31:[] 2f:{"title":"Ganja.js Template Test","cells":[{"id":0,"value":"md`# Ganja.js Template Test\n\nFirst, we load ganja.js`","pinned":false,"hidden":false,"mode":"ojs"},{"id":165,"value":"Algebra = require('ganja.js')","pinned":true,"hidden":false,"mode":"ojs"},{"id":170,"value":"md `I've upgraded the 'inline' function so it can be used directly as a template string function.\n\nThis makes it very easy to define a template function for the algebra of your choice : `","pinned":false,"hidden":false,"mode":"ojs"},{"id":4,"value":"PGA2D = Algebra(2,0,1).inline ","pinned":true,"hidden":false,"mode":"ojs"},{"id":7,"value":"md`That's the templating function. Lets define some points, connect them into some lines and graph that.\n\nFirst, two points **a** and **b**, we start by defining a PGA function that returns the PGA representation of a euclidean point.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":46,"value":"point = PGA2D`(x,y)=>1e12-x*1e02+y*1e01`","pinned":true,"hidden":false,"mode":"ojs"},{"id":176,"value":"md`Using this function, we now define two points **a** and **b**`","pinned":false,"hidden":false,"mode":"ojs"},{"id":195,"value":"md`And to make it interesting, we'll animate point a using a counter.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":189,"value":"move = { \n var count=0;\n while(true) yield ((count++)%100/100);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":9,"value":"a = point(-0.5 + move,-1.3 )","pinned":true,"hidden":false,"mode":"ojs"},{"id":14,"value":"b = point(-1,1)","pinned":true,"hidden":false,"mode":"ojs"},{"id":19,"value":"md`next we'll join these in a line`","pinned":false,"hidden":false,"mode":"ojs"},{"id":17,"value":"ab = PGA2D`${a}&${b}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":23,"value":"md` and we'll find a second line orthogonal to **ab** and through point **a**`","pinned":false,"hidden":false,"mode":"ojs"},{"id":26,"value":"orth_ab = PGA2D`${ab}<<${a}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":32,"value":"md`now, let's graph all these items.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":35,"value":"PGA2D`this.graph([${a},\"a\",${b},\"b\",${ab},\"ab\",${orth_ab},\"orth_ab\"])`","pinned":true,"hidden":false,"mode":"ojs"},{"id":57,"value":"md `ofcourse all other features of ganja.js are also available`","pinned":false,"hidden":false,"mode":"ojs"},{"id":59,"value":"numbers = [1,2,3,4,5]","pinned":true,"hidden":false,"mode":"ojs"},{"id":63,"value":"even_numbers = PGA2D`${numbers}*2`","pinned":true,"hidden":false,"mode":"ojs"},{"id":66,"value":"md`Lets try an integrator :`","pinned":false,"hidden":false,"mode":"ojs"},{"id":70,"value":"RK4 = PGA2D`(f,y,h)=>{\n var k1=f(y), \n k2=f(y+0.5*h*k1), \n k3=f(y+0.5*h*k2), \n k4=f(y+h*k3); \n return y+(h/6)*((k2+k3)*2+k1+k4); \n}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":77,"value":"md `And use it to approximate ${tex`\\mathbb{e}`} (in just one step)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":81,"value":"almost_e = RK4(x=>x,1,1)","pinned":true,"hidden":false,"mode":"ojs"},{"id":84,"value":"md`We can just as easily call it with arrays :`","pinned":false,"hidden":false,"mode":"ojs"},{"id":90,"value":"almost_sin_cos = RK4(x=>[x[1],-x[0]],[1,0],1)","pinned":true,"hidden":false,"mode":"ojs"},{"id":108,"value":"here = md`## orthocenter\n\nLets do one more, given three points A,B,C - find the orthocenter`","pinned":false,"hidden":false,"mode":"ojs"},{"id":112,"value":"A=point(0,0.5)","pinned":true,"hidden":false,"mode":"ojs"},{"id":115,"value":"B=point(0.5,-0.5)","pinned":true,"hidden":false,"mode":"ojs"},{"id":117,"value":"C=point(-0.5,-0.5)","pinned":true,"hidden":false,"mode":"ojs"},{"id":119,"value":" orthocenter = PGA2D`(${B}&${C}<<${A})^(${C}&${A}<<${B})`","pinned":true,"hidden":false,"mode":"ojs"},{"id":133,"value":"md `hmm that's quite convoluted - we could clean this up by defining a function first ..`","pinned":false,"hidden":false,"mode":"ojs"},{"id":135,"value":"ortho2 = PGA2D`(A,B,C)=>(B&C<{\n \n var point = (x,y)=>1e12-x*1e02+y*1e01;\n \n var A=point(0,0.5),B=point(0.5,-0.5),C=point(-0.5,-0.5);\n \n var orthocenter=(B&C<