Cramer’s rule for 2x2/3x3 systems + determinant calculator, step-by-step results

# Eq System Solver - NumWorks
# Created by Alvar Laigna - https://alvarlaigna.com
# Arrows:select OK:choose Back:back
from kandinsky import fill_rect as F,draw_string as D
from ion import keydown as K
from time import sleep as Z
SW,SH=320,222
BK=(0,)*3;WH=(255,)*3
BL=(50,110,230);TL=(0,190,190)
YL=(220,200,60);GN=(60,190,60)
DG=(120,)*3

okv=1 if K(4)or K(52) else 0

def okd():
 return K(4)or K(52)

def okp():
 global okv
 d=okd()
 if d and not okv:
  okv=1
  return True
 if not d:okv=0
 return False

def wup():
 while okd():Z(0.02)
 Z(0.12)

def menu(title,items,sub=False):
 sel=0;n=len(items)
 while True:
  F(0,0,SW,SH,BK)
  D(title,SW//2-len(title)*5,6,TL,BK)
  F(0,24,SW,2,(40,)*3)
  for i in range(n):
   y=34+i*22
   if i==sel:
    F(8,y,SW-16,20,BL)
    D("> "+items[i],14,y+2,WH,BL)
   else:
    D("  "+items[i],14,y+2,DG,BK)
  if sub:D("Back=return",100,SH-16,(60,)*3,BK)
  else:D("Back=quit",115,SH-16,(60,)*3,BK)
  while True:
   if K(1):sel=(sel-1)%n;Z(0.15);break
   if K(2):sel=(sel+1)%n;Z(0.15);break
   if okp():wup();return sel
   if K(17):return-1
   Z(0.04)

def inp(prompt):
 try:
  v=input(prompt)
  return float(v)
 except:return None

def show(lines):
 F(0,0,SW,SH,BK)
 D("RESULT",130,6,TL,BK)
 F(0,24,SW,2,(40,)*3)
 for i,ln in enumerate(lines):
  c=YL if i==len(lines)-1 else WH
  D(str(ln),14,34+i*20,c,BK)
 D("OK=back",130,SH-16,DG,BK)
 while True:
  if okp()or K(17):wup();return
  Z(0.04)

def r(v):
 return round(v,6)

def det2(a,b,c,d):
 return a*d-b*c

def det3(a):
 return(a[0][0]*(a[1][1]*a[2][2]-a[1][2]*a[2][1])
  -a[0][1]*(a[1][0]*a[2][2]-a[1][2]*a[2][0])
  +a[0][2]*(a[1][0]*a[2][1]-a[1][1]*a[2][0]))

def sys2():
 D("Equation 1: a1*x+b1*y=c1",14,34,WH,BK)
 a1=inp("a1: ")
 if a1 is None:return
 b1=inp("b1: ")
 if b1 is None:return
 c1=inp("c1: ")
 if c1 is None:return
 D("Equation 2: a2*x+b2*y=c2",14,56,WH,BK)
 a2=inp("a2: ")
 if a2 is None:return
 b2=inp("b2: ")
 if b2 is None:return
 c2=inp("c2: ")
 if c2 is None:return
 dt=det2(a1,b1,a2,b2)
 e1=str(r(a1))+"x+"+str(r(b1))+"y="+str(r(c1))
 e2=str(r(a2))+"x+"+str(r(b2))+"y="+str(r(c2))
 if dt==0:
  show([e1,e2,"","Det = 0","No unique solution"])
  return
 x=det2(c1,b1,c2,b2)/dt
 y=det2(a1,c1,a2,c2)/dt
 show([e1,e2,"","Determinant = "+str(r(dt)),
  "x = "+str(r(x)),"y = "+str(r(y))])

def sys3():
 D("Eq 1: a1x+b1y+c1z=d1",14,34,WH,BK)
 a1=inp("a1: ")
 if a1 is None:return
 b1=inp("b1: ")
 if b1 is None:return
 c1=inp("c1: ")
 if c1 is None:return
 d1=inp("d1: ")
 if d1 is None:return
 D("Eq 2: a2x+b2y+c2z=d2",14,56,WH,BK)
 a2=inp("a2: ")
 if a2 is None:return
 b2=inp("b2: ")
 if b2 is None:return
 c2=inp("c2: ")
 if c2 is None:return
 d2=inp("d2: ")
 if d2 is None:return
 D("Eq 3: a3x+b3y+c3z=d3",14,78,WH,BK)
 a3=inp("a3: ")
 if a3 is None:return
 b3=inp("b3: ")
 if b3 is None:return
 c3=inp("c3: ")
 if c3 is None:return
 d3=inp("d3: ")
 if d3 is None:return
 m=[[a1,b1,c1],[a2,b2,c2],[a3,b3,c3]]
 dt=det3(m)
 e1=str(r(a1))+"x+"+str(r(b1))+"y+"+str(r(c1))+"z="+str(r(d1))
 e2=str(r(a2))+"x+"+str(r(b2))+"y+"+str(r(c2))+"z="+str(r(d2))
 e3=str(r(a3))+"x+"+str(r(b3))+"y+"+str(r(c3))+"z="+str(r(d3))
 if dt==0:
  show([e1,e2,e3,"","Det = 0","No unique solution"])
  return
 dx=det3([[d1,b1,c1],[d2,b2,c2],[d3,b3,c3]])
 dy=det3([[a1,d1,c1],[a2,d2,c2],[a3,d3,c3]])
 dz=det3([[a1,b1,d1],[a2,b2,d2],[a3,b3,d3]])
 x=dx/dt;y=dy/dt;z=dz/dt
 show([e1,e2,e3,"","Det = "+str(r(dt)),
  "x = "+str(r(x)),"y = "+str(r(y)),
  "z = "+str(r(z))])

def det2m():
 D("Matrix [[a,b],[c,d]]",14,34,WH,BK)
 a=inp("a: ")
 if a is None:return
 b=inp("b: ")
 if b is None:return
 c=inp("c: ")
 if c is None:return
 d=inp("d: ")
 if d is None:return
 dt=det2(a,b,c,d)
 show(["| "+str(r(a))+"  "+str(r(b))+" |",
  "| "+str(r(c))+"  "+str(r(d))+" |","",
  "det = a*d - b*c",
  "Determinant = "+str(r(dt))])

def det3m():
 D("Matrix 3x3 row by row",14,34,WH,BK)
 D("Row 1:",14,56,WH,BK)
 a1=inp("a1: ")
 if a1 is None:return
 b1=inp("b1: ")
 if b1 is None:return
 c1=inp("c1: ")
 if c1 is None:return
 D("Row 2:",14,78,WH,BK)
 a2=inp("a2: ")
 if a2 is None:return
 b2=inp("b2: ")
 if b2 is None:return
 c2=inp("c2: ")
 if c2 is None:return
 D("Row 3:",14,100,WH,BK)
 a3=inp("a3: ")
 if a3 is None:return
 b3=inp("b3: ")
 if b3 is None:return
 c3=inp("c3: ")
 if c3 is None:return
 m=[[a1,b1,c1],[a2,b2,c2],[a3,b3,c3]]
 dt=det3(m)
 show(["| "+str(r(a1))+" "+str(r(b1))+" "+str(r(c1))+" |",
  "| "+str(r(a2))+" "+str(r(b2))+" "+str(r(c2))+" |",
  "| "+str(r(a3))+" "+str(r(b3))+" "+str(r(c3))+" |","",
  "Determinant = "+str(r(dt))])

def run():
 items=["2x2 System","3x3 System",
  "2x2 Determinant","3x3 Determinant"]
 while True:
  s=menu("Eq System Solver",items)
  if s<0:break
  F(0,0,SW,SH,BK)
  D("Enter coefficients",14,6,TL,BK)
  F(0,24,SW,2,(40,)*3)
  if s==0:sys2()
  elif s==1:sys3()
  elif s==2:det2m()
  elif s==3:det3m()

run()