resp�onse� to�the�clien���t,�R�whic�h����#P��344�����Y�IJincludes�UUSV���G�graphics�for�the�graph.����#P��345�����e�IJIn��6Windo���ws��7MathXp�Gert,���double-buering�is�used�for�ecien���t,���
ic�k�er-free����#P��346�����Y�IJup�Gdating.���Mo�dern�]�bro���wsers�]�use�\la�y�ers",���whic�h�]�presumably�use�double-����#P��347�����Y�IJbuering.���The��GEngine's��Fresp�Gonsibilit���y�ends�when�the�SV���G���graphics�has����#P��348�����Y�IJb�Geen��passed��to�the�clien���t.�	IjIn�the�planning�stage,�Y�I��!w���as�w�orried��ab�Gout����#P��349�����Y�IJthe���fact���that�double-buering�migh���t�b�Ge�needed.�P�But�as�it�turned�out,��Cthe����#P��350�����Y�IJbro���wsers�UUhandle�it�b�Geautifully��*�,�so�nothing�additional�had�to�b�e�done.����#P��351��������O�ø����Y���Scr��}'ol���ling.�2k�It�@7is�@6the�in���terface's�resp�Gonsibilit�y�@7to�handle�the�displa���y�of�the����#P��352�����Y�IJdo�Gcumen���t.�2�In���particular,���if�new�lines�are�generated�at�the�b�ottom�of�a����#P��353�����Y�IJcalculation,���scrolling���the���windo���w�will�b�Ge�required.�-BThat�is�the�resp�Gonsibilit���y����#P��354�����Y�IJof���the���in���terface,��Snot�the�Engine.�f�The�Engine�do�Ges�not�kno���w�the�heigh���t�of����#P��355�����Y�IJthe�UUbro���wser�windo�w.����#P��356��������O�ø����Y�IJThe����L��}'o�c�alizer�,���whic���h�is�resp�Gonsible�for�displa�ying���natural-language�text�in����#P��357�����Y�IJthe����sele��}'cte�d���language�.��7Natural-language�text���is�used�in�in���terface�elemen�ts����#P��358�����Y�IJsuc���h�:as�men�us,��
\reason�strings"�(justications�of�steps),��error�messages,�etc.����#P��359�����Y�IJF��*�or�:7eac���h�:8supp�Gorted�language,�r�there�are�C�9�source�les�con���taining�the�required����#P��360�����Y�IJstrings�nin�text�arra���ys�of�UTF-8�strings.��When�suc�h�text�is�required,�P�the����#P��361�����Y�IJfunctions�i�in�i��natlang.c��are�called;�s�these�functions�all�return�strings�in�the����#P��362�����Y���sele��}'cte�d�_blanguage�,�'�whic���h�>is�?set�b�y�?calling��set���E�ff&f��ǫlanguage�.�^�(This�arc�hitecture����#P��363�����Y�IJsupp�Gorts�5�the�abilit���y�5�to�switc�h�from�English�5�to�F��*�renc�h�mid-computation.)��� �10�����#P��364�����e�IJThe�ԆLo�Gcalizer�ԇcon���trols�translations�of�strings�generated�b���y�the�Engine.����#P��365�����Y�IJThere�sKare�sJalso�a�few�h���undred�strings�used�only�b���y�the�in���terface.�˨These����#P��366�����Y�IJare��.translated�b���y��-Ja�v��q�ascript��.in�the�in���terface;�Htranslation�tables�are�found����#P��367�����Y�IJin��"�T��;�r��}'anslateEnterPages.js��and��EnterPr�oblem.php�.��/These�tables�are�used����#P��368���6ट	w��ff<��͍�����h�9���s�These���problems���ha�Îv�e�b�<reen�carefully�constructed���and�the�auto-generated�solutions�ha�Îv�e�all��
�b�<reen��examined��b�Îy�hand.�y�It�is�not�en�Îvisaged�to�expand�this�list�of�problems�for�W��J�ebMathXp�<rert.���Also,��Xthese�problems�are�used�in�autotesting�MathXp�<rert�after�c�Îhanges�to�the�source�co�de.��
�r������h�10����If�	�y�Îou�	�switc�h�languages�	�mid-computation,��sa�y�from�	�English�to�Chinese,��only�the�part��after���the��switch��_�will�b�<re��^in�Chinese.��4Y��J�ou�could�alw�Îa�ys��_undo�some�steps�and�redo�them�in�Chinese.��4But���the��English�steps�ma�Îy�ha�v�e�some�strange�italics�that�they�didn't�ha�v�e�b�<refore�y�ou�switc�hed�to���Chinese.�y�This��is�a��consequence�of�some�co�<rde�that�decides,��for�example,��whether�\b�Îy"�should�b�e���prin�Îted��(in��'italics�(as�t�w�o�v��ariables)��'or�in�Roman�(as�an�English�w�Îord).�D�This�co�<rde�is�dieren�Ît�for���eac�Îh�i�language.���Since�\b�y"�is�not�a�Chinese�w�ord,��it�is�prin�ted�in�italics�after�i�the�switc�h,��as�in���\divide�wJ�by��12."���Only�the�do�<rcumen�Ît�as�a�whole�has�a�language,��not�eac�h�line�within�the�do�<rcumen�t,���so��ev�Îery�line�is�prin�ted�using�the�rules�for�Chinese.�LNot�man�y�p�<reople�will�switc�h�languages�mid-���do�<rcumen�Ît���and���those�that�do,���will�not�care�ab�<rout�italics�v�Îery�m�uc�h,���so�w�e���judge�this�situation���acceptable.�����
���7
��������6ऱ10���,'MICHAEL���BEESON���V������Y�IJto��translate��the�text�in�v��q�arious�kinds�of�HTML�mand�SV���G�elemen�ts.���The����#P��369�����Y�IJEngine�Hsends�HJa���v��q�ascript�to�dene�the�v��q�ariable��languageNumb��}'er�,���whic���h�is����#P��370�����Y�IJused�UUto�con���trol�these�translations.����#P��371��������O�ø����Y�IJThe�[Engine�resp�Gonds�[to�the��A���utoStep��and��A�utoFinish�[�messages�with�SV���G����#P��372�����Y�IJgraphics.�4�This��9is�the�most�delicate�and��8complex�part�of�the�Engine;��BI��advise����#P��373�����Y�IJagainst�qxattempting�to�impro���v�e�qxit,��b�Gecause�an���y�c�hange�alw�a�ys�has�unforeseen����#P��374�����Y�IJeects�UUon�other�auto-generated�solutions.����#P��375��������O�ø����Y���Do��}'cument�tInitialization�.�L�The�H�in���terface�H�m�ust�pro�vide�H�a�w�a�y�(or�H�w�a�ys)�to����#P��376�����Y�IJselect��\a��topic��and��[a��problem�.�R�These�are�the�parameters�to�the��Cr��}'e�ateDo�c-����#P��377�����Y���ument��3�message.�Q�The��4dieren���t�w�a�ys�in�whic�h��4this�can�b�Ge�done�are�discussed����#P��378�����Y�IJb�Gelo���w.����#P��379����B�����β8.���H��P�� arsing��and�displa��UTying�terms����#P��380�����BलThe�:clien���t�can�9issue�a�request��ParseA���ndDisplay�.�]iRemem�b�Ger�that�9the�clien�t�do�Ges����#P��381�����6लnot���kno���w�what�a�term���is,��{so�it�cannot�directly�receiv�e�a�term.�EUIt�can�only�receiv�e����#P��382�����6लSV���G�UUgraphics.����#P��383�����BलThe�{a�ParseA���ndDisplay�{`�request�has�a�string�parameter�for�the�(text�form�of�the)����#P��384�����6लterm�.�to�.�b�Ge�parsed,�eJand�a�p�Goin���t�represen�ting�.�the�upp�Ger�left�corner�of�the�desired����#P��385�����6लdispla���y��*�.�SIf�Q�the�Q�term�do�Ges�not�parse,���the�Engine�resp�Gonds�with�a�parser�error�message,����#P��386�����6लwhic���h��5is�in�the�selected�language.��gIt�will�b�Ge�returned�as�an�SV�G��elemen�t�of�class����#P��387�����6��ParserErrorMessage�.���If��the��term�do�Ges�parse�to�a�term��t�,��the�Engine�uses�its����#P��388�����6��termT��;�oSV���G�,���whic���h���returns�SV�G��^graphics�co�Gde�for���displa�ying��t�.��The���clien�t�can����#P��389�����6लthen�UUdispla���y�the�term,�but�m�ust�supply�the��<svg>��tags.����#P��390�����BलThe�m�use�of�SV���G�mzgraphics�is�the�main�inno�v��q�ation�m�in�the�Engine,���compared�to����#P��391�����6लWindo���ws��MathXp�Gert.�Z�Therefore�it�has��b�een�demonstrated�in�the�pro�of-of-�concept����#P��392�����6लprogram�UU�ParseA���ndDisplay�,�whic���h�can�b�Ge�seen�at����#P��393�����B��www.mathxpert.org/ParseAndDisplay.php����#P��394�����BलThis�UUprogram�w���as�used�to�ne-tune�MathXp�Gert's�t�yp�Gesetting.����#P��395����4��6ल8.1.��Selecting���terms,���or�parts���of�a�graph.��The�?�clien���t�?�m�ust�b�Ge�able�?�to�manage����#P��396�����6लthe��	mouse��(or�other�p�Goin���ter)�and�allo���w�the�user�to�select�a�rectangle�in�a�do�Gcumen���t����#P��397�����6लwindo���w.�:In��a�sym�b�Golic�view,���that�rectangle�will��b�e�used�to�select�a��term�that�the����#P��398�����6लuser� 9can� :do�something�to�or�with.�`In�a�graphics�do�Gcumen���t,�*�it�will�b�Ge�used�to�select����#P��399�����6लthe�UUnext�dra���wing�windo�w.����#P��400�����BलOn��2�mouse���E�ff&f��ǫup�,�ۡor�more�generally��*�,��pointer���E�ff&f��ǫup�,�۠it�sends��3a��Sele��}'cte�dR�e�ctangleSymb�ol����#P��401�����6लor�ج�Sele��}'cte�dR�e�ctangleGr�aph��message�حto�the�Engine�and�a���w�aits�the�resp�Gonse,���whic�h����#P��402�����6लwill�UUb�Ge�SV���G�co�de�generated�b���y��SendSymb��}'olDo�cument�.�q�or�UU�SendGr�aphDo�cument�.����#P��403�����BलThe�o:Engine�resp�Gonds�to�a��Sele��}'cte�dR�e�ctangleSymb�ol�o;�message�o:b���y�nding�the�largest����#P��404�����6लsubterm��>of��=the�activ���e�line�that�is�con���tained�in�the�selected�rectangle.�H�That�term����#P��405�����6लb�Gecomes�
�the��sele��}'cte�d�Q�term�
��(whic���h�is�stored�as�part�of�
�the�do�cumen���t).�Y�The�resp�onse����#P��406�����6लto�jthe�message�is�kSV���G�Zgraphics�for�jthe�whole�do�Gcumen�t;�,�the�selected�term�receiv�es����#P��407�����6लdieren���t�1coloring,���so�the�2selected�term�will�app�Gear�highligh�ted.��\A�&�<rect>��elemen�t����#P��408�����6लfor���the���rectangle�of�that�term�is�also�included,��|whic���h�is�b�Ge�displa���y�ed���rst,��|b�efore�the����#P��409�����6लterms�]�are�written�o���v�er�]�it.��� �11��2�The�resp�Gonse�also�includes�a�list�]�of�op�erations,��^whic���h�the����#P��410�����6लuser���ma���y���c�ho�Gose�from.�<�The�clien�t���will�ha�v�e�to���presen�t�that�list���to�the�user�and�allo���w����#P��411�����6लa���c���hoice.�LWhen�the���user�selects�an�item�from�that�list,���a�message��ApplyOp��}'er�ation����#P��412���6टM��ff<��͍�����h�11����Color�selection,�K�including�the�highligh�Ît�color,�K�is�stored�in�the�do�<rcumen�Ît;���the�clien�t�ma�y��
�pro�Îvide��Xto�<rols�for�c�hanging�those�selections,�as�is�p�<rossible�in�Windo�ws�MathXp�<rert.������"��7
����������WEB���MA��Z�THXPER�T����^11����V������6लwill���b�Ge�sen���t�to�the�Engine,��$with�the�selected�op�eration�as�a�parameter.�=�(The�Engine����#P��413�����6लalready�L2kno���ws�the�L1selected�subterm).�n�If�the�op�Geration�succeeds,�Nthe�do�cumen���t�will����#P��414�����6लb�Ge��up�dated�as�describ�ed�ab�o���v�e.���If�it�do�Ges�not,��the�resp�onse�con���tains�(in�addition����#P��415�����6लto�%the�%other�SV���G�$�co�Gde)�an�SV���G�$�elemen�t�%of�class��matherror��to�explain�wh���y�the����#P��416�����6लop�Geration��dfailed�(or�at�least,�i��that��it�failed).�	o�The�in���terface�should�displa�y�that����#P��417�����6लmessage�UUand�allo���w�it�to�b�Ge�dismissed.��� �12�����#P��418���fd����`�9.���'�SendGraphDocument����#P��419�����BलMan���y��>of�the��?messages�that�can�b�Ge�sen���t�to�the�Engine�result�in�certain�c���hanges����#P��420�����6लto�IIthe�do�Gcumen���t,��Ffollo�w�ed�IIb�y�a�IHcall�to��SendGr��}'aphDo�cument�,��Fwhic���h�sends��<svg>����#P��421�����6लelemen���ts���to�the�PHP���page���that�sen�t�a�message�to�the���Engine.�/�These��<svg>��elemen�ts����#P��422�����6लare��5tagged�with�a��4�class��and�an��id�.�QSome�of�them�are�mark���ed�with��display:none�,����#P��423�����6लso���they���can�b�Ge�displa���y�ed���on�demand�b���y�Ja�v��q�ascript���that�c�hanges���their��display����#P��424�����6लprop�Gert���y��*�.�YF�or�?example,�there�>are�elemen�ts�of�class�>�hint��and�class��assumption��that����#P��425�����6लare�~{treated�~zthat�w���a�y��*�.�*)Then�~{the�user's�request�to�get�a�hin���t,��sor�view�the�assumptions,����#P��426�����6लcan�UUb�Ge�handled�in�the�bro���wser�b�y�Ja�v��q�ascript,�without�going�bac�k�to�the�Engine.����#P��427�����BलIn���T��*�able���1,���w���e�presen�t���a�complete���table�of�the�p�Gossible�elemen���ts�that�comp�Gose����#P��428�����6लa��graphical��view�of�a�do�Gcumen���t,�Ki.e.,�elemen�ts��that��migh�t�b�Ge�receiv�ed��from��send-����#P��429�����6��Gr��}'aphDo�cument�.�*�These��elemen���ts�receiv�e�ids�that�b�Gegin�with���the�class�name,��ksuc�h����#P��430�����6लas�E��graph1�E��or��param2�.�l�Note�that�elemen���ts�of�class��authorscommentary��are�send�as����#P��431�����6लan��nordinary��m�<div>��with��style=display:none�,���b�Gecause�the�bro���wser�cannot�break����#P��432�����6लlines��in��SV���G��itext.�4wAll�the�other�elemen���ts�are�sen���t�as�SV���G.��graph��elemen���ts�ha�v�e����#P��433�����6लabsolute���p�Gositioning,��\so�they�need���to�b�e���placed�inside�an�elemen���t�with�relativ���e�or����#P��434�����6लabsolute�UUp�Gositioning.����#P��435����[,���t������J��T�� able��1.��Elemen���ts�UUof�a�Graphical�Do�Gcumen�t����I������ϳ1���z��Class��͟���ff�����Description���RNߟ�ff1#��fd���$��graph��͟���ff���H��graph,�UUwith�axes,�tic���ks,�lab�Gels������$��param��͟���ff���H��parameter�UU(of�the�graph�function)������$��title��͟���ff���H��co�Gde�UUto�displa���y�the�form�ula�as�the�title�of�the�graph������)���jump��͟���ff���H��one�UUen���try�in�the�table�of�jumps�������singularity��͟���ff���H��one�UUen���try�in�the�table�of�singularities������
?��assumption��͟���ff���H��one�UUassumption������
?��commentary��͟���ff���H��commen���tary�UUb�y�the�author�of�a�stored�problem���������tooltip��͟���ff���H��to�Goltip�UUtext��������x��B�Except��for�classes���graph��and��title�,�	)the�Engine�sends�these�elemen���ts�with�prop-����#P��436�����6लert���y����display:none�,�ߛso�they���are�in�visible�un�til���the�in�terface�(using���Ja�v��q�ascript�and����#P��437�����6लthe�m�DOM)�mqc���hanges�that�prop�Gert�y��*�,��for�example�to�displa�y�the�m�singularities�in�a�p�Gopup����#P��438�����6लwindo���w.�q�The�UUpage��Gr��}'aphDo�c.php�UU�illustrates�these�tec�hniques.����#P��439����������10.���W��SendSymbolDocument����#P��440�����BलMan���y��>of�the��?messages�that�can�b�Ge�sen���t�to�the�Engine�result�in�certain�c���hanges����#P��441�����6लto��Xthe��Wdo�Gcumen���t,�!follo�w�ed�b�y��Xa�call�to��SendSymb��}'olDo�cument�,�!whic���h�sends��X�<svg>����#P��442�����6लelemen���ts���to�the�PHP���page�that���sen�t�a�message�to�the�Engine.��Some�messages�are����#P��443���6ट�ljff<��͍�����h�12����Windo�Îws��MathXp�<rert��supp�orts�selecting��more�than�one�term�at�once.��LThis�feature�is�not��
�supp�<rorted��Xin�W��J�eb�MathXp�ert.������u��7
��������6ऱ12���,'MICHAEL���BEESON���V���>}&���t�������d�T�� able��2.��Initial�UUvisibilit���y����I������ϳ1����`��Class��͟���ff����`��display��������ffr̟fd���$�graph��͟���ff���H��block������$�param��͟���ff���H��block������$�title��͟���ff���H��block������)��jump��͟���ff���H��none������singularity��͟���ff���H��none������
?�assumption��͟���ff���H��none������
?�commentary��͟���ff���H��none��������tooltip��͟���ff���H��none����������6लappropriate��cfor�a��bsym���b�Golic�(view�of�a)�do�cumen���t,��fwhile�others�are��bfor�a�graphical����#P��444�����6ल(view�m�of�a)�do�Gcumen���t.�$�The�Engine�answ�ers�ev�ery�message,��+so�it�is�up�to�the�in�terface����#P��445�����6लprogrammer�u�not�u�to�send�a�sym���b�Golic�message�from�a�graphical�view.��� �13���Z�The�task�of����#P��446�����6लthe��Hclien���t��Gis�to�displa�y�these��Gv��q�arious�SV�G��4elemen�ts��Gto�the�user�at�the�appropriate����#P��447�����6लtime��and�place.�1T��*�able�3�sho���ws�the�classes��of�SV�G��
elemen�ts��that�are�generated�b�y����#P��448�����6��sendSymb��}'olDo�cument�.����#P��449���ꗹ���,t�������'�T�� able��3.��Elemen���ts�UUof�a�Sym�b�Golic�Do�cumen���t����s��������1�������Class��͟���ff������Description���U ���ff+�fd���9��line��͟���ff���Xزone�UUline�of�the�solution������.���reason��͟���ff���Xزthe�UUjustication�for�a�line������?��highlight��͟���ff���Xزthe�UUterm�selection�rectangle(s)���������assumption��͟���ff���Xزone�UUassumption������9��hint��͟���ff���Xزone�UUhin���t������$��menuitem��͟���ff���Xزone�UUmen���u�item�������needsargprompt��͟���ff���Xزprompt�UUfor�a�dialog������.���remark��͟���ff���Xزone�UUremark������)���comment��͟���ff���Xزone�UUcommen���t���������finalremark��͟���ff���Xزfor�UUexample,��That's���the�answer.������?��matherror��͟���ff���Xزwh���y�UUan�op�Geration�failed������)���tooltip��͟���ff���Xزto�Goltip�UUtext������
?��progressTitle��͟���ff���Xزtitle�UUof�a�progress-rep�Gort������$��progress��͟���ff���Xزtext�UUto�put�in�a�progress�rep�Gort���������commentary��͟���ff���Xزcommen���tary�UUb�y�the�author�of�a�stored�problem�������7��B�Lines,�UUreasons,�highligh���ts,�nalremarks,�and�some�commen�ts�arriv�e�with����#P��450�����6��display:block�;���the��lother�elemen���ts�arriv�e��mwith��display:none�.�/
Elemen�ts�that�ar-����#P��451�����6लriv���e�`�with��display:block��ha�v�e�co�Gordinates�already�and�need�no�further�manipula-����#P��452�����6लtion�ˈb���y�the�clien�t.�C�Elemen�ts�that�arriv�e�with��display:none��can�b�Ge�displa�y�ed�at�the����#P��453�����6लin���terface's��discretion.���Men�u��items�are�mean�t�to�b�Ge�assem�bled�in�to�a��men�u,�9�from����#P��454���6ट�>�ff<��͍�����h�13����Only��?one�message,���gr���aphButton�,�is��?sen�Ît�from��Symb�olDo�c.php��@�and�pro�<rcessed�b�Îy��Gr�aph-��
�Do���c.php�.��Other��|messages��}from�those�t�Îw�o��|les�are�pro�<rcessed�b�Îy�the�sending�le.��But�in�Îterface���programmers���m�Îust�tak�e�care���to�pro�<rcess�(the�resp�onses�to)�pre-do�cumen�Ît���messages�in�the�correct���le.�����
ڑ��7
����������WEB���MA��Z�THXPER�T����^13����V������6लwhic���h�xthe�wuser�can�mak���e�a�c���hoice,�">sending�a��Sele��}'ctMenuChoic�e��message.�\}Hin���ts,�">as-����#P��455�����6लsumptions,��>matherrors,�and���authorscommen���tary�are�in�tended�for�displa�y�in�a�mo�Gdal����#P��456�����6लdialog,��whic���h��the�user�will�read�and��then�dismiss;�also�commen�ts�and�remarks�with����#P��457�����6��display:none�.�B>See�Ƹ�Symb��}'olDo�c.php�ƹ�for�a�demonstration�of�ho���w�the�in���terface�carries����#P��458�����6लout�UUthe�task�of�displa���ying�the�SV�G�elemen�ts.����#P��459���fd�����=�11.����\�Initializing��a�Document����#P��460�����BलA�do�Gcumen���t� requires�!a�problem�and�a�topic�to�initialize.�_�There�are�sev���eral�w�a�ys����#P��461�����6लto�	5request�a�	6new�do�Gcumen���t.�XgThe��topic��is�one�of�those�sp�Gecied�in��topics.h�.�XgThere����#P��462�����6लab�Gout��a�h���undred�dieren�t�topics.�e�The��pr��}'oblem��is�a�term,�%�but�not�just�an�y�term:����#P��463�����6लit��km���ust�b�Ge�appropriate�for�the�topic.�
	In�order�to�initialize��la�do�cumen���t,��pthere�are����#P��464�����6लsev���eral�UUp�Gossible�paths:����#P��465���������O�ø����Y�IJSelect�UUa�topic�and�problem�from�the�MathXp�Gert�Problem�Library��*�.����#P��466��������O�ø����Y�IJSelect�na�topic�and�problem�from�the�Problem�Library��*�,�N4and�then�edit�the����#P��467�����Y�IJproblem.����#P��468��������O�ø����Y�IJPic���k�oEone�oDof�ab�Gout�20�kinds�of�graphs,�u�or�ab�Gout�20�kinds�of�sym���b�Golic�prob-����#P��469�����Y�IJlems,�UUand�then�en���ter�y�our�o�wn�problem.����#P��470��������O�ø����Y�IJBegin�ʘas�ʗif�en���tering�a�problem,���but�then�use�the�\arro���w�button"�to�get�a����#P��471�����Y�IJrandom�UUproblem�of�the�c���hosen�kind�(whic�h�y�ou�can�then�edit�or�accept).����#P��472�����BलIn���this���section,��w���e�describ�Ge�and�discuss�the�\pre-do�Gcumen���t"�part�of�the�in���terface.����#P��473�����6लW��*�eb�UUMathXp�Gert's�in���tro�ductory�page�presen���ts�the�user�with�three�c�hoices:����#P��474��������O�ø����Y�IJMak���e�UUa�Graph����#P��475��������O�ø����Y�IJEn���ter�UUa�Problem����#P��476��������O�ø����Y�IJMathXp�Gert�UUProblem�Library����#P��477�����6लThese�+.c���hoices�+/represen�t�three�dieren�t�path�w�a�ys,�3�eac�h�of�whic�h�ev�en�tually�+/leads�to����#P��478�����6लthe��selection�of��a�problem�and�a�topic.��W��*�e�will�discuss�these�three�c���hoices�one�b�y����#P��479�����6लone,�UUin�rev���erse�order.����#P��480�����6ल11.1.��The�m�MathXp�Q�ert�m�Problem�Library��
�.��The��QEngine�con���tains�(in�C���source����#P��481�����6लco�Gde)�B�ab�out�6500�problems.�k�T��*�o�understand�ho���w�this�library�B�can�b�e�used,�F�it�is�nec-����#P��482�����6लessary�+�to�understand�+�ho���w�a�MathXp�Gert�do�cumen���t�is�+�created.�c�Cho�osing��MathXp��}'ert����#P��483�����6��Pr��}'oblem���Libr�ary�]Ҳleads�to�]��GetProblem.php�.��?This�page�pro���vides�a�Ja���v��q�ascript�pic�k�er����#P��484�����6लelemen���t�}�to�}�access�the�problems�from�the�Problem�Library�and�displa���y�them.��� �14��䋲A�t����#P��485�����6लthe��5top��6of�the�page,��the�user�can�access�the�Lo�Gcalizer�to�select�one�of�the�supp�Gorted����#P��486�����6लnatural�"�languages.���Then�the�user�"�can�bro���wse�the�a�v��q�ailable�"�topics�and�problems.����#P��487�����6लOne�UUproblem�at�a�time�will�b�Ge�displa���y�ed�UUor�\selected."����#P��488�����BलThe���user���can�clic���k�on��A��}'c�c�ept�)�the�)�Sele�cte�d�Pr�oblem���to���initialize�a�MathXp�Gert�do�c-����#P��489�����6लumen���t�?iand�?hpro�Gceed�to�use�it�with�the�Engine.�jxThe�newly�initialized�do�Gcumen���t�will����#P��490�����6लb�Ge��sen���t�(in�SV�G�graphics�form)�via��SendGr��}'aphDo�cument���or��SendSymb��}'olDo�cument�,����#P��491�����6लaccording��to�the�topic.�M<The�in���terface�le��GetPr��}'oblem.php�紲ensures�that�the�Engine's����#P��492�����6लresp�Gonse�K�is�K�directed�to�a�PHP�Kqpage�designed�for�a�graphical�view�or�a�sym���b�Golic����#P��493�����6लview,��fas�Ėappropriate,�e.g.,��gto�Sym���b�GolDo�c.php�or�GraphDo�c.php.���Those�t���w�o�PHP����#P��494�����6लles���constitute���the�in���terface�for�w���orking�with�a�MathXp�Gert�do�cumen���t�once���it�has����#P��495�����6लb�Geen�UUcreated.����#P��496�����BलThe��rest�of��this�subsection�is�of�in���terest�only�to�programmers�who�ma���y�try�to����#P��497�����6लimpro���v�e�UUthe�in���terface�to�the�Problem�Library��*�.����#P��498���6ट�ljff<��͍�����h�14����This��Jis��Ia�third-part�Îy�\spinner"�con�Îtrol.���P�erhaps�someone��Jcan�design�a�b�<retter�w�Îa�y��Jto�access��
�the��XProblem�Library��J�,�but�this�do�<res�w�Îork.��������7
��������6ऱ14���,'MICHAEL���BEESON���V������BलThe��Ble�tdefn.h�denes��Ctopic�n���um�b�Gers��Band�names�for�the�topics.��Those�names����#P��499�����6लare�UUjust�in���ternal�iden�tiers.�q�F��*�or�example�tdefn.h�con�tains�the�line����#P��500�����B��#define���B�ff&f��	�ordinary���E�ff&f��ǫgraph���E�ff&f��sincos�?�10����#P��501�����6लA�x�programmer�x�can�x�ask�the�Engine�for�all�the�problems�for�a�giv���en�topic.��lY��*�ou�can����#P��502�����6लask��cfor�eac���h�of�these��dthings�to�b�Ge�deliv�ered�as�parseable�ascii�text,��'or�as�an�SV�G����#P��503�����6लgraphics���elemen���t.�UNSee�T��*�able�4.�One���can�also�ask�for�the�information,��ho���w�man�y����#P��504�����6लproblems�UUdo�Ges�the�Library�con���tain�for�a�sp�ecied�topic?����#P��505���X#����:����{�E�T�� able��4.��Messages�UUto�access�the�Problem�Library����)�������1���|�]�Message�.ޮ����ff���Ԣhp��}'ar�ameter���w�\��ff漐�fd����AskProblemsT��*�ext�l͟���ff���] topic������AskProblemsSV���G��͟���ff���] topic������AsknProblems�ޕ����ff���] (un���used�UUnonempt�y�parameter)��������	��B�F��*�or�Tthe�message�requesting�SV���G,�eac�h�SV�G�@elemen�t�is�a�string�(con�taining�new-����#P��506�����6लlines�u
and�ending�with�ua�newline)�suitable�for�placing�in�an�existing��<svg>��elemen���t����#P��507�����6ल(or��\a��]dynamically�created�elemen���t).�8The��<svg>��and��</svg>��tags�are��not��included�in����#P��508�����6लthe�{�message�{�resp�Gonse.��� �15��",�After�eac���h�problem,��Qa�second�newline�is�added,��Rso�the�prob-����#P��509�����6लlems���are���separated�b���y�double�newlines�in�the�resp�Gonse;���then�an�arra���y�of�problems����#P��510�����6लis�UUeasily�created�b���y�\explo�Gding"�the�resp�onse�on�double�newline.����#P��511�����BलIn��6GetProblem.php,���the�\sub��8jects"��7are�hard-co�Gded,���and�the�range�of�topics�for����#P��512�����6लeac���h�WRsub��8ject�WQis�also�hard-co�Gded,���tak���en�from�tdefn.h.�w�Then�the�problems�are�re-����#P��513�����6लquested���using����AskPr��}'oblemsSV���G�.�The�message��asknPr��}'oblems��is�used�to�initialize�a����#P��514�����6लcon���trol�v�while�the�problems�are�still�do�wnloading.���The�\sub��8jects"�b�Gelong�to�the����#P��515�����6लin���terface�Ionly;�,�the�Engine�Hkno�ws�nothing�of�grouping�topics�Hb�y�sub��8ject,�$~so�this�can����#P��516�����6लb�Ge�UUc���hanged�arbitrarily�in�GetProblem.php.����#P��517�����BलWhen�Q7the�user�accepts�a�problem,��/the�message��InitSymb��}'olDo�cF��;�r�omT�opicA���nd-����#P��518�����6��Pr��}'oblem���is��sen���t.���Its�parameter�carries�the�topic�n���um�b�Ger��and�the�text�form�of�the����#P��519�����6लselected�7!problem,�=,separated�b���y�'+',�whic���h�generally�serv�es�to�7"com�bine�sev�eral�data����#P��520�����6लitems�UUin���to�one�(string)�parameter.����#P��521�����BलIn�Z�the�case�of�a�Z�problem�from�the�MathXp�Gert�Problem�Library��*�,��it�is�guaran-����#P��522�����6लteed��that��the�problem�will�b�Ge�compatible�with�the�topic,��so�the�resp�Gonse�to�that����#P��523�����6लmessage�O�will�O�b�Ge�generated�b���y��sendGr��}'aphDo�cument�Oòor��sendSymb�olDo�cument�,��^and����#P��524�����6��GetProblem.php�۲�will�۳direct�the�output�to�either��GraphDoc.php��or��SymbolDoc.php�.����#P��525���V6ल11.2.��En��9tering�,Ly�our�,Ko�wn�problem.��Initializing��Xa��YMathXp�Gert�do�cumen���t��Yrequires����#P��526�����6लa�%�problem�and�a�topic;�5xit�is�not�enough�just�to�ha���v�e�%�a�parseable�form���ula�as�a�prob-����#P��527�����6लlem.�_�There�OJare�ab�Gout�a�h���undred�OKtopics;��Eev�en�OJsho�wing�them�to�a�OKuser�w�ould�b�Ge����#P��528�����6लb�Gewildering,���as�vPthe�MathXp�ert�vQProblem�Library�probably�is.�ԹInstead,���the�page����#P��529�����6��EnterProblem.php��P�reduces�the�c���hoice��Qto�16�\kinds"�of�problem,��starting�with��Sim-����#P��530�����6��plify�;�and��Solve�{�an�{�Equation�.�i	In�a�;few�cases�there�is�an�additional�selector�elemen���t;����#P��531�����6लfor�v�example,��aunder��Solve��^Line��}'ar��_Equations�,��`a�selector�oers�v�the�c���hoice�of�man�y����#P��532�����6लw���a�ys��Fto�solv���e��Glinear�equations.�M�The�user's�(optional)�selection�tells�MathXp�Gert�ho���w����#P��533�����6लto�T@pro�Gceed�if��A���utostep��or��Showstep��or��A�utonish��is�selected.�qjThis�is�one�use�of�the����#P��534�����6ल\topic":��it���con���trols���the�c�hoice���of�metho�Gd.�u�Another�use�is�to�con���trol�the�step�size:����#P��535���6ट�ff<��͍�����h�15����The��E�GetPr���oblem.php��D�le�demonstrates�ho�Îw�suc�h��DSV�G��Ctext�can�b�<re�dynamically��Dwritten�in�to��
�an��XSV�ÎG�elemen�t�in�the�w�eb�page.������'��7
����������WEB���MA��Z�THXPER�T����^15����V������6लb�Geginners��should�see�all�the��steps�of�solving�4�x�:t�+�2��=�11,��more��exp�erienced�studen���ts����#P��536�����6लw���an�t�UUthat�solv���ed�in�one�or�t�w�o�steps.����#P��537�����BलCho�Gosing��Aa�\kind��Bof�problem"�leads�to�a�\problem�en���try�page."�T�There�are�man�y����#P��538�����6लof�&these�&pages,�ZIwith�names�lik���e��EnterSimplify.php�.��Eac�h�&one�has�one,�ZHt�w�o,�or����#P��539�����6लin�{�some�cases�{�optionally�more,��elds�in�whic���h�form�ulas�can�b�Ge�en�tered.��vBelo�w�the����#P��540�����6लen���try��eelds�is�a��Display��d�button;��if�all�go�Ges�w�ell,��athe�en�tered�problem�app�Gears�b�elo���w����#P��541�����6लthe����Display��button���in�t���yp�Geset�mathematical�notation.��1This�means�that�not�only����#P��542�����6लdid���the���en���tered�problem�parse�correctly�(i.e.,�Wthe�syn���tax�w�as�correct),�Wbut���also�that����#P��543�����6लthe��HEngine��Ihas�judged�that�the�form���ulas�en�tered�are�compatible��Iwith�the�selected����#P��544�����6लkind�UUof�problem.����#P��545�����BलHere��is�what�happ�Gens�b�ehind�the�scenes:���First,�J�the�\en���try�page"�has�selected����#P��546�����6लa�;topic,�tthe�\default�;topic"�for�this�kind�of�problem.�"�There�ma���y�ha�v�e�;b�Geen�dif-����#P��547�����6लferen���t���p�Gossible���c�hoices,�for�example���one�ma���y�pro�vide���more�details�in�the�steps;����#P��548�����6लbut�h4some�h3c���hoice�is�made.��cThen�a�message��setupA���ndChe��}'ckSymb�ol�h4�is�sen���t,�l�with�cer-����#P��549�����6लtain���parameters,��including���the�text�form�of�the�problem�and�the�topic�n���um�b�Ger.����#P��550�����6लWhen���that���message�is�pro�Gcessed,�the�Engine�c���hec�ks���whether�the�problem�is�accept-����#P��551�����6लable��,for�that�topic.��LIf��+not,��bit�resp�Gonds�with�error�messages,��awhic���h�the�en�try�page����#P��552�����6लdispla���ys.��The�7�user�can�7�then�try�again.�But�if�7�(or�when)�the�problem�is�accept-����#P��553�����6लable,���the��;Engine��<creates�and�initializes�an�appropriate�do�Gcumen���t.�zThe�resp�onse��;it����#P��554�����6लsends���to�the�en���try�page�is�the�SV�G��nto�displa�y�the�problem�in�t�yp�Geset�form.�YKThat����#P��555�����6लis�Q�an�Q�elemen���t�with�class��termSVG�QO�and�id��parsedTerm�.�fyWhen�suc���h�a�resp�Gonse�is����#P��556�����6लreceiv���ed,�Qthe�O�en�try�O�page�mak�es�visible�the��Do���the���Math��button.�o�Clic�king�that�but-����#P��557�����6लton��:sends�a��;�startSolving��message�to�the�Engine,���whic���h�in�turn�results�in�a�call�to����#P��558�����6��sendSymb��}'olDo�cument�,��Rwhose�V resp�Gonse�Vis�directed�to��SymbolDoc.php�,��Rcompleting����#P��559�����6लthe�UUdo�Gcumen���t-initialization�phase.����#P��560���K��6ल11.3.��Making�2'a�2&Graph.��Similarly��*�,��:when��making�a�graph��
y���ou�m�ust�c�ho�Gose�what����#P��561�����6लkind�~�of�~�graph�y���ou�w�an�t�to�~�mak�e;���y�ou�are�sen�t�to�~��MakeGraph.php�,��*where�there�~�are����#P��562�����6लt���w�elv�e�I�kinds�to�I�c���ho�Gose�from.��Eac�h�c�hoice�I�is�illustrated�b�y�a�small�sample�I�of�that�kind����#P��563�����6लof�$xgraph.��1In�t���w�o�$xof�those�$ycases,�X@namely��Dier��}'ential�RxEquations�$x�and��Appr�oximate����#P��564�����6��Inte��}'gr�ation�,��	a�|Kselector�allo���ws�|Lthe�user�a�selector�to�rene�what�kind�of�problem����#P��565�����6लis�{in���tended.��Pic�king�one�of�{those�t�w�elv�e�kinds�of�{graphs�sends�y�ou�to�{an�en�try����#P��566�����6लpage,�Q�for�Mexample��EnterOrdinaryGraph.php�.�ϯY��*�ou�Lget�one�or�t���w�o,�or�Msometimes����#P��567�����6लoptionally�>�more,�yen���try�elds�>�and�a��Display��button.�-�As�with�sym�b�Golic�problems,����#P��568�����6��Display�c�leads�to�da�t���yp�Geset�v�ersion�and�da�c�hec�k�whether�the�dinput�is�appropriate.����#P��569�����6लBehind�_}the�_~scenes,��a��setupA���ndChe��}'ckGr�aph��message�_~is�sen���t.��@If�all�go�Ges�w���ell,��the����#P��570�����6��Dr��}'aw�ϐ�button�is�sho���wn.�E1Clic�king�ϐ�Dr�aw��sends�a��dr�awA���l���l��message�(\all"�b�Gecause�there����#P��571�����6लma���y�$�b�Ge�sev�eral�graphs).�a�The�result�of�that�is�a��sendGr��}'aphDo�cument�$��message,�.Ywith����#P��572�����6लresp�Gonse�Odirected�Oto��GraphDoc.php�,�PPcompleting�the�do�Gcumen���t-initialization�phase.����#P��573���������pR�12.���7q�Messa��ges����#P��574�����BलIn��`this�section,�
"w���e�list�all�p�Gossible�messages�to�whic�h�the�Engine�can�resp�Gond.����#P��575�����6लThe���real�authorit���y�for�this���is�le��Pr��}'o�c�essMessage.c�;�[;at���the�time�of�writing,��the����#P��576�����6लfollo���wing�UUcorresp�Gonds�to�that�le.����#P��577���,_��6��//�
�pre-document�?�messages����#P��578�����6��askTopicStrings����#P��579�����6��askSubjectStrings����#P��580�����6��askProblemsText����#P��581������I��7
��������6ऱ16���,'MICHAEL���BEESON���V������6��askProblemsSVG����#P��582�����6��asknProblems����#P��583�����6��initSymbolDocFromLibrary����#P��584�����6��initGraphDocFromLibrary����#P��585�����6��setupAndCheckGraph����#P��586�����6��setupAndCheckSymbol����#P��587�����6��startSolving����#P��588������#P�589�����6��//�?�Ajax�messages,�
�response�is�NOT�the�whole�document����#P��590�����6��//�?�but�a�message�for�local�use�in�javascript.����#P��591�����6��randomProblem����#P��592�����6��checkArg����#P��593�����6��askPointSlope����#P��594������#P�595�����6��//�?�Messages�from�and�to�a�symbol�document.����#P��596�����6��//�?�Response�is�sendSymbolDoc����#P��597�����6��autoStep����#P��598�����6��showStep����#P��599�����6��autoFinish����#P��600�����6��undo����#P��601�����6��hint����#P��602�����6��finished����#P��603�����6��selectedRectangleSymbol����#P��604�����6��selectMenuChoice����#P��605�����6��execOpWithArg����#P��606�����6��symbolWindowResized����#P��607������#P�608�����6��//�?�one�message�from�a�symbol�document�to�a�graph�document����#P��609�����6��graphButton����#P��610������#P�611�����6��//�?�Messages�from�and�to�a�graph�document.����#P��612�����6��//�?�Response�is�SendGraphDoc����#P��613�����6��selectedRectangleGraph����#P��614�����6��incrementActiveParameter����#P��615�����6��decrementActiveParameter����#P��616�����6��decrementParameter����#P��617�����6��incrementParameter����#P��618�����6��horizontalzoomout����#P��619�����6��horizontalzoomin����#P��620�����6��verticalzoomout����#P��621�����6��verticalzoomin����#P��622�����6��doublezoomout����#P��623�����6��doublezoomin����#P��624�����6��graphWindowResized����#P��625�����6��toggleDirectionField����#P��626�����6��toggleErase����#P��627�����6��circularAspect����#P��628�����6��setGraphPaper����#P��629������"#��7
����������WEB���MA��Z�THXPER�T����^17����V������6��updateParameters����#P��630�����6��parameterIncrementChanged����#P��631�����6��drawAll����#P��632�����6��zoomAtPoint����#P��633�����6��graphMoved����#P��634�������X��13.�����O��Uver��rview��of�the�interf�a��ce����#P��635�����BलWhile���the�main�fo�Gcus���of�this�do�cumen���t�is�the�comm�unication���b�Get�w�een�the�Engine����#P��636�����6लand�pthe�pin���terface,�v�nev�ertheless�w�e�pwill�describ�Ge�the�arc���hitecture�of�the�in���terface�as����#P��637�����6लw���ell.�m�There�IMis�ILnothing�particularly�inno���v��q�ativ�e�IMab�Gout�it:�k�it�is�all�standard�PHP�IIand����#P��638�����6लJa���v��q�ascript.�gDOne��~thing��w�orth�y�of��note�is�that,�&Iunlik���e�the�usual�W��*�eb�arc���hitecture,����#P��639�����6लthere��Vis�no�database�whatso�Gev���er.�=MathXp�ert��Vdo�es��Wnot�collect�or�use�an���y�data�ab�out����#P��640�����6लits��ousers�or��nwhat�they�do.��Y��*�ou�can�use�MathXp�Gert�completely�anon���ymously��*�.��On����#P��641�����6लthe�sother�hand,���y���ou�are�not�s�c��}'omp�el���le�d�s�to�b�Ge�anon�ymous;�y�ou�scan�pro�vide�some����#P��642�����6लinformation�mthat�will�enable�MathXp�Gert�to�lrep�ort�y���our�p�erformance�to�an�external����#P��643�����6लserv���er.�q�The�UUp�Goten�tial�uses�of�this�feature�will�b�Ge�discussed�b�elo���w.����#P��644�����BलIn��programming�this�in���terface,���I���stuc�k��to�pure�PHP�and��Ja���v��q�ascript,���esc�hewing����#P��645�����6लall�Ψ\mo�Gdern�Χframew���orks."�ݿMy�reasons�for�this�are�(1)�it�w���as�not�v�ery�Χdicult�to����#P��646�����6लaccomplish��:all�that�I��(required;���(2)�PHP�and�Ja���v��q�ascript�ha�v�e�b�Geen�p�ounded�on�for����#P��647�����6लman���y��jy�ears��ino�w,���and�b�Goth��jof�them�w���ork�quite�reliably;��sand�(3)�framew���orks�come����#P��648�����6लand���go,�Ŏwhile�PHP��nand�Ja���v��q�ascript���are�here�to�sta���y��*�,�ōso�b�y���writing�in�those�languages,����#P��649�����6लI�UUa���v�oid�obsolescence.����#P��650�����BलI�]~follo���w�ed�]�this�]�principle:����Don���P't��-hassle��,the�user.��
�Don't�ask�them�]�questions�to����#P��651�����6लclarify��their�in���ten�t,�suc�h��as���What�5Tis�the�indep��}'endent�variable?�O��Don't�ev���en��tell�them����#P��652�����6लwhat�ױthe�rules�are�for�determining�the�indep�Genden���t�ײv��q�ariable.���Just�get�it�righ�t�b�y����#P��653�����6लy���ourself,���and�L�the�user�L�will�nev�er�ev�en�kno�w�it�L�w�as�an�issue.�W�Don't�L�ask�them�to����#P��654�����6लsp�Gecify���the���ranges�of��x��and��y�&Ȳfor�a�graph{just�get�them�righ���t.�ҕAnd,��Ub�Ge�sure�that����#P��655�����6लif�g
the�guser�w���an�ts�to�g
adjust�them,�kwthe�graph�can�b�Ge�directly�manipulated�after�it�is����#P��656�����6लdra���wn.��Of�\�course,�^�if�the�\�program�exp�Gects�v��q�ariables�in�the�last�half�of�the�alphab�Get����#P��657�����6लand���parameters���in�the�rst�half,��a�user�who�exp�Gects�otherwise�ma���y�b�Ge�surprised;����#P��658�����6लbut�UUthat�is�the�price�of�getting�things�mostly�righ���t�and�mostly�hassle-free.����#P��659�����BलThere�)is�only�)one�t���yp�Ge�of�do�cumen���t�in�W��*�eb�)MathXp�ert,�1�but�a�)do�cumen���t�can�b�e����#P��660�����6लview���ed���sym�b�Golically���or�graphically��*�.�06It�is�a�useful�shorthand�to�sp�Geak�of�\sym���b�Golic����#P��661�����6लdo�Gcumen���ts"��5or�\graphical��4do�cumen���ts",�'-dep�ending�on�ho���w�the��4do�cumen���t�is�b�eing����#P��662�����6लview���ed.�j*Hence�>|the�>}t�w�o�most�>}imp�Gortan�t�pages�>}in�the�in���terface�are��Symb��}'olicDo�c.php����#P��663�����6लand��4�Gr��}'aphDo�c.php�,��lwhic���h�manage�the�sym�b�Golic�and�graphical�views,��lresp�ectiv���ely��*�.����#P��664�����6लBut���b�Gefore�a�do�cumen���t�is�created,���the�user�m�ust�someho�w�get�a�problem�to�w�ork�on;����#P��665�����6लthere�>are�sev���eral�>w�a�ys�>to�accomplish�that.��Therefore�the�in���terface�falls�naturally�in���to����#P��666�����6लthree�4�parts:�a�Sym���b�GolicDo�c,�;`GraphDo�c,�;_and�the�\pre-do�cumen���t"�pages�for�getting�a����#P��667�����6लproblem.�q�W��*�e�UUwill�dev���ote�the�next�three�sections�to�these�topics.����#P��668�������G&�14.����_�Mana��ging��a�symbolic�document����#P��669�����6ल14.1.��Do�Q�cumen��9t��re-sen�t��at�ev�ery��step.��It�HKis�HLfundamen���tal�to�the�design�that����#P��670�����6लmost��ymessages�are�sen���t�to�the�Engine�with��xthe�submission�of�a�form,�
rso�the�curren�t����#P��671�����6लpage�V�will�close,���and�the�resp�Gonse�to�the�message�will�b�e�the�V�en���tire�SV�G�VUneeded����#P��672�����6लto��*displa���y��)the�do�Gcumen�t.��DThat�will��)not�b�Ge�apparen���t�to�the�user,��who�will�see�for����#P��673�����6लexample��"just�one�more��!line�in�a�calculation.�;aA���few�messages�are�Ajax�messages�that����#P��674������)���7
��������6ऱ18���,'MICHAEL���BEESON���V������6लdo�;Unot�close�the�page.�iExcept�for�these�messages,�@�the�;Vresp�Gonse�to�ev���ery�message�is����#P��675�����6लthe��whole�do�Gcumen���t:�'!either��sendSymb��}'olDo�cument���or��	�sendGr�aphDo�cument��is�called.����#P��676����͍�6ल14.2.��T��
�ranslation.��As�#}men���tioned�ab�Go�v�e,��the�#~Engine�pro�vides�natural-language����#P��677�����6लtext��in�the�supp�Gorted�languages��for�text�used�in�reasons�for�steps,�-khin���ts,�-jerror����#P��678�����6लmessages,�>�remarks,�>�and�?the�>lik���e.���T��*�ext�that�is�created�only�in�the�in���terface,�>�suc�h����#P��679�����6लas��qprompts�for�data�en���try�elds,���is�translated�in��translateEntryPages.js�,�with����#P��680�����6लa���similar���tables�also�in��EnterProblem.php��and��MakeGraph.php�.��IOther�pages�call����#P��681�����6लup�Gon����translateEntryPages.js��۲to�replace�text�b���y�its�translation,��Zusing�the�id�of�an����#P��682�����6लHTML�1uor�1~SV���G�elemen�t�1~and�Ja�v��q�ascript�1}to�replace�the�text�b�y�its�translation,�8�using����#P��683�����6लthe�޹v��q�ariable��language�.�J>That�v�ariable�is�set�b���y�a�selector�in�the�top�page��index.php�,����#P��684�����6लor��in��SymbolicDoc.php��after�a�calculation�has�b�Gegun.���It�is�passed�as�a�parame-����#P��685�����6लter�œwith�›most�messages�to�the�Engine,���so�the�Engine�can�kno���w�what�language�to����#P��686�����6लgenerate.����#P��687�����6ल14.3.��T��9yp�Q�e�9/Size.��In����index.php��and��SymbolicDoc.php�,��!there�is�a���selector�pro-����#P��688�����6लviding�cc���hoices�to�con�trol�the�t�yp�Ge�size.���The�c�hoices�from�this�selector�determine����#P��689�����6लthe��v��q�alue��of��sc��}'aleF��;�actor�,�whic���h�is�1�:�0�when��Normal�!�size��is�c���hosen.�@YThe�eects�of����#P��690�����6लthis���selector�are���managed�in��TypeSize.js�.�&�The�v��q�alue�of��sc��}'aleF��;�actor��is�used�to����#P��691�����6लc���hange���the����width�,�&��height�,�and��style.top��of���SV���G���elemen�ts,�&�but�the����viewBox��is����#P��692�����6लnot��c���hanged,�&�resulting�in�c�hanging�the��size�of�the�text�on�the�screen.�^HNot�c���hanging����#P��693�����6��style.right�Ss�results�in�the�reasons�b�Geginning�at�ab�out�the�same�column.�q&In�order����#P��694�����6लthat���the���size�should�not�rev���ert�to�\normal"�at�eac���h�line,��when�the�page�is�re-sen���t�b�y����#P��695�����6लthe��2Engine,��j�sc��}'aleF��;�actor��is�sa���v�ed��3in��2Ja�v��q�ascript's�\lo�Gcal��3storage."��^The�Engine�nev���er����#P��696�����6लkno���ws��|an�ything��}ab�Gout��sc��}'aleF��;�actor�.�=There�is�no�suc���h�thing�as�a��T��;�yp��}'eSizeChange�d����#P��697�����6लmessage.����#P��698����̍�6ल14.4.��Selection��Rectangle.��The� �user� �selects�a�rectangle�with�the�mouse�or�other����#P��699�����6लp�Goin���ter���device.�<�Sym�b�olicDo�c.php���manages�that���selection,�գand�at��p��}'ointerUp��it�sends����#P��700�����6लa��;�sele��}'cte�dR�e�ctangleSymb�ol��:�message�to�the�Engine.�>It�has�to�de-scale�the�co�Gordinates����#P��701�����6लof���the�rectangle�b���y��sc��}'aleF��;�actor�,�*eas�the�Engine�kno�ws���where�form�ulas�w�ould�b�Ge�if����#P��702�����6��sc��}'aleF��;�actor����w���ere�1.��The�Engine���nds�the�selected�term�and�\snaps"�the�rectangle����#P��703�����6लto���the�b�Go���x�that�just���con�tains�that�term,�/sending�it�bac�k���with�the�do�Gcumen�t�as�SV�G����#P��704�����6लof�UUclass��highlight�,�con���taining�one�or�more��<rect>��elemen�ts.����#P��705�����6ल14.5.��Op�Q�eration�weSelection�wfMen��9u.��A���t��Bthe��Csame�time,�~the�Engine�pro�Gduces�the����#P��706�����6लmen���u�c�items�c�for�the�Op�Geration�Selection�Men���u,��and�sends�them�as�SV���G�cKof�class����#P��707�����6��menuitem�.�`Sym���b�GolicDo�c.php��assem�bles��these�items��in�to�a�men�u�and��decides�where����#P��708�����6लto��.put�it,�i�and�op�Gerates�the�men���u.�	oQWhen�the��-user�mak�es�a�c�hoice,�i�it�sends�a����#P��709�����6��sele��}'ctMenuChoic�e�oi�message�telling�the�ohEngine�whic���h�c�hoice�w�as�made.��The�Engine����#P��710�����6लthen��~tries��}to�execute�that�op�Geration�(either�on�or�with�the�selected�term);�;�if�it����#P��711�����6लsucceeds��the��do�Gcumen���t�is�up�dated�with��the�new�line,��and�sen���t�to�the�bro���wser�(of����#P��712�����6लcourse�a�without�the�a�selected�term�and�men���u);���if�it�fails,��Gthere�will�b�Ge�an�error�message����#P��713�����6ल(SV���G�UUof�class��mathError�)�instead�of�a�new�line.����#P��714�����6ल14.6.��Buttons�'�at�'�the�top�of�Sym��9b�Q�olicDo�c.php.��There���is���a�ro���w�of�buttons�at����#P��715�����6लthe���top,��including��A���utoStep�,��A�utoFinish�,��and����ShowStep�.�8��A�utostep��tak���es���one�step����#P��716�����6लin�՗auto�Ֆmo�Gde,���sending�bac���k�a�do�Gcumen���t�with�one�more�line�(unless�it's�nished).����#P��717�����6��A���utonish�2��sends�2�bac���k�a�completed�do�Gcumen���t.�	j�Showstep��is�in���tended�to�sho���w�the����#P��718�����6लuser���ho���w���they�could�accomplish�the��A���utoStep��result�using�the�men���u;��a�term�will�b�Ge����#P��719�����6लautomatically��selected,��the�Op�Geration��Selection�Men���u�will�app�ear,��and�an��item�will����#P��720������=M��7
����������WEB���MA��Z�THXPER�T����^19����V������6लb�Ge���highligh���ted�in���that�men�u,���whic�h���if�selected,���should�duplicate�the��A���utoStep��result.����#P��721�����6लI���cannot���guaran���tee���that�this�will�alw���a�ys���w�ork,�Ǧbut�it���is�prett�y�go�Go�d.��$In�Windo���ws����#P��722�����6लMathXp�Gert,���the��ecursor�w���as�animated��fto�imitate�the�term�selection�and�men���u�c�hoice,����#P��723�����6लbut���for�securit���y�reasons,�3Ja�v��q�ascript�is�not���allo�w�ed�to�mo�v�e�the�cursor,�3so�w�e�just����#P��724�����6लhighligh���t��wthe��xsuggested�selection�(in�a�color�that�usually�do�Gesn't�app�ear��xin�the����#P��725�����6लmen���u).�tlThe�V7men�u�will�still�op�Gerate�normally��*�.�tl�Undo��causes�the�V6do�cumen���t�to�rev�ert����#P��726�����6लto��its�condition�b�Gefore��~the�last�step.�dE(That�is�surprisingly�complex,�%	but�happ�Gens����#P��727�����6लen���tirely�UUinside�the�Engine{all�the�in�terface�has�to�do�is�displa�y�the�do�Gcumen�t.)����#P��728�����BलThe�UUbuttons�themselv���es�are�dra�wn�with�SV�G�graphics,�as�dened�in����#P��729�����6��ButtonDefinitions.svg�.���Sev���eral�}of�what�app�Gear�to�b�e�}
images�are�just�UTF-8����#P��730�����6लc���haracters,�UUsuc�h�as�the�\ey�e"�that�is�used�for�the�Sho�w�Assumptions�button.����#P��731���+��6ल14.7.��Assumptions.��MathXp�Gert�z�analyzes�the�domain�of�z�the�problem�when�the����#P��732�����6लdo�Gcumen���t�(
is�initialized,�\�and�main�tains�a�list�of�assumptions�that�starts�with�the����#P��733�����6लdomain��:of�the�problem,��3but��;ma���y�gro�w�as�certain�op�Gerations�require�making�more����#P��734�����6लassumptions;�bfor��0example��/y���ou�can�only�tak���e�the�square�ro�Got�of�p�Gositiv���e�things.����#P��735�����6लThe�&:curren���t�&9assumptions�are�sen�t�&9with�the�do�Gcumen�t�&9as�SV�G�&.of�&9class��assumption�.����#P��736�����6लSym���b�GolicDo�c.php��displa�ys�them��(in�a�mo�Gdal�p�opup)�when��the�Assumptions�button����#P��737�����6लis�UUclic���k�ed.����#P��738�������� ��15.������Mana��ging��a�graphical�document����#P��739�����BलThe��graphical�view�of�a�do�Gcumen���t�is�managed�b�y��GraphDoc.php�.�}EThe�bro�wser����#P��740�����6लwindo���w���is���divided�in�to�t�w�o���parts:�>
at�the���left�is���the�Graph�T��*�o�Golbar,��con�taining�to�Gols����#P��741�����6लwith���whic���h�to���manipulate�the�graph.�-A�t���the�righ�t�is�the�graph�itself.�-The�Engine����#P��742�����6लkno���ws�UUonly�ab�Gout�the�graph,�and�do�es�not�manage�the�T��*�o�olbar�at�all.����#P��743�����6ल15.1.��Initial�Ddispla��9y.��Although��1the�Engine�do�Gesn't�manage�the�T��*�o�olbar,���it�m���ust����#P��744�����6लkno���w�
Gthe��width��of�
Hthe�T��*�o�Golbar,�Jin�order�to�send�the�graph�in�CSS�
4pixel�co�Gordinates����#P��745�����6लin�pXthe�bro���wser�windo�w.���This�is�accomplished�b�y�sending�the�pYwidth�of�the�T��*�o�Golbar����#P��746�����6लas�r�a�r�parameter�with�some�messages�and�storing�it�as�a�PHP�r�session�v��q�ariable.���The����#P��747�����6लinitial�|�job�of�GraphDo�Gc.php�is�to�displa���y�the�T��*�o�olbar�and�the�graph�itself,���as�sen���t����#P��748�����6लb���y�Sthe�Engine�Rusing��sendGr��}'aphDo�cument�.�W�The�displa���y�Sof�the�graph�is�done�just�b���y����#P��749�����6लthe��PHP����echo��command,��outputting��the�SV���G�pro�Gduced�b���y��sendGr��}'aphDo�cument�.����#P��750�����6लThe��'initial�displa���y�of�the�T��*�o�Golbar�has�a��&little�sublet�y��*�,���in�that�exactly�whic�h�to�Gols�are����#P��751�����6लa���v��q�ailable�dvdep�Gends�on�the�dutopic.��*F��*�or�example,�h>on�p�olar�dugraphs,�h>asp�ect�ratio�1�m���ust����#P��752�����6लb�Ge�dTmain���tained,���so�y�ou�don't�dUha�v�e�buttons�that�allo�w�dUhorizon�tal�or�v�ertical�zo�Gom,���but����#P��753�����6लonly�u�zo�Goming�u�in�b�oth�directions�u�at�the�same�time.��CAnd�the�DirectionField�button����#P��754�����6लonly���app�Gears�on�dieren���tial�equations�where�a�direction�eld�mak�es�sense.�4IThe�co�Gde����#P��755�����6लfor��Rdeciding�whic���h�buttons�to�sho�w�and��Qwhere�to�put�them�is�in��AdjustToolbar.js�.����#P��756�����6ल15.2.��Implemen��9ting���the���T��
�o�Q�olbar.��Some��Sof��Rthe�T��*�o�Golbar�buttons�immediately����#P��757�����6लsend�dYa�dZmessage�to�the�Engine,�hwhic���h�in�resp�Gonse�c���hanges�the�do�Gcumen�t�dZand�sends����#P��758�����6लit��afresh�with��sendGr��}'aphDo�cument�.���That��applies,��kfor�example,��lto�all�the�zo�Gom����#P��759�����6लbuttons,��4and��the�Circle��button�(whic���h�enforces�asp�Gect�ratio�1),��4and�the�Sho���w�Di-����#P��760�����6लrection�"�Field�"�button.���Then�there�are�sev���eral�buttons�that�con���trol�what�function����#P��761�����6लthe��mouse�(or�p�Goin���ter)��will�ha�v�e.�(It�can�b�Ge��used�for�the�P�oin�t-Slop�Ge�to�ol,��Mor�for�a����#P��762�����6लselection��rectangle,��whic���h�can��b�Ge�either�cen�tered��at�mousedo�wn,��or�ha�v�e��a�corner����#P��763�����6लat���mousedo���wn.��VSimple�Ja�v��q�ascript�dra�ws�the�selection�rectangle,�̻and�a�message�is����#P��764�����6लsen���t�UUonly�when�the�Dra�w�button�is�pressed.����#P��765������R���7
��������6ऱ20���,'MICHAEL���BEESON���V������6ल15.3.��Direct�wmanipulation.��T��*�ouc���hscreens��Qand��Rtrac�kpads�giv�e��Qthe�user�the�abilit���y����#P��766�����6लto���directly���scroll�(using�t���w�o�ngers)���or�zo�Gom�(using�pinc���h�gestures).��These�eects����#P��767�����6लare��Qmanaged��Rin�Ja���v��q�ascript,�Ras�y�ou��Rcertainly�cannot�mak�e��Ra�roundtrip�to�the�Engine����#P��768�����6लat�c�ev���ery�c�mousemo�v�e.�!HWhen�the�c�scroll�or�zo�Gom�is�completed,��"the�Engine�is�notied�of����#P��769�����6लthe��Lc���hange,���and�at�that�p�Goin�t�the�do�Gcumen�t��Kis�sen�t�again�with��sendGr��}'aphDo�cument�.����#P��770�����BलThe��graph��is�actually�dra���wn�with�three�times�the�visible�width�and�heigh���t,�%so����#P��771�����6लwhen�rsit�is�initially�displa���y�ed,���y�ou�rsare�lo�Goking�at�the�middle�rrof�nine�rectangles.�&'There����#P��772�����6लis�݄th���us�݅a�lot�of�SV���G��ain�the�bro���wser�that�y���ou�do�not�see.�
UThat�SV���G��acan�b�Ge�used����#P��773�����6लto�r�supp�Gort�scrolling�r�and�zo�oming.�ɿY��*�ou�can�scroll�or�r�zo�om�as�m���uc�h�r�as�r�one�windo���w����#P��774�����6लwidth��For�heigh���t.�֚If�y�ou�try�hard,��y�ou�can��Escroll�to�that�limit�and�see�the�edge�of����#P��775�����6लthe�Y�Univ���erse,�[but�Y�normally��*�,�[y�ou�w�ould�Y�release�the�mouse�or�p�Goin���ter�b�efore�Y�mo���ving����#P��776�����6लthat�UUfar.����#P��777�����BलDuring�<|zo�Goming,�Authe�graph�<}pap�er�ma���y�<}c�hange�<|the�n�um�b�Ger�<|of�lines�p�Ger�inc���h,�Aubut����#P��778�����6लwhen�UUthe�graph�is�sen���t�again,�the�graph�pap�Ger�will�resume�its�normal�app�earance.����#P��779����͍�6ल15.4.��Graph�apap�Q�er.��The��ET��*�o�Golbar��Doers�a�button�sho���wing�samples�of�the�dieren���t����#P��780�����6लgraph���pap�Gers�a���v��q�ailable���(including�plain�blac�k�and���plain�white).�}�Y��*�ou�can�view�the����#P��781�����6लsamples�UUand�then�select�a�new�graph�pap�Ger�if�desired.����#P��782�����6ल15.5.��Color�#�selection�#�not�a��9v��\railable.��There���is�no�w���a�y���to�c���hange�the�color�sc�heme����#P��783�����6लof�޺a�graph�(other�than�c���hanging�the�graph�pap�Ger).�J>Since�MathXp�ert�is�anon���ymous,����#P��784�����6लthere��is�no�w���a�y��to�sa���v�e��a�user's�color��preferences�(other�than�PHP�psession�v��q�ariables����#P��785�����6लor��Ja���v��q�ascript�lo�Gcal�storage),�#�so�suc�h�c�hoices�w�ould�only�b�Ge�temp�orary��*�,�#�and�the����#P��786�����6लdefaults�1@are�go�Go�d,�8wso�1@in�our�1?view�this�is�one�less�distraction�from�the�mathematics.����#P��787�����6लIn��the�future,��xif�a�w���a�y��to�c���hange���colors�should�b�Ge�desired,�it�should�b�Ge�accomplished����#P��788�����6लb���y�޶direct�manipulation:���righ�t-clic�k�on�the�thing�y�ou�w�an�t�to�c�hange,�rather�than����#P��789�����6लthrough�UUcomplicated�dialogs.����#P��790����̍�6ल15.6.��Singularities���and�assumptions.��The��Engine��calculates�and�sends�these,����#P��791�����6लas�WqSV���G�W/elemen�ts�of�class��singularity��and��assumption�.�xThe�in�terface�displa�ys����#P��792�����6लthem�&�in�a�mo�Gdal�&�elemen���t�when�the�corresp�onding�T��*�o�olbar�buttons�&�are�clic���k�ed.�bLF��*�or����#P��793�����6लexample�J}if�J|y���ou�graph�1�=������p���UW����fe��3荵x����s�,�L�y�ou�will�get�J|the�assumption�0���<�x�J}�and�the�singularit���y����#P��794�����6वx���=�0.����#P��795�����6ल15.7.��P��9arameters.��It���is���encourage�to�mak���e�graphs�with�parameters,��efor�example����#P��796������6लsin��D�j�ax�.��BThere�k�will�k�b�Ge�a�button�on�the�to�Golbar�for�eac���h�parameter.��BIn�the�example,����#P��797�����6लthere��fwill�b�Ge��ea�button�lab�eled��a�,��band�next�to�it��et���w�o��fbuttons�lab�eled�+�and��e��,��cwhic���h����#P��798�����6लwill�o�incremen���t�and�decremen�t�the�o�v��q�alue�of��a�.���If�y�ou�w�an�t�to�o�c�hange�the�v��q�alue�of��a����#P��799�����6लdirectly��*�,�Dor��c���hange��the�incremen�t,�Dclic�k�on��a��itself;�the�dialog�y�ou�get�is�created�and����#P��800�����6लmanage�Qb���y�le��AdjustParameter.js�.�^qNext�to�the�incremen�t/decremen�t�buttons�is����#P��801�����6लa��green-circle��button,���whose�to�Goltip�explains�that�green�means�sho���w�only�the�graph����#P��802�����6लfor���the�curren���t�v��q�alue�of���the�parameter,�Җand�red�means�k�eep�all���the�graphs.��cT�ypi-����#P��803�����6लcally��6with��5an�ordinary�graph,��ny���ou�w�an�t��5just�one�at�a�time,��mand�with�a�dieren���tial����#P��804�����6लequation,�UUy���ou�w�an�t�a�lot�of�solutions�sho�wing.����#P��805�����6ल15.8.��Instan��9t�6Kanimation�of�6Lparameters.��In��
addition�to�c���hanging��the�parameter����#P��806�����6लb���y�'�one�'�incremen�t�at�'�a�time,�0�y�ou�'�can�also�use�a�slider�to�v��q�ary�the�parameter�mo���vie-����#P��807�����6लst���yle�Fthrough�Fa�range�of�v��q�alues.�l�F��*�or�example,�Iy���ou�migh�t�Ftry��sin��7ȵax��or��y�"�=���x���^��3������;�ax�.����#P��808�����6लThe�
1displa���y�will�mo�v�e�rapidly�through�a�
2range�of�ft�y�graphs�for�dieren�t�v��q�alues�of����#P��809�����6लthe��4parameters.�.This�is�accomplished�without��5a�round-trip�to�the�serv���er,���b�y��4sending����#P��810�����6लall�ft���y�graphs�to�the�bro���wser�with�the�do�Gcumen���t;�,yeac�h�graph�is�really�just�a�list�of����#P��811������g���7
����������WEB���MA��Z�THXPER�T����^21����V������6लco�Gordinates�rDof�rCab�out�600�p�oin���ts.�ȓThen�rCwhen�the�slider�is�used,�yJa���v��q�ascript�c�hanges����#P��812�����6लthe���visibilit���y��of�those�graphs,���making�just�one�visible{the�one�that�corresp�Gonds�to����#P��813�����6लthe�UUp�Gosition�of�the�slider.��� �16�����#P��814�����BलWhen��there�are��t���w�o��(or�more)�parameters,��as�in�the�example��y��=��G�ax����+��b�,��y���ou����#P��815�����6लget�:�a�:�slider�for�b�Goth�parameters.�h�But�just�one�of�them�at�a�time�is�\activ���e",�?�whic�h����#P��816�����6लmeans�mSit�mRhas�ft���y�in�visible�mRgraphs�for�the�slider�v��q�alues.���The�activ���e�slider�has�a����#P��817�����6लgreen�x�knob.�ۺWhen�x�y���ou�clic�k�another�slider,��zy�ou�mak�e�that�x�one�activ�e,��zand�the����#P��818�����6लEngine�(@sends�(?a�dieren���t�ft�y�graphs,�\�and�(?giv�es�its�slider�a�(?green�knob.��� �17���m�In�the����#P��819�����6लspirit���of���\don't�hassle�the�user",�/y���ou�are�not�ask���ed�ab�Gout�the�incremen���t�b�Get�w�een����#P��820�����6लy���our�5�parameter�v��q�alues.�`Ma�yb�Ge�y�ou�think�y�our�5�slider�is�to�Go�jerky��*�.�`Then�use�the����#P��821�����6लparameter�-�button,�5�and�-�y���ou�can�decrease�the�parameter�incremen���t,�5�after�whic�h�-�y�ou����#P��822�����6लwill�UUha���v�e�new�in�visible�graphs�and�y�our�slider�ma�y�w�ork�b�Getter.��� �18�����#P��823���F!��6ल15.9.��In��9teger�6Iv�ersus�6Hreal�parameters.��.�C�P���arameters��with�names��n�,�沵m�,�汵k�P��,�or��the����#P��824�����6लsame�obin�ocupp�Gercase,��`will�not�get�sliders.�%!They�should�b�Ge�used�when�a�slider�w���ould�not����#P��825�����6लmak���e�L�sense,�NVas�L�in�the�upp�Ger�limit�of�a�sum,�NUor�a�Lissa��8jous�pattern�(�sin��
�Ƶmx;���cosnx�).����#P��826���������q�16.���S��Getting��a�pr��oblem����#P��827�����BलHere�hw\problem"�also�can�mean�\function�to�graph."��-T��*�o�understand�the�pro�Gcess����#P��828�����6लof���getting���a�problem,���y���ou�m�ust���remem�b�Ger�that�y�ou�m�ust���c�ho�Gose�or�en�ter���not�only����#P��829�����6लa��dproblem,��but�the��e�topic��of�that�problem;�(�there�are�179�topics,��whic���h�is�an�o���v�er-����#P��830�����6लwhelming��quan���tit�y��of�c�hoices.��oThe�topics�are��organized�in�to�a��more�manageable����#P��831�����6लn���um�b�Ger�;.of�;-\problem�t���yp�es",�@iso�;-the�pro�cess�;-can�b�e�view���ed�;-as�a�t�w�o-step�;-pro�Gcess,�@iof����#P��832�����6लselecting�UUa�problem�t���yp�Ge�and�then�a�topic.����#P��833�����BलT��*�o��)get��(a�problem,���y���ou�b�Gegin�b���y�c�ho�Gosing��(either��Make�/wa�Gr��}'aph�,����Enter�a�Pr�oblem�,����#P��834�����6लor�UU�MathXp��}'ert���Pr�oblem�Libr�ary�.�q�W��*�e�UUwill�describ�Ge�ho���w�eac�h�of�these�w�orks�in�turn.����#P��835���F ��6ल16.1.��Mak��9e���a�graph�or���en�ter�a�problem.��If�*<y���ou�c�ho�Gose��Make�lAa�l@gr��}'aph�,�2�y�ou�will����#P��836�����6लgo�i�to�i��MakeGraph.php�,���whic���h�presen�ts�i�a�c�hoice�i�of�kinds�of�graph�y���ou�can�mak���e.����#P��837�����6लThese�J�c���hoices�corresp�Gond�J�to�problem�t�yp�Ges.�RSimilarly��*�,��"�Enter�u�a�pr��}'oblem�JƲleads�to����#P��838�����6��EnterProblem.php�,��4whic���h��+presen�ts�a��,c�hoice�of�the��,kinds�of�problems�y�ou��,can�solv�e.����#P��839�����6लHa���ving�C�pic�k�ed�a�problem�t�yp�Ge�C�from�one�of�these�pages,�Gy�ou�C�go�to�an�\en�try�page",����#P��840�����6लwhere���y���ou���can�en�ter�y�our���actual�problem.�VtY��*�ou�then�clic���k��Display��to�conrm�that����#P��841�����6लy���ou�E�t�yp�Ged�it�correctly��*�,���and�then��Do�qthe�qMath��or�E��Solve�the�qEquation��or��Dr��}'aw��to����#P��842�����6लmo���v�e�UUon�to�the�calculation�or�graph.����#P��843�����BलThese� Ven���try�pages�ha�v�e�names� Ub�Geginning�with��Enter�;���there�are�quite�a�few�of����#P��844�����6लthem.�YA�<�few�=of�=them�ha���v�e�=include�commands�leading�to,�ufor�example,�u�OneGraph.php����#P��845�����6लor�q5�SeveralGraphs.php�,�x,but�q4there�is�a�tension�b�Get���w�een�q5co�de�q4re-use�and�co�Gde�com-����#P��846�����6लplexit���y��*�,�>]as�8�if�8�the�same�co�Gde�is�used�for�sev���eral�topics,�>]there�is�a�lot�of�ec���hoing�PHP����#P��847���6ट
;U�ff<��͍�����h�16����F��J�or�Euprogrammers:�.bro�Îwsers�are�Etproprietary�,�b=so�w�Îe�Eucan't�see�Etexactly�ho�w�this�Etis�accomplished,��
�but�[.there�[-m�Îust�b�<re�double-buering�of�the�\la�Îy�ers"�[.in�v�olv�ed.��gY��J�ou�can�[-c�hange�the�visibilit�y�[-of�man�y���graphs�;instan�Îtly��J�.��!By�con�trast,�Tmif�y�ou�try�to�insert�and�remo�v�e�things�;from�the�DOM,�it�tak�es�a���comparativ�Îely��Xlong�time,�p�<rerhaps�b�ecause�the�DOM�is�laid�out�again�after�ev�Îery�insertion.��
�r������h�17����The�Rneed�for�a�Rround-trip�to�the�serv�Îer�in�tro�<rduces�a�200-millisecond�Rdela�y;��oso�clic�k�slo�wly���when��Xc�Îhanging�the�activ�e�parameter.��������h�18����F��J�or��programmers:���Therefore,��$the��p���ar�ameterIncr�ementChange�d�message��m�Îust�get�the�whole���do�<rcumen�Ît���in�resp�onse;��Osince�nothing�visible�will���c�Îhange,��|it�could�otherwise�ha�v�e���b�<reen�an�Ajax���message,�but���as�men�Îtioned,�it's���slo�w���to�insert�ft�Îy�new�graphs�in�Îto�the�DOM,�y�Îou�migh�t���as�w�ell���send��Xthe�whole�do�<rcumen�Ît.�����}i��7
��������6ऱ22���,'MICHAEL���BEESON���V������6लin���to���Ja�v��q�ascript���that�is�hard�to�read�and�main���tain,���so�I��often�c�hose���to�write�separate����#P��848�����6लco�Gde,�UUwhose�common�parts�I�pasted�and�edited.����#P��849�����6ल16.2.��The�.�arro��9w�button.��In��?the��>en���try�pages,���there�is�an�\arro���w�button"�to�the����#P��850�����6लrigh���t�Z6of�the�Z5rst�en�try�eld.��iClic�king�that�button�Z5pic�ks�a�random�topic�Z5(under�the����#P��851�����6लproblem��t���yp�Ge��y�ou�ha�v�e�c�hosen)�and��a�random�problem�from�the�Problem�Libary��*�.����#P��852�����6लIf�"�y���ou�do�#not�ha�v�e�a�particular�#problem�already�in�mind,�Vjthis�is�an�easy�w���a�y�"�to����#P��853�����6लget�sda�seproblem;��land�y���ou�also�can�edit�that�problem.��The�co�Gde�to�handle�the�arro���w����#P��854�����6लbutton��9is��:in��arrowButton.js�.�HtIt�is�a�bit�tric���ky�as�it�in���v�olv�es��9creating�new�en���try����#P��855�����6लelds���dynamically��*�.�d�F�or�example�if���the�random�problem�is�three�linear�equations,����#P��856�����6लw���e�UUwill�need�to�create�a�new�en�try�eld�for�the�third�equation.����#P��857�����6ल16.3.��MathXp�Q�ert���Problem�Library.��This�!Ac���hoice�leads�y�ou�!Bto�a�three-column����#P��858�����6लselector��con���trol,��whic�h�allo�ws�y�ou�to�select�a�problem�t�yp�Ge,��a�topic,�and�a�problem.����#P��859�����6लThe��?curren���tly��>selected�problem�is�visible�against�a�ligh���t�blue�bac�kground��>b�Gelo�w�the����#P��860�����6लselector.�Z�Y��*�ou�pha���v�e�ot�w�o�buttons�at�othe�top�of�the�page:�OT�A��}'c�c�ept�T�sele�cte�d�pr�oblem�p�and����#P��861�����6��Edit��@sele��}'cte�d��Apr�oblem�.�;1If���y���ou�accept,��Ty�ou�will���go�immediate�to�either�GraphDo�Gc.php����#P��862�����6लor�UUSym���b�GolicDo�c.php.�q�Problem�selection�is�nished.����#P��863�����BलI�y�wrote�zEpage�zF�GetProblem.php�,�Áwhic���h�do�wnloads�zFthe�en�tire�zFMathXp�Gert�Prob-����#P��864�����6लlem��Library��*�,�=some��6500�problems,�so��it�can�b�Ge�examined�b���y�the�selector�con���trol.����#P��865�����6लThat,���ho���w�ev�er,���to�Gok��/an��.unacceptably�long�time.�+SSo,���I��wrote�the�m���uc�h��/more�com-����#P��866�����6लplex�yGetProblemAsync.php,�whic���h�do�wnloads�the�zproblems�async�hronously��*�,�so�the����#P��867�����6लscrolling��selector��con���trol�is�immediately�resp�Gonsiv���e.�k�An�y��programmer�who�w���an�ts����#P��868�����6लto���study���this�co�Gde�should�probably�rst�lo�Gok�at�the�sync���hronous�v�ersion,���whic�h�is����#P��869�����6लnot�UUactually�used�no���w,�but�still�included�for�study��*�.����#P��870�����BलA���t�p�the�p�top�of��GetProblem.php�,�w�y���ou�ha�v�e�p�t�w�o�buttons:����A��}'c�c�ept��@Sele�cte�d�Pr�oblem����#P��871�����6लand�/�Edit�E�Sele��}'cte�d�E�Pr�oblem�.�UfCho�Gosing��Edit��tak���es�0y�ou�to�the�appropriate�0en�try�page,����#P��872�����6लwith�\9the�selected�\8problem�pre-en���tered.��(This�is�accomplished�using�the�same�co�Gde�as����#P��873�����6लthe���arro���w�button�uses,���but�for�the�selected���problem�rather�than�a�random�problem.)����#P��874�����6लCho�Gosing��U�A��}'c�c�ept��T�tak���es�y�ou��Tdirectly�to�either�GraphDo�Gc.php�or�Sym���b�GolicDo�c.php.����#P��875�����6लProblem�UUselection�is�nished.����#P��876�������8���;��7
���(�C�scmtt8�'��<x

cmtt10�!�':

cmti10� �-�

cmcsc10��s6�cmss8��"V

cmbx10�#�f�cmti8��2cmmi8�|{Ycmr8�
!",�

cmsy10�
�b>

cmmi10�K�`y

cmr10�ٓ�Rcmr7����������

Sindbad File Manager Version 1.0, Coded By Sindbad EG ~ The Terrorists