CM.js

;register.push({
   id:'cm'
   ,name:'Crane matrix system'
   ,display:matrix_display
   ,able:matrix_limit
   ,compare:matrix_compare
   ,FS:(()=>{
      var data={}
      ,expand = (m1,FSterm)=>{
         var parent = (m,cache,x,y)=>{
            var str=x+','+y
            if(cache[str]!==undefined) return cache[str]
            for(var p=x;(p=y?parent(m,cache,p,y-1):p-1)>=0;){
               if(m[p][y]<m[x][y]) break
            }
            return cache[str]=p
         }
         ,L = (m,cache,x1,x2)=>{
            var x,y
            for(y=ymax;y>=0;--y){
               if(!m[x2][y]) continue
               for(x=x2;x1<x;) x=parent(m,cache,x,y)
               if(x===x1) return y
            }
            return -1
         }
         ,ascending = (r,x,y)=>{
            var str=r+','+x+','+y
            if(ascending_cache[str]!==undefined) return ascending_cache[str]
            return ascending_cache[str] = r<=x&&(r===x||ascending(r,parent(m1,m1cache,x,y),y))
         }
         ,m1cache={},m2cache={},ascending_cache={}
         ,endcol = m1.length-1
         ,m2 = m1.slice(0,endcol)
         ,child = m1[endcol]
         ,ymax = child.length-1
         ,LNZ
         for(LNZ=ymax;LNZ>=0;--LNZ){
            if(child[LNZ]>0) break
         }
         if(LNZ<0||!FSterm) return m2
         var BR = parent(m1,m1cache,endcol,LNZ)
         ,BRcolumn = m1[BR]
         ,offset = child.map((value,y)=>y<LNZ?value-BRcolumn[y]:0)
         ,offset_asc = Array(endcol).fill(0,BR).map((t,x)=>offset.map((value,y)=>ascending(BR,x,y)?value:0))
         ,col,n
         for(n=0;++n<=FSterm;){
            for(col=BR;col<endcol;++col){
               m2.push(m1[col].map((value,y)=>value+offset_asc[col][y]*n))
            }
         }
         for(col=endcol;BR<--col;) if(L(m1,m1cache,BR,col)>LNZ) break
         if(col===BR){
            if(ymax>0&&m2.every(column=>column[ymax]===0)) m2 = m2.map(column=>column.slice(0,ymax))
            return m2
         }
         m2.push(child.map((value,y)=>value+(y<=LNZ?value-BRcolumn[y]:0)*FSterm))
         var c = col
         ,c_ = c+(endcol-BR)
         ,d = m2.length-1
         ,D=[]
         for(col=endcol;col<d;++col) D.push(m2[col].map((value,k)=>{
            if(k>LNZ) return value
            var u = 0
            ,ss = col
            ,nextss
            while(true){
               nextss = parent(m2,m2cache,ss,k)
               if(nextss<endcol) break
               ++u
               ss = nextss
            }
            if(L(m2,m2cache,ss,d)>=k-1) return m2[c_][k]+u
            else return value
         }))
         m2 = m2.slice(0,c_).concat(D)
         if(ymax>0&&m2.every(column=>column[ymax]===0)) m2 = m2.map(column=>column.slice(0,ymax))
         return m2
      }
      return (m,FSterm)=>{
         if(''+m==='Infinity') return [Array(FSterm+1).fill(0),Array(FSterm+1).fill(1)]
         if(m.length===0) return []
         var datakey=matrix_display(m)
         if(!data[datakey]) data[datakey] = []
         else if(data[datakey][FSterm]!==undefined) return data[datakey][FSterm]
         return data[datakey][FSterm] = expand(m,FSterm)
      }
   })()
   ,init:()=>([
      {expr:[[Infinity]],low:[[]],subitems:[]}
      ,{expr:[],low:[[]],subitems:[]}
   ])
   ,semiable:m=>m.length>0
})