Creating a factoring calculator

Zacharias · November 2016

Hey Codea,

I'm attempting to code a program that will factor polynomials. Firstly, though, I have created a program that finds the factors of the inputted number. If you know how to factor, this basically will be part of the "x-box" method. This is just the beginning of a big project I have in mind.

-- Factor

function setup()

        parameter.integer("n", 0, 300, 0) 
        parameter.action("Factors", factor)
        print("Factors of "..n.." are: ")
        factorsList = { }
end

function factor()

    i = 1
    while(i <= n) do
        if(n%i==0) then
            print(i)
            table.insert(factorsList, i)
        end
        i = i + 1
    end
    drawFactors = true
end

function draw()

    background(40, 40, 50)
    fill(172, 22, 22, 255)
    rect(WIDTH/4, HEIGHT/4, 500, 400)
    fill(255, 255, 255, 255)
    fontSize(50)
    text(n, WIDTH/2+50, 550)
    for i = 1, #factorsList do
        text(factorsList[i], WIDTH/2-50, HEIGHT/2)
    end
end

I would like to draw the factors in a list format (with commas and such), however, they are overlapping each other. Also, in the print command, I want to have it in pairs. I'm trying to do for i,v in pairs(factorsList) do print(i,v) end but v doesn't have any value. Is there a way to have pairs with a single variable like i? So if the input was 10, the output (print and/or text) should read 1 10, 2 5.

dave1707 · November 2016

@Zacharias Here's your code modified a little.

-- Factor

function setup()
    parameter.integer("n", 0, 300, 0,factor) 
    factorsList = {}
end

function factor()
    factorsList = {}
    i = 1
    while(i <= n) do
        if(n%i==0) then
            table.insert(factorsList, i)
        end
        i = i + 1
    end
end

function draw()
    background(40, 40, 50)
    fill(172, 22, 22, 255)
    fontSize(25)
    text(n,WIDTH/2,HEIGHT-30)
    for i = 1, #factorsList do
        text(factorsList[i], WIDTH/2, HEIGHT-30*i-60)
    end
end

Zacharias · November 2016

@dave1707 Thanks a lot! It serves its purpose well. Now I just have to figure how to use this with factoring polynomials. Should be fun

Ignatz · November 2016

@Zacharias - your loop only needs to run from 2 (1 is always a factor) to the square root of n. That should make it much faster.

For example, take the number 24. Loop from 2 to 4 (integer of square root of 5).

2 is a factor, so 12 must be as well (since 24/2=12).

3 is a factor, so 8 must be too.

4 is a factor, so 6 must be too

Factors are 1, 2, 3, 4, 6, 8, 12

NB if you are going to want to factor primes, there are faster methods.

CamelCoder · November 2016

@Zacharias I believe a good way to do is something I learned last year in math class, I don't know if it is the best way or it even works, but search up the Gausse-Jordan method. It deals with matrices and solving and factoring polynomials. That's how I know graphing calculators are able to do that.

Zacharias · November 2016

@Ignatz I see what you mean. When I figure out how to do the rest of the factoring and what not, I'll come back and optimize it.

@CamelCoder Thanks for the suggestion. It looks complex, and I'd like to use my already obtained knowledge of math for what I'm coding. Feel free to try it out, though.

Zacharias · November 2016

[resolved]

Zacharias · November 2016

[resolved]

Ceres · November 2016

Going back to Ignatz's idea, I'd go from 2 up to the square root on n, which gives you the first half of the factors, and then take that list and work backwards through it, dividing n by each factor, to get the second half of the list. Much, much faster than going all the way up to n if n is large.

Zacharias · November 2016

Alright thanks @Ceres and @Ignatz. I'll try and use those instructions and implement them into the code. Will update code here.

Zacharias · November 2016

So I added pseudo code to clarify parts and added some aesthetic (not much) to the program. I'm confused with changing the loop to 2, math.sqrt(ac) and what to do inside, so I left it for later. Here is what I have:

-- Factor

function setup()
    --DISPLAY
    displayMode(STANDARD)
    supportedOrientations(LANDSCAPE_ANY)
    --PARAMETERS
    parameter.integer("a", 1, 1, 1)
    parameter.integer("b", 0, 50, 5)
    parameter.integer("c", 0, 50, 6)
    parameter.text("term", "x")
    parameter.action("Factor", factor)
    --LISTS
    factorsList = {}
    drawFactors = {}
    --VARIABLES
    local ac
    local factor1
    local factor2
end

function factor()

    ac = a * c
    factorsList = {} -- list of factors
    drawFactors = {} -- list of factors to draw

    --DETERMING FACTORS OF AC AND INPUTTING FACTORS IN A LIST
    i = 1
    while(i <= ac) do
        if(ac%i==0) then
            table.insert(factorsList, i)
            table.insert(drawFactors, i)
        end
        i = i + 1
    end
    --DETERMINING FACTORS FOR FACTORED FORM
    for i=1, #drawFactors do 
        factor1 = tonumber(factorsList[#factorsList])
        factor2 = tonumber(factorsList[#factorsList-(#factorsList-1)])

        if((factor1 + factor2 == b) and (factor1 * factor2 == ac)) then
            return
        else
            table.remove(factorsList, #factorsList)
            table.remove(factorsList, #factorsList-(#factorsList-1))
        end
    end
end

function draw()
    background(40, 40, 50)

    for i = 1, #drawFactors do
        --LIST OF FACTORS
        fill(236, 236, 236 , 255)
        fontSize(25)
        text("Factors of "..ac, WIDTH/2-225, HEIGHT/2+350)
        text(drawFactors[i], WIDTH/2-225, HEIGHT-30*i-60)
        --AC AND B IN X, AND POLYNOMIAL/FACTORED FORMS AT BOTTOM
        fill(172, 22, 22, 255)
        fontSize(50)
        text(""..ac.."", WIDTH/2, HEIGHT/2+75) --in the X 
        text(""..b.."", WIDTH/2, HEIGHT/2-75)  -- in the X
        fontSize(35)
        text(""..term.."^2 + "..b..term.." + "..c.."", WIDTH/2, HEIGHT/2-225) -- polynomial
        text("("..term.." + "..factor1..")("..term.." + "..factor2..")", WIDTH/2, HEIGHT/2-300) --factored
        --FACTORS FOR FACTORED FORM OF POLYNOMIAL
        fill(41, 184, 20, 255)
        fontSize(50)
        text(""..factor1.."", WIDTH/2-75, HEIGHT/2) -- in the X
        text(""..factor2.."", WIDTH/2+75, HEIGHT/2) -- in the X
    end

    --"POLYNOMIAL:/FACTORED:" AT BOTTOM
    fill(236, 236, 236, 255)
    fontSize(35)
    text("Your polynomial: ", WIDTH/2-225, HEIGHT/2-225)
    text("Factored: ", WIDTH/2-173, HEIGHT/2-300)
    --X LINES IN MIDDLE
    lineCapMode(ROUND)
    smooth()
    strokeWidth(7)
    line(WIDTH/2+100, HEIGHT/2+150, WIDTH/2-100, HEIGHT/2-150)
    line(WIDTH/2-100, HEIGHT/2+150, WIDTH/2+100, HEIGHT/2-150)
end

Zacharias · November 2016

I also need to do complex polynomial so where a > 1. That program can only solve simple polynomials.

CamelCoder · November 2016

I was sort of getting a headache from making my game, i really do hate 3D. I thought I would take a break and make my own version of this calculator. I added a UI just because I didn't like the parameters. The UI is sort of bad because I in all spent about an hour on this program, so it will probably have errors. I would like to post the code, but I do not know how to post code on this forum. Can u please tell me what to do so I can post it

dave1707 · November 2016

@CamelCoder To post code in the forum, just select all of your code then copy it. After that, just paste the code in the forum. Put 3 ~'s on a line before and after your code so it formats correctly.

CamelCoder · November 2016

That's what I did, but it said that my body (the post) had too many characters in it

dave1707 · November 2016

@CamelCoder If your code is too big then you can post it in github, or split your code into 2 or more posts.

Ignatz · November 2016

@CamelCoder - but there is little point in posting your code if it is rushed and has errors and doesn't work properly. Why would we want to look at it?

dave1707 · November 2016

Here's an example that uses the quadratic equation to solve for X. Just change the X2, X1, X0 values and see the results as you change the values. An example is shown when the program is started.

EDIT: Corrected an error.

supportedOrientations(PORTRAIT_ANY)

function setup()
    fontSize(30)
    parameter.text("X2",0)
    parameter.text("X1",0)
    parameter.text("X0",0)
    X2=8    -- for example only
    X1=2
    X0=-15
end

function draw()
    background(0)
    fill(255)       
    X2=tonumber(X2)
    if X2=="" or X2==nil then
        X2=0
    end   
    strA=X2.."x^2"
    X1=tonumber(X1)
    if X1=="" or X1==nil then
        X1=0
    end   
    strB=X1.."x"
    if X1>=0 then
        strB="+"..X1.."x"
    end    
    X0=tonumber(X0)
    if X0=="" or X0==nil then
        X0=0
    end
    strC=X0
    if X0>=0 then
        strC="+"..X0
    end  
    solve()  
    text(strA..strB..strC.." = 0",WIDTH/2,HEIGHT-100)
    text(str1,WIDTH/2,HEIGHT-200)
    text(str2,WIDTH/2,HEIGHT-250)
end

function solve()
    if X2=="" or X1=="" or X0=="" then
        str1,str2="",""    
    else
        str1="x = "..(-X1+math.sqrt(X1*X1-4*X2*X0))/(2*X2)
        str2="x = "..(-X1-math.sqrt(X1*X1-4*X2*X0))/(2*X2)
    end
end

CamelCoder · December 2016

@Ignatz Although it was rushed, I found it to have few errors. I don't know the cause because I didn't look into it that much. It still works great for the most part. [Edit] I fixed the error it had, now I hope you think it is worth looking at.
Here is the first part:

--# Main
-- MyFactorCalc
displayMode(FULLSCREEN)
supportedOrientations(ANY)
function setup()
    vara,varb,varc,var=readLocalData("vara",1),readLocalData("varb",2),readLocalData("varc",1),""
    txt,bpos,cpos,counter="",readLocalData("bpos",true),readLocalData("cpos",true),readLocalData("counter",120)
    arrows={upArrow={},downArrow={}}
    for i=1,6 do table.insert(arrows.upArrow,Arrow{size=vec2(70,35)})
    table.insert(arrows.downArrow,Arrow{size=vec2(70,35),angle=180}) end
    factorButton=TextButton{text=string.upper("Factor"),pos=vec2(WIDTH/2,HEIGHT/8),
    fill=color(255, 0, 186, 255),font="Baskerville-Bold",fontSize=80}
    establishArrowFuncs()
end
function draw()
    var=string.char(counter)
    if cpos then varc=math.abs(varc) else varc=-math.abs(varc)end
    if bpos then varb=math.abs(varb) else varb=-math.abs(varb)end
    background(255, 255, 255, 255)
    textMode(CENTER)
    textAlign(CENTER)
    fill(0, 45, 255, 255)
    textWrapWidth(500)
    fontSize(30)
    text("Modify the variables, then click factor to factor the formula.",WIDTH/2,HEIGHT-100)
    fontSize(50)
    font("AmericanTypewriter-Bold")
    fill(0)
    local s=getString(vara,varb,varc,var)
    text(s,WIDTH/2,HEIGHT*3/4)
    textWrapWidth(-1)
    text(txt,WIDTH/2,HEIGHT/4)
    drawSelections()
    for i,v in pairs(arrows) do
        for n,m in ipairs(v) do
            if m.counter and m.counter>1.2 then
                if math.floor(m.counter*25)%2==0 then m.func(BEGAN) end
            end
        end
    end
    factorButton:draw()
end
function factor(a,b,c)
    txt="Factoring..."
    local signb,signc=sign(b),sign(c)
    local mm=math.greatestCommonFactor(a,b)
    local m=math.abs(math.greatestCommonFactor(mm,c))
    a,b,c=a/m,b/m,c/m
    local ac=a*c
    local factors=math.findAllFactors(ac)
    local sol
    for i,v in ipairs(factors) do
        for n,m in ipairs(factors) do
            if i~=n or #factors==1 then
                if m+v==b and m*v==ac then
                    sol=vec2(m,v)
                elseif -m+v==b and -m*v==ac then
                    sol=vec2(-m,v)
                elseif m-v==b and m*-v==ac then
                    sol=vec2(m,-v)
                elseif -m-v==b and -m*-v==ac then
                    sol=vec2(-m,-v)
                end
            end
        end
    end
    if sol then
        local function func(a,b,sol,s)
            local gcf=math.greatestCommonFactor
            local aa=gcf(a,sol.x)
            local bb=gcf(b,sol.y)
            local cc=gcf(a,sol.y)
            local dd=gcf(b,sol.x)
            local ab=math.abs(aa)+math.abs(bb)
            local cd=math.abs(cc)+math.abs(dd)
            local soll=vec2(aa,bb)
            if not s or s==1 then
            if ab<cd and sign(cc)~=-1 or sign(aa)==-1 then soll=vec2(cc,dd) end elseif s==2 then
            soll=vec2(cc,dd) end
            return soll:unpack()
        end
        local tt
        ::place::
        local aa,cc=func(a,c,vec2(sol.y,sol.x),tt)
        local f=a/aa
        local ff=sol.x/aa
        if cc*ff~=c and ff==-1 then
            ff=2
        end
        if sign(aa)==-1 then
            aa=-aa
            f=-f
            ff=-ff
        end
        if not (aa*f==a and (cc*f)+(aa*ff)==b and cc*ff==c) then
            tt=2
            goto place
        end
        txt=getFactoredString(aa,cc,f,ff,m)
    else txt="NOT FACTORABLE"
        if m~=1 then
            txt=tostring(m).."("..getString(a,b,c,var)..")"
        end
    end
end

function drawSelections()
    local tab={
    {txt="a",tag="math.floor(vara)"},{txt="+/-",tag="stringSign(varb)"},
    {txt="b",tag="math.floor(math.abs(varb))"},{txt="+/-",tag="stringSign(varc)"},
    {txt="c",tag="math.floor(math.abs(varc))"},{txt="var.",tag="var"}}
    for i,v in ipairs(tab) do
        pushStyle()
        local a=color(255,0,0)
        if i==2 or i==3 then a=color(0,0,255) 
        elseif i==4 or i==5 then a=color(67, 255, 0, 255) 
        elseif i==6 then a=color(0, 255, 223, 255) end
        fill(0)
        fontSize(30)
        textMode(CENTER)
        local pos=vec2(WIDTH*i/(#tab+1),HEIGHT/2+150)
        text(tostring(v.txt),pos:unpack())
        pos.y=HEIGHT/2-30
        fill(a)
        rectMode(CENTER)
        rect(pos.x,pos.y,100,100)
        fill(255)
        font("Baskerville-SemiBold")
        fontSize(55)
        text(tostring(loadstring("return "..v.tag)()),pos:unpack())
        arrows.upArrow[i].pos.x=pos.x
        arrows.upArrow[i].pos.y=pos.y+90
        arrows.upArrow[i]:draw()
        arrows.downArrow[i].pos.x=pos.x
        arrows.downArrow[i].pos.y=pos.y-90
        arrows.downArrow[i]:draw()
        popStyle()
    end
end

function establishArrowFuncs()
    local s=ENDED
    arrows.upArrow[1].func=function(a)if a==s then vara=vara+1;saveLocalData("vara",vara) end end
    arrows.downArrow[1].func=function(a)if a==s then vara=math.max(vara-1,1)saveLocalData("vara",vara) end end
    arrows.upArrow[2].func=function(a)if a==s then bpos=not bpos;saveLocalData("bpos",bpos) end end
    arrows.downArrow[2].func=function(a)if a==s then bpos=not bpos;saveLocalData("bpos",bpos) end end
    arrows.upArrow[3].func=function(a)if a==s then varb=math.abs(varb)+1;saveLocalData("varb",varb) end end
    arrows.downArrow[3].func=function(a)if a==s then varb=math.max(math.abs(varb)-1,0)saveLocalData("varb",varb) end end
    arrows.upArrow[4].func=function(a)if a==s then cpos=not cpos;saveLocalData("cpos",cpos) end end
    arrows.downArrow[4].func=function(a)if a==s then cpos=not cpos;saveLocalData("cpos",cpos) end end
    arrows.upArrow[5].func=function(a)if a==s then varc=math.abs(varc)+1;saveLocalData("varc",varc) end end
    arrows.downArrow[5].func=function(a)if a==s then varc=math.max(math.abs(varc)-1,0)saveLocalData("varc",varc) end end
    arrows.downArrow[6].func=function(a)if a==s then
            counter=counter+1
            if counter>122 then counter=97 end
            saveLocalData("counter",counter)
        end
    end
    arrows.upArrow[6].func=function(a)if a==s then
            counter=counter-1
            if counter<97 then counter=122 end
            saveLocalData("counter",counter)
        end
    end
end

function touched(t)
    for i,v in pairs(arrows) do
        for n,m in ipairs(v) do
            if m:touched(t) then txt="" end
        end
    end
    factorButton:touched(t)
    if factorButton.state==ENDED then
        factor(vara,varb,varc)
    end
end

function orientationChanged(o)
    if factorButton then factorButton.pos=vec2(WIDTH/2,HEIGHT/8) end
end

CamelCoder · December 2016

Here is the second part:

--# Math
function math.findAllFactors(n)
    local factors={}
    for i=1,math.abs(n) do
        local a=n/i
        if a==math.floor(a) then
            table.insert(factors,math.floor(i*sign(a)))
            if a==i then
                table.insert(factors,math.floor(i*sign(a)))
            end
        end
    end
    return factors
end

function math.greatestCommonFactor(a,b)
    local ans=1
    for i,v in pairs(math.findAllFactors(a)) do
        for n,m in pairs(math.findAllFactors(b)) do
            if v==m or -v==-m then
                ans=v
            elseif -v==m or v==-m then
                ans=-v
            end
        end
    end
    return ans
end

function sign(x)
    if x==x and x~=0 then
        return x/math.abs(x)
    end
    return(0)
end
--# String
function stringSign(a) if a<0 then return "-" end return "+" end

function getString(a,b,c,x)
    local space=string.rep(" ",2)
    local s=""
    local function concatVals(n,pow)
        if n~=0 then
            local a=tostring(math.floor(math.abs(n)))
            local p=""
            local t=stringSign(n)
            if pow>=1 then
            if a=="1" then a="" end
            p=x if pow==2 then p=p.."²"t="" end end
            s=s..t..space..a..p..space
        end
    end
    concatVals(a,2)
    concatVals(b,1)
    concatVals(c,0)
    return s
end

function getFactoredString(fo,fi,li,lo,m)
    local space=string.rep(" ",2)
    local s=""
    if m~=1 then s=s..tostring(m) end
    if fi~=0 then s=s.."(" end
    if fo~=1 then s=s..tostring(math.floor(fo)) end
    s=s..var
    if fi~=0 then s=s..space..stringSign(fi)..space..tostring(math.floor(math.abs(fi)))..")" end
    if lo~=0 then s=s.."(" end
    if li~=1 then s=s..tostring(math.floor(li)) end
    s=s..var
    if lo~=0 then s=s..space..stringSign(lo)..space..tostring(math.floor(math.abs(lo)))..")" end
    if string.sub(s,1+string.len(m),math.ceil(string.len(s)/2))
        ==string.sub(s,math.ceil(string.len(s)/2)+1,string.len(s)) then
        s=string.sub(s,1,math.ceil(string.len(s)/2)).."²"
    end
    return s
end
--# Arrow
Arrow=class()

function Arrow:init(args)args=args or {}
    self.strokeWidth=args.strokeWidth or 20
    self.stroke=args.stroke or color(0, 0, 0, 255)
    self.ang=args.angle or 0
    self.size=args.size or vec2(200,200)
    self.pos=args.pos or vec2(0,0)
    self.lineCapMode=args.lineCapMode or ROUND
    self.func=args.func or function()end
    self.counter=nil
end

function Arrow:draw()
    pushMatrix()
    pushStyle()
    translate(self.pos.x,self.pos.y)
    rotate(self.ang)
    lineCapMode(self.lineCapMode)
    strokeWidth(self.strokeWidth)
    stroke(self.stroke)
    for i=-1,1,2 do
        line(self.size.x/2*i,-self.size.y/2,0,self.size.y/2)
    end
    if self.counter then self.counter = self.counter + DeltaTime end
    popStyle()
    popMatrix()
end

function Arrow:touched(touch)
    local shift=vec2(0,10)
    if touch.x>self.pos.x-self.size.x/2-shift.x and touch.y>self.pos.y-self.size.y/2-shift.y and touch.x<self.pos.x+self.size.x/2+shift.x
        and touch.y<self.pos.y+self.size.y/2+shift.y then
        if touch.state==BEGAN then self.counter=0 elseif touch.state==ENDED then self.counter=nil end
        self.func(touch.state)
        return true
    end
    return false
end
--# TextButton
TextButton=class()

function TextButton:init(args)args=args or {}
    self.font=args.font or nil
    self.fontSize=args.fontSize or 50
    self.fill=args.fill or color(0)
    self.txt=args.text or ""
    self.pos=args.pos or vec2(0,0)
    self.w,self.h=0,0
end

function TextButton:draw()
    pushStyle()
    textMode(CENTER)
    textAlign(CENTER)
    fill(self.fill)
    if self.font then font(self.font) end
    fontSize(self.fontSize)
    self.w,self.h=textSize(self.txt)
    text(self.txt,self.pos:unpack())
    popStyle()
end

function TextButton:touched(t)
    if t.x>self.pos.x-self.w/2 and t.x<self.pos.x+self.w/2 and t.y>self.pos.y-self.h/2 and t.y<self.pos.y+self.h/2 then
        self.state=t.state
    else
        self.state=nil
    end
end

dave1707 · December 2016

@CamelCoder Nice job. One question, you don't allow the first variable for x^2 to be negative.

CamelCoder · December 2016

@dave1707 Thanks! Ya, I just didn't want to mess up the technique I used. Honestly, what I did was just thought about how I would factor a normal equation, and told the computer to do the same. That's probably why it's not too efficient. If you want, feel free to change it, I think that the leading coefficient shouldn't be negative.

dave1707 · December 2016

@CamelCoder I'm not going to modify your code, but the leading coefficient could be negative as much as it could be positive. If the leading coefficient is negative, then there are 2 sets of answers. They're the same set of numbers, just with the signs flipped. Maybe I'll try writing something similar and see what I come up with. It's always good to see different coding styles.

Ignatz · December 2016

Assuming you wrote this for fun, I have no criticism, because it's good practice - but if intended for practical use, I would far rather enter a series of numbers such as 43,-345,12,3 and have the program factor them. This allows as many numbers as you like, positive or negative, and if you want to enter 187, you don't have to press an arrow key 187 separate times.

dave1707 · December 2016

@Ignatz I think 99% of the programs written here are for fun or by new coders just trying to learn how to write programs. If it's a program someone wants to make some money from, they may write it in Codea, but they're not going to post it here. Any program written can be improved upon by someone else. Pressing the up or down arrows to change a number could take awhile depending on the number, but it was an interesting idea anyways. Maybe a change could be if you press and hold the up/down arrows, the number starts changing until you lift your finger.

CamelCoder · December 2016

@Ignatz I didn't intend on making a UI aside from the parameters, but I just wanted to go a bit further, that's why it is awful. I will modify the code to make it possible to hold the arrow and zoom through the numbers. [Edit] I have added the ability to hold on the arrows to get to the number quicker

dave1707 · December 2016

Here's another version. Tap a box and input the values then tap Solve.

displayMode(FULLSCREEN)
supportedOrientations(LANDSCAPE_ANY)

function setup()
    rectMode(CENTER)
    fontSize(30)
    ans={}
    tab={}
    table.insert(tab,box(400,600,150,50,0,"x^2"))
    table.insert(tab,box(525,600,100,50,0,"x"))
    table.insert(tab,box(625,600,100,50,0,""))
    table.insert(tab,box(WIDTH/2,500,150,50,"","Solve"))
end

function draw()
    background(0)
    fill(255)
    for a,b in pairs(tab) do
        b:draw()
    end
    if #ans==0 then
        text("No solution found.",WIDTH/2,HEIGHT/2)
    else
        for a,b in pairs(ans) do
            v1=string.format("%d",b.x)
            v2=string.format("%+d",b.y)
            v3=string.format("%d",b.z)
            v4=string.format("%+d",b.w)
            text("("..v1.."x"..v2..") ("..v3.."x"..v4..")",WIDTH/2,HEIGHT/2-a*50+100)
        end
    end
end

function touched(t)
    for a,b in pairs(tab) do
        b:touched(t)
    end
end

function keyboard(k)
    for a,b in pairs(tab) do
        b:keyboard(k)
    end    
end

function solve()
    ans={}
    t1=vals(a)
    t2=vals(c)
    cnt=0
    for a1=1,#t1 do
        for a2=1,#t2 do 
            for b1=1,#t1 do
                for b2=1,#t2 do
                    aa=t1[a1]*t1[b1]
                    bb=t1[a1]*t2[b2]+t1[b1]*t2[a2]
                    cc=t2[a2]*t2[b2]
                    if aa==a and bb==b and cc==c then
                        cnt=cnt+1
                        if a<0 and cnt<3 or a>0 and cnt<2 then
                            table.insert(ans,vec4(t1[a1],t2[a2],t1[b1],t2[b2]))
                        end
                    end
                end
            end
        end
    end  
end

function vals(v)
    local t={}
    for z=1,math.abs(v) do
        if math.abs(v)%z==0 then
            table.insert(t,z)
            if v<0 then
                table.insert(t,-z)
            end
        end
    end
    return t    
end

box=class()

function box:init(x,y,w,h,v,s)
    self.x=x
    self.y=y
    self.w=w
    self.h=h
    self.v=v
    self.s=s
    self.sel=false
end

function box:draw()
    fill(255)
    if self.sel then
        fill(0, 255, 88, 255)
    end
    rect(self.x,self.y,self.w,self.h)
    fill(0, 141, 255, 255)
    str=""
    if string.sub(self.v,1,1)~="-" then
        str="+"
        if self.s=="x^2" or self.s=="Solve" then
            str=""
        end
    end
    text(str..self.v..self.s,self.x,self.y)
end

function box:touched(t)
    if t.state==BEGAN then
        ans={}
        self.sel=false
        if t.x>self.x-self.w/2 and t.x<self.x+self.w/2 and
                t.y>self.y-self.h/2 and t.y<self.y+self.h/2 then
            if self.s=="Solve" then
                a=tonumber(tab[1].v)
                b=tonumber(tab[2].v)
                c=tonumber(tab[3].v)
                hideKeyboard()
                if a==nil or b==nil or c==nil then
                    return
                end
                solve()
            else
                self.sel=true
                self.v=""
                showKeyboard()
            end
        end
    end
end

function box:keyboard(k)
    if k>="0" and k<="9" or k=="-" or k=="+" or k==BACKSPACE then
        if self.sel then            
            if k==BACKSPACE then
                self.v=string.sub(self.v,1,#self.v-1)
            end
            self.v=self.v..k
        end
    end
end

CamelCoder · December 2016

@dave1707 I'm sorry to say, but every equation I would type in would give me no solution found.

dave1707 · December 2016

@CamelCoder Try 3x^2+13x-10 or 6x^2+11x-10 or -6x^2+19x-15.

Zacharias · December 2016

I'm glad my little post sparked some inspiration. @CamelCoder I enjoyed your UI. I have lots of diff ideas of projects and learning how to do UI like yours seems prudent. Thanks @dave1707 for that program. Some don't work but it's definitely better than mine

dave1707 · December 2016

@Zacharias I didn't post the program to be better than yours, I posted it to show a different style and for others to learn from it. Everyone has a different style of coding and I still learn from others even though I've been coding for what seems like forever. You said some don't work, but not every equation will have factors. Do you have any examples of equations that should work and don't. As for your code sparking interest, yes it did. I'm working on a program that will factor equations such as x^3+x^2+x+#=0 and even higher orders.

Zacharias · December 2016

@dave1707 Oh I know that. I just admire your work. And I just realized right now I wasn't changing a to 1 in your code. Totally my fault (I was checking your code late at night). Great work on the factoring by grouping. The code works! (:

dave1707 · December 2016

Here's a program that will factor third order equations like 1x3-5x2+2x+8 . Just enter 1,-5,2,8 in the parameter text area and press Factor. I included 6 examples to try. If there are more factors then the screen will show, just slide them up. I didn't spend a lot of time making it fancy, so if you want you can do it.

function setup()
    print("-24,72,-18,-30")
    print("15,109,25,-21")
    print("6,-33,-27,54")
    print("1,-5,2,8")
    print("1,-3,-4,12")
    print("455,675,145,-75")
    dy=0
    sh={}
    tab={}
    delay=0
    fontSize(30)
    p2=string.char(194)..string.char(178)
    p3=string.char(194)..string.char(179)
    parameter.text("nbrs")
    parameter.action("Factor",createTab)
    fill(255)
end

function factor()
    t1=vals(tab[4])
    t2=vals(tab[1])
    solve()
    yy={}
    for z=1,#n1 do
        tt=order(n1[z],n2[z],n3[z])
        table.insert(yy,toInt(tt[1]).."  "..toInt(tt[2]).."  "..toInt(tt[3]))
    end 
    table.sort(yy)
    h=""
    sh={}
    for z=1,#yy do
        if yy[z]~=h then
            table.insert(sh,yy[z])
            h=yy[z]
        end
    end
end

function createTab()
    tab={}
    sh={}
    delay=0
    str=""
    for z=1,#nbrs do
        val=string.sub(nbrs,z,z)
        if val=="," then
            table.insert(tab,tonumber(str))
            str=""
        else
            str=str..val 
        end         
    end
    table.insert(tab,tonumber(str))
    nbrs=""
end

function draw()
    background(0)
    if #tab>0 then
        delay=delay+1
        fill(255)
        s2,s3,s4="","",""
        if tab[2]>=0 then
            s2="+"
        end
        if tab[3]>=0 then
            s3="+"
        end
        if tab[4]>=0 then
            s4="+"
        end
        text(tab[1].."x"..p3..s2..tab[2].."x"..p2..s3..tab[3].."x"..s4..tab[4],
                WIDTH/2,HEIGHT-50+dy)
        if #sh==0 then
            text("Factoring, please wait...",WIDTH/2,HEIGHT/2)
        end
        for a,b in pairs(sh) do
            text(a.."   "..b,WIDTH/2,HEIGHT-70-a*50+dy)
        end
    else
        text("If factors go off bottom, slide them up.",WIDTH/2,HEIGHT/2)
    end
    if delay==4 then
        showKeyboard()
        hideKeyboard()
        factor()
    end
end

function order(a,b,c)
    local tab={a}
    if b.x<=a.x then
        table.insert(tab,1,b)
    else
        table.insert(tab,2,b)
    end
    if c.x<=tab[1].x then
        table.insert(tab,1,c)
    elseif c.x<=tab[2].x then
        table.insert(tab,2,c)
    else
        table.insert(tab,3,c)
    end
    return tab
end

function toInt(a)
    aa=math.tointeger(a.x)
    bb=math.tointeger(a.y)
    bp=""
    if bb>=0 then
        bp="+"
    end
    return("("..aa.."x"..bp..bb..")")
end

function solve()
    n1,n2,n3={},{},{}
    for a=1,#t2 do
      for b=1,#t1 do
        for c=1,#t2 do
          for d=1,#t1 do
            for e=1,#t2 do
              for f=1,#t1 do
                aa=t2[a]*t2[c]*t2[e]
                bb=t2[e]*t2[a]*t1[d]+t2[e]*t2[c]*t1[b]+t1[f]*t2[a]*t2[c]                            
                cc=t2[e]*t1[b]*t1[d]+t1[f]*t2[a]*t1[d]+t1[f]*t2[c]*t1[b]                            
                dd=t1[b]*t1[d]*t1[f]
                if aa==tab[1] and bb==tab[2] and 
                        cc==tab[3] and dd==tab[4] then
                    table.insert(n1,vec2(t2[a],t1[b]))
                    table.insert(n2,vec2(t2[c],t1[d]))
                    table.insert(n3,vec2(t2[e],t1[f]))
                end
              end
            end
          end                
        end
      end
    end
end

function vals(v)
    local t={}
    for z=1,math.abs(v) do
        if math.abs(v)%z==0 then
            table.insert(t,-z)
            table.insert(t,z)
        end
    end
    return t    
end

function touched(t)
    if t.state==MOVING then
        dy=dy+t.deltaY
        if dy<0 then
            dy=0
        end
    end
end

MattthewLXXIII · December 2016

@dave1707 with your quadratic factoring calculator, you didn't allow for -ve value, so I just (inelegantly) tweaked it:


--# Main
displayMode(FULLSCREEN)
supportedOrientations(LANDSCAPE_ANY)

function setup()
    rectMode(CENTER)
    fontSize(30)
    ans={}
    tab={}
    table.insert(tab,box(400,600,150,50,0,"x^2"))
    table.insert(tab,box(525,600,100,50,0,"x"))
    table.insert(tab,box(625,600,100,50,0,""))
    table.insert(tab,box(WIDTH/2,500,150,50,"","Solve"))
end

function draw()
    background(0)
    fill(255)
    for a,b in pairs(tab) do
        b:draw()
    end
    if #ans==0 then
        text("No solution found.",WIDTH/2,HEIGHT/2)
    else
        for a,b in pairs(ans) do
            v1=string.format("%d",b.x)
            v2=string.format("%+d",b.y)
            v3=string.format("%d",b.z)
            v4=string.format("%+d",b.w)
            text("("..v1.."x"..v2..") ("..v3.."x"..v4..")",WIDTH/2,HEIGHT/2-a*50+100)
        end
    end
end

function touched(t)
    for a,b in pairs(tab) do
        b:touched(t)
    end
end

function keyboard(k)
    for a,b in pairs(tab) do
        b:keyboard(k)
    end    
end

function solve()
    ans={}
    t1=vals(a)
    t2=vals(c)
    cnt=0
    for a1=1,#t1 do
        for a2=-#t1,#t2 do 
            for b1=-#t1,#t1 do
                for b2=-#t2,#t2 do
                    aa=t1[a1]*t1[b1]
                    bb=t1[a1]*t2[b2]+t1[b1]*t2[a2]
                    cc=t2[a2]*t2[b2]
                    if aa==a and bb==b and cc==c then
                        cnt=cnt+1
                        if a<0 and cnt<3 or a>0 and cnt<2 then
                            table.insert(ans,vec4(t1[a1],t2[a2],t1[b1],t2[b2]))
                        end
                    end
                end
            end
        end
    end  
end

function vals(v)
    local t={}
    t[0]=0
    for z=1,math.abs(v) do
        if math.abs(v)%z==0 then
            table.insert(t,z)
            if v<0 then
                table.insert(t,-z)
            end
        end
    end
    for i=1,#t do
        t[-i]=-t[i]
    end
    return t    
end

box=class()

function box:init(x,y,w,h,v,s)
    self.x=x
    self.y=y
    self.w=w
    self.h=h
    self.v=v
    self.s=s
    self.sel=false
end

function box:draw()
    fill(255)
    if self.sel then
        fill(0, 255, 88, 255)
    end
    rect(self.x,self.y,self.w,self.h)
    fill(0, 141, 255, 255)
    str=""
    if string.sub(self.v,1,1)~="-" then
        str="+"
        if self.s=="x^2" or self.s=="Solve" then
            str=""
        end
    end
    text(str..self.v..self.s,self.x,self.y)
end

function box:touched(t)
    if t.state==BEGAN then
        ans={}
        self.sel=false
        if t.x>self.x-self.w/2 and t.x<self.x+self.w/2 and
                t.y>self.y-self.h/2 and t.y<self.y+self.h/2 then
            if self.s=="Solve" then
                a=tonumber(tab[1].v)
                b=tonumber(tab[2].v)
                c=tonumber(tab[3].v)
                hideKeyboard()
                if a==nil or b==nil or c==nil then
                    return
                end
                solve()
            else
                self.sel=true
                self.v=""
                showKeyboard()
            end
        end
    end
end

function box:keyboard(k)
    if k>="0" and k<="9" or k=="-" or k=="+" or k==BACKSPACE then
        if self.sel then            
            if k==BACKSPACE then
                self.v=string.sub(self.v,1,#self.v-1)
            end
            self.v=self.v..k
        end
    end
end

dave1707 · December 2016

@MattthewLXXIII Thanks for the fix. I think I ran into that error when I did the next program for third order equations. The way I fixed it there was in the function vals() where I always created - values instead of checking for v<0 before creating them.

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Creating a factoring calculator

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