x = var'x'
 GOOD time: 0.019000ms
stack: size: 0

    
    		


    

    

    

    y = func('y', {x}, x^2)
    
    		

GOOD

time: 0.190000ms
    
stack: size: 0
      

      

      
TODO what to display...
      

      
      		


      

      
y = x
      

      
      		


      

      
y(x) = x
      

      
      		


      

      
y(x) := x
      

      
      		


      

      

      

      print(y(x))
      
      		
$y\left(  x\right)$

GOOD

time: 0.036000ms
      
stack: size: 0
        

        

        

        

        print(y(x)())
        
        		
${x}^{2}$

GOOD

time: 0.953000ms
        
stack: size: 11
        • Init
        • y:Prune:apply
        • Prune
        • ^:Expand:integerPower
        • Expand
        • +:Prune:combineConstants
        • *:Prune:combinePows
        • Prune
        • Factor
        • Prune
        • Tidy
        

        

        

        

        printbr(y:defeq())
        
        		
${y\left(  x\right)} = {{x}^{2}}$

        

GOOD
        		
time: 0.119000ms
        
stack: size: 0
          

          

          

          

          assert(UserFunction.registeredFunctions.y == y)
          
          		

GOOD

time: 0.012000ms
          
stack: size: 0
            

            

            

            

            
            		


            

            
if UserFunction is not a Variable then this is invalid
            

            
            		


            

            
because you cannot have Functions as Variables in the arg list
            

            
            		


            

            
f = func('f', {x, y}, x*y)
            

            
            		


            

            
print(f:defeq())
            

            
            		


            

            
assert(UserFunction.registeredFunctions.f == f)
            

            
            		


            

            

            

            
            		


            

            
instead, if UserFunction returns Functions, this is what you would see
            

            
            		


            

            
and with this the derivative evaluation is obvious
            

            
            		


            

            

            

            f = func('f', {x}, x*y(x))
            
            		

GOOD

time: 0.057000ms
            
stack: size: 0
              

              

              

              

              print(f:defeq())
              
              		
${f\left(  x\right)} = {{{x}} {{y\left(  x\right)}}}$

GOOD

time: 0.229000ms
              
stack: size: 0
                

                

                

                

                assert(UserFunction.registeredFunctions.f == f)
                
                		

GOOD

time: 0.016000ms
                
stack: size: 0
                  

                  

                  

                  

                  
                  		


                  

                  
diff() is partial derivative
                  

                  
                  		


                  

                  
totalDiff() is total derivative
                  

                  
                  		


                  

                  

                  

                  
                  		


                  

                  
total derivative evaluation
                  

                  
                  		


                  

                  
substitute chain rule for all terms
                  

                  
                  		


                  

                  
df/dx, when simplified, does not go anywhere, because f is dependent on x
                  

                  
                  		


                  

                  
for that reason, I can just build the equality f:eq(f.def) and apply :diff() to the whole thing:
                  

                  
                  		


                  

                  

                  

                  print(f:defeq():diff(x):prune())
                  
                  		
${{{3}} {{{x}^{2}}}} = {{{3}} {{{x}^{2}}}}$

GOOD

time: 2.768000ms
                  
stack: size: 12
                  • f:Prune:apply
                  • y:Prune:apply
                  • +:Prune:combineConstants
                  • *:Prune:combinePows
                  • y:Prune:apply
                  • +:Prune:combineConstants
                  • *:Prune:combinePows
                  • Derivative:Prune:self
                  • Derivative:Prune:eval
                  • Derivative:Prune:self
                  • Derivative:Prune:eval
                  • Derivative:Prune:eval
                  

                  

                  
but TODO wrt total derivatives ... diff(y) ...
                  

                  
                  		


                  

                  
y(x) above is a UserFunction subclass
                  

                  
                  		


                  

                  
which means it isn't a Variable
                  

                  
                  		


                  

                  
which means you can't diff(y) ...
                  

                  
                  		


                  

                  
though you could diff(y(x)) ...
                  

                  
                  		


                  

                  
but that would be diff'ing wrt expressions, which I don't have support for
                  

                  
                  		


                  

                  

                  

                  print(f:defeq():diff(y):prune())
                  
                  		
BAD
                  [string "/home/chris/Projects/lua/symmath/Expression.lua"]:49: attempt to call a table value
                  
stack traceback:
                  
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:260: in function 
                  
	[string "/home/chris/Projects/lua/symmath/Expression.lua"]:49: in function 'clone'
                  
	[string "/home/chris/Projects/lua/symmath/Expression.lua"]:46: in function 'clone'
                  
	[string "/home/chris/Projects/lua/symmath/Expression.lua"]:46: in function 'clone'
                  
	[string "/home/chris/Projects/lua/symmath/op/mul.lua"]:90: in function 'flatten'
                  
	[string "/home/chris/Projects/lua/symmath/Expression.lua"]:327: in function '__mul'
                  
	[string "/home/chris/Projects/lua/symmath/op/pow.lua"]:58: in function 'evaluateDerivative'
                  
	[string "/home/chris/Projects/lua/symmath/Derivative.lua"]:367: in function 'func'
                  
	[string "/home/chris/Projects/lua/symmath/visitor/Visi..."]:224: in function 'apply'
                  
	[string "/home/chris/Projects/lua/symmath/visitor/Visi..."]:183: in function 'apply'
                  
	[string "/home/chris/Projects/lua/symmath/Derivative.lua"]:367: in function 'func'
                  
	[string "/home/chris/Projects/lua/symmath/visitor/Visi..."]:224: in function 'prune'
                  
	[string "print(f:defeq():diff(y):prune())"]:1: in main chunk
                  
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:252: in function 
                  
	[C]: in function 'xpcall'
                  
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:251: in function 'exec'
                  
	func.lua:65: in function 'cb'
                  
	[string "/home/chris/Projects/lua/ext/timer.lua"]:101: in function 'timer'
                  
	func.lua:6: in main chunk
                  
	[C]: at 0x5569e268c390
                  		
time: 1.136000ms
                  
stack: size: 7
                  • f:Prune:apply
                  • y:Prune:apply
                  • +:Prune:combineConstants
                  • *:Prune:combinePows
                  • y:Prune:apply
                  • +:Prune:combineConstants
                  • *:Prune:combinePows
                  

                  

                  

                  

                  print(f:defeq():diff(y(x)):prune())
                  
                  		
${0} = {0}$

GOOD

time: 1.296000ms
                  
stack: size: 15
                  • f:Prune:apply
                  • y:Prune:apply
                  • +:Prune:combineConstants
                  • *:Prune:combinePows
                  • y:Prune:apply
                  • y:Prune:apply
                  • +:Prune:combineConstants
                  • *:Prune:combinePows
                  • Derivative:Prune:other
                  • *:Prune:apply
                  • Derivative:Prune:eval
                  • Derivative:Prune:other
                  • *:Prune:apply
                  • Derivative:Prune:eval
                  • Derivative:Prune:eval
                  

                  

                  

                  

                  
                  		


                  

                  

                  

                  s = var's'
                  
                  		

GOOD

time: 0.014000ms
                  
stack: size: 0
                    

                    

                    

                    

                    t = var't'
                    
                    		

GOOD

time: 0.007000ms
                    
stack: size: 0
                      

                      

                      

                      

                      x = func('x', {s,t})
                      
                      		

GOOD

time: 0.031000ms
                      
stack: size: 0
                        

                        

                        

                        

                        y = func('y', {s,t})
                        
                        		

GOOD

time: 0.026000ms
                        
stack: size: 0
                          

                          

                          

                          

                          f = func('f', {x,y})
                          
                          		
BAD
                          [string "/home/chris/Projects/lua/symmath/UserFunction..."]:140: args must be a table of Variables
                          
stack traceback:
                          
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:260: in function 
                          
	[C]: in function 'assert'
                          
	[string "/home/chris/Projects/lua/symmath/UserFunction..."]:140: in function 'func'
                          
	[string "f = func('f', {x,y})"]:1: in main chunk
                          
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:252: in function 
                          
	[C]: in function 'xpcall'
                          
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:251: in function 'exec'
                          
	func.lua:65: in function 'cb'
                          
	[string "/home/chris/Projects/lua/ext/timer.lua"]:101: in function 'timer'
                          
	func.lua:6: in main chunk
                          
	[C]: at 0x5569e268c390
                          		
time: 0.063000ms
                          
stack: size: 0
                            

                            

                            
∂f/∂x
                            

                            print(f:diff(x):prune())
                            
                            		
BAD
                            [string "/home/chris/Projects/lua/symmath/Expression.lua"]:49: attempt to call a table value
                            
stack traceback:
                            
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:260: in function 
                            
	[string "/home/chris/Projects/lua/symmath/Expression.lua"]:49: in function 'clone'
                            
	[string "/home/chris/Projects/lua/symmath/Derivative.lua"]:365: in function 'func'
                            
	[string "/home/chris/Projects/lua/symmath/visitor/Visi..."]:224: in function 'prune'
                            
	[string "print(f:diff(x):prune())"]:1: in main chunk
                            
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:252: in function 
                            
	[C]: in function 'xpcall'
                            
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:251: in function 'exec'
                            
	func.lua:65: in function 'cb'
                            
	[string "/home/chris/Projects/lua/ext/timer.lua"]:101: in function 'timer'
                            
	func.lua:6: in main chunk
                            
	[C]: at 0x5569e268c390
                            		
time: 0.192000ms
                            
stack: size: 0
                              

                              

                              
∂f/∂y
                              

                              print(f:diff(y):prune())
                              
                              		
BAD
                              [string "/home/chris/Projects/lua/symmath/Expression.lua"]:49: attempt to call a table value
                              
stack traceback:
                              
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:260: in function 
                              
	[string "/home/chris/Projects/lua/symmath/Expression.lua"]:49: in function 'clone'
                              
	[string "/home/chris/Projects/lua/symmath/Derivative.lua"]:365: in function 'func'
                              
	[string "/home/chris/Projects/lua/symmath/visitor/Visi..."]:224: in function 'prune'
                              
	[string "print(f:diff(y):prune())"]:1: in main chunk
                              
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:252: in function 
                              
	[C]: in function 'xpcall'
                              
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:251: in function 'exec'
                              
	func.lua:65: in function 'cb'
                              
	[string "/home/chris/Projects/lua/ext/timer.lua"]:101: in function 'timer'
                              
	func.lua:6: in main chunk
                              
	[C]: at 0x5569e268c390
                              		
time: 0.169000ms
                              
stack: size: 0
                                

                                

                                
∂f/∂x ∂x/∂s + ∂f/∂y ∂y/∂s
                                

                                print(f:diff(s):prune())
                                
                                		
BAD
                                [string "/home/chris/Projects/lua/symmath/Expression.lua"]:49: attempt to call a table value
                                
stack traceback:
                                
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:260: in function 
                                
	[string "/home/chris/Projects/lua/symmath/Expression.lua"]:49: in function 'clone'
                                
	[string "/home/chris/Projects/lua/symmath/Derivative.lua"]:365: in function 'func'
                                
	[string "/home/chris/Projects/lua/symmath/visitor/Visi..."]:224: in function 'prune'
                                
	[string "print(f:diff(s):prune())"]:1: in main chunk
                                
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:252: in function 
                                
	[C]: in function 'xpcall'
                                
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:251: in function 'exec'
                                
	func.lua:65: in function 'cb'
                                
	[string "/home/chris/Projects/lua/ext/timer.lua"]:101: in function 'timer'
                                
	func.lua:6: in main chunk
                                
	[C]: at 0x5569e268c390
                                		
time: 0.308000ms
                                
stack: size: 0
                                  

                                  

                                  
∂f/∂x ∂x/∂t + ∂f/∂y ∂y/∂t
                                  

                                  print(f:diff(t):prune())
                                  
                                  		
BAD
                                  [string "/home/chris/Projects/lua/symmath/Expression.lua"]:49: attempt to call a table value
                                  
stack traceback:
                                  
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:260: in function 
                                  
	[string "/home/chris/Projects/lua/symmath/Expression.lua"]:49: in function 'clone'
                                  
	[string "/home/chris/Projects/lua/symmath/Derivative.lua"]:365: in function 'func'
                                  
	[string "/home/chris/Projects/lua/symmath/visitor/Visi..."]:224: in function 'prune'
                                  
	[string "print(f:diff(t):prune())"]:1: in main chunk
                                  
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:252: in function 
                                  
	[C]: in function 'xpcall'
                                  
	/home/chris/Projects/lua/symmath/tests/unit/unit.lua:251: in function 'exec'
                                  
	func.lua:65: in function 'cb'
                                  
	[string "/home/chris/Projects/lua/ext/timer.lua"]:101: in function 'timer'
                                  
	func.lua:6: in main chunk
                                  
	[C]: at 0x5569e268c390
                                  		
time: 0.101000ms
                                  
stack: size: 0
                                    

                                    

                                    
TODO I need something to represent ∂/∂x "the def of f", rather than ∂/∂x "f", which is zero.
                                    

                                    
                                    		


                                    

                                    
in contrast ∂/∂x "the def of f" would be a placeholder (in absense of f's provided definition)