(* ::Package:: *)

qTrunc1[a0_]:=If[IntegerQ[Ceiling[100*a0]/100], Ceiling[100*a0]/100, N[Ceiling[100*a0]/100]];
qTrunc2[a0_]:=N[Floor[100*a0]/100];
qTrunc3[a0_]:=N[Ceiling[10*a0]/10];
qTrunc4[a0_]:=N[Floor[10*a0]/10];
qTrunc5[a0_]:=N[Round[10*a0]/10];
qTrunc6[a0_]:=If[IntegerQ[Ceiling[100*a0]/100], Ceiling[100*a0]/100,
If[FractionalPart[a0*100]>=0.5,
N[Ceiling[a0*100]/100],
If[IntegerQ[Floor[a0*100]/100],Floor[a0*100]/100,N[Floor[a0*100]/100]]]
];
qTrunc7[a0_]:=If[FractionalPart[a0]>=0.5,
Ceiling[a0],
Floor[a0]]; 


(*rounding only from 2 to 6 decimal places *) (*ANNA: changed qTrunc8*)
qTrunc8[a0_,n_]:= If[RealDigits[a0][[1]][[RealDigits[a0][[2]]+n+1]]>=5,
(*rounding up*)
(*TO DO : simpler method to do rounding up*)
	If[ToExpression[StringJoin@(ToString/@Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+n}])]==ToExpression[StringJoin[ToString/@ConstantArray[9,n]]],
		ToString[ToExpression[StringJoin@(ToString/@Take[RealDigits[a0][[1]],RealDigits[a0][[2]]])]+1] (*example 2.9999999999*)
		,
		If[ToExpression[StringJoin@(ToString/@Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+n}])]<9, (*example 2.0000007  : rounding to 6 decimal places*)
			StringJoin@(ToString/@Take[RealDigits[a0][[1]],RealDigits[a0][[2]]])<>
Which[Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]!= 0,
".",
Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]==0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+2,RealDigits[a0][[2]]+2}][[1]]!= 0,
".0",
Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]==0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+2,RealDigits[a0][[2]]+2}][[1]]== 0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+3,RealDigits[a0][[2]]+3}][[1]]!= 0,
".00",
Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]==0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+2,RealDigits[a0][[2]]+2}] [[1]]==  0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+3,RealDigits[a0][[2]]+3}][[1]]==  0
&& Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+4,RealDigits[a0][[2]]+4}][[1]]!= 0,
".000"
,
Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]==0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+2,RealDigits[a0][[2]]+2}][[1]] ==  0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+3,RealDigits[a0][[2]]+3}][[1]]==  0
&& Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+4,RealDigits[a0][[2]]+4}][[1]]== 0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+5,RealDigits[a0][[2]]+5}][[1]]!= 0,
".0000"
,
Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]==0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+2,RealDigits[a0][[2]]+2}][[1]] ==  0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+3,RealDigits[a0][[2]]+3}][[1]]==  0
&& Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+4,RealDigits[a0][[2]]+4}][[1]]== 0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+5,RealDigits[a0][[2]]+5}][[1]]==  0
&& Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+6,RealDigits[a0][[2]]+6}][[1]]!= 0,
".00000"
]
<>ToString[ToExpression[StringJoin@(ToString/@Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+n}])]+1]
			,
			If[Mod[b123=ToExpression[StringJoin@(ToString/@Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+n}])]+1,10]==0,
				StringJoin@(ToString/@Take[RealDigits[a0][[1]],RealDigits[a0][[2]]])<>
If[Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]== 0,
Which[
Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]==0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+2,RealDigits[a0][[2]]+2}][[1]]!= 0,
".",
Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]==0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+2,RealDigits[a0][[2]]+2}][[1]]== 0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+3,RealDigits[a0][[2]]+3}][[1]]!= 0,
".0",
Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]==0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+2,RealDigits[a0][[2]]+2}] [[1]]==  0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+3,RealDigits[a0][[2]]+3}][[1]]==  0
&& Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+4,RealDigits[a0][[2]]+4}][[1]]!= 0,
".00"
,
Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]==0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+2,RealDigits[a0][[2]]+2}][[1]] ==  0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+3,RealDigits[a0][[2]]+3}][[1]]==  0
&& Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+4,RealDigits[a0][[2]]+4}][[1]]== 0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+5,RealDigits[a0][[2]]+5}][[1]]!= 0,
".000"
,
Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]==0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+2,RealDigits[a0][[2]]+2}][[1]] ==  0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+3,RealDigits[a0][[2]]+3}][[1]]==  0
&& Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+4,RealDigits[a0][[2]]+4}][[1]]== 0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+5,RealDigits[a0][[2]]+5}][[1]]==  0
&& Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+6,RealDigits[a0][[2]]+6}][[1]]!= 0,
".0000"
],
"."]
<>
ToString[(ToExpression[StringJoin@(ToString/@Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+n}])]+1)/
If[Mod[b123,10000]==0,10000,If[Mod[b123,1000]==0,1000 ,If[Mod[b123,100]==0,100,If[Mod[b123,10]==0,10 ] ]]]
]
				,
				StringJoin@(ToString/@Take[RealDigits[a0][[1]],RealDigits[a0][[2]]])<>
(*TO DO : check if all cases are included in below Which*)
Which[Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]!= 0,
".",
Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]==0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+2,RealDigits[a0][[2]]+2}][[1]]!= 0,
".0",
Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]==0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+2,RealDigits[a0][[2]]+2}][[1]]== 0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+3,RealDigits[a0][[2]]+3}][[1]]!= 0,
".00",
Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]==0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+2,RealDigits[a0][[2]]+2}] [[1]]==  0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+3,RealDigits[a0][[2]]+3}][[1]]==  0
&& Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+4,RealDigits[a0][[2]]+4}][[1]]!= 0,
".000"
,
Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]==0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+2,RealDigits[a0][[2]]+2}][[1]] ==  0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+3,RealDigits[a0][[2]]+3}][[1]]==  0
&& Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+4,RealDigits[a0][[2]]+4}][[1]]== 0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+5,RealDigits[a0][[2]]+5}][[1]]!= 0,
".0000"
,
Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+1}][[1]]==0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+2,RealDigits[a0][[2]]+2}][[1]] ==  0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+3,RealDigits[a0][[2]]+3}][[1]]==  0
&& Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+4,RealDigits[a0][[2]]+4}][[1]]== 0 && Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+5,RealDigits[a0][[2]]+5}][[1]]==  0
&& Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+6,RealDigits[a0][[2]]+6}][[1]]!= 0,
".00000"
]
<>ToString[ToExpression[StringJoin@(ToString/@Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+n}])]+1]
			]
		]
	]
	,
(*Rounding down: everything is ok *)
	If[Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+n}]==ConstantArray[0,n], (*example: 2.000000000*)
		StringJoin@(ToString/@Take[RealDigits[a0][[1]],RealDigits[a0][[2]]])
		,
		If[Mod[a123=ToExpression[StringJoin@(ToString/@Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+n}])],10]==0,
			StringJoin@(ToString/@Take[RealDigits[a0][[1]],RealDigits[a0][[2]]])<>
"."
<>ToString[StringJoin@(ToString/@Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+
If[Mod[a123,100000]==0,n-5,If[Mod[a123,10000]==0,n-4,If[Mod[a123,1000]==0,n-3, If[ Mod[a123,100]==0,n-2,n-1 ]   ]]]
   }])]
			,
			StringJoin@(ToString/@Take[RealDigits[a0][[1]],RealDigits[a0][[2]]])<>
"."
<>StringJoin@(ToString/@Take[RealDigits[a0][[1]],{RealDigits[a0][[2]]+1,RealDigits[a0][[2]]+n}])
			]
		]
];


(* sol is the solution provided by the Module, a1 is the SPLIT student answer, a2 is the original from inputfield *)
(* TODO: this is very specific to a particular Module, but could be generalized *)
err1[sol_,a1_,a2_]:=Module[{pr},

pr=MemberQ[WordStem[StringSplit[StringReplace[ToLowerCase[a2],{","->" ",";"->" ",":"-> " ","."->" "}]]],#]&/@{sol,IntegerName[ToExpression[sol]],"increas", "mark", "score", "grade" };

If[(pr[[1]]||pr[[2]]==True)&& Count[pr, True]>=2, True, False]

];



(* this error function compares the two results and only equates *)
errNO[sol_,a1_,a2_]:=ToExpression[sol]===ToExpression[a1];

errNO3[sol_,a1_,a2_]:= sol===a1;
errNO31[sol_,a1_,a2_]:= sol===a2;



errNO4[sol_,a1_,a2_]:= MemberQ[sol,a2];


err2[sol_,a1_,a2_]:=qTrunc6[ToExpression[sol]]===ToExpression[a2]; 



err3[sol_,a1_,a2_]:=If[IntegerQ[ToExpression[a2]]==True,
	If[(*IntegerQ[ToExpression[sol]]\[Equal]True,  *)  Take[RealDigits[ToExpression[sol]][[1]],{RealDigits[ToExpression[sol]][[2]] + 1,RealDigits[ToExpression[sol]][[2]] +2}]=={0,0},
		qTrunc7[ToExpression[sol]]===ToExpression[a2], 
		Abs[ToExpression[ToExpression[sol]]-ToExpression[a2]]<=1
		],
	False
	];  (*ANNA: added error for q#1d*)


err41[sol_,a1_,a2_]:=qTrunc8[ToExpression[sol],2]===a2;  (*error for q#9*)





err4[sol_,a1_,a2_] := If[my`class[a2,ClassPriors-><|"OK"->0.4,"GOOD"->0.3|>] === "OK" || my`class[a2,ClassPriors-><|"OK"->0.4,"GOOD"->0.3|>] === "GOOD", True, False];



err5[sol_,a1_,a2_] := If[SLOPE`class[a2,ClassPriors-><|"OK"->0.4,"GOOD"->0.3|>] === "OK" || SLOPE`class[a2,ClassPriors-><|"OK"->0.4,"GOOD"->0.3|>] === "GOOD", True, False];
err6[sol_,a1_,a2_] := If[YINTERCEPT`class[a2,ClassPriors-><|"OK"->0.4,"GOOD"->0.3|>] === "OK" || YINTERCEPT`class[a2,ClassPriors-><|"OK"->0.4,"GOOD"->0.3|>] === "GOOD", True, False];



qSign[a0_]:=Which[a0>0, "+"<>ToString[Abs[a0]], a0<0, "-"<>ToString[Abs[a0]], a0==0, "0"]; 
qSign2[a0_]:=Which[a0>0, "+", a0<0, "-", a0==0, ""];
qSign3[a0_]:=Which[a0>0, "+"<>ToString[Abs[a0]], a0<0, "-"<>ToString[Abs[a0]], a0==0, "-0"];
qSign4[a0_]:=Which[a0>0, "+"<>ToString[Abs[a0]], a0<0, "-"<>ToString[Abs[a0]], a0==0, "+0"];
qSign5[a0_]:=Which[a0>0, "+"<>ToString[Abs[a0],StandardForm], a0<0, "-"<>ToString[Abs[a0],StandardForm], a0==0, ""];
qSign6[a0_]:=Which[a0==1, "",a0>0, "+"<>ToString[Abs[a0],StandardForm], a0<0, "-"<>ToString[Abs[a0],StandardForm], a0==0, ""];



errNO2[sol_,a1_,a2_]:=ToExpression[sol]===ToExpression[a2]; 



errMIX[sol_,a1_,a2_]:=If[qTrunc6[ToExpression@ToExpression[sol][[1]]]===ToExpression[a2] || ToExpression@ToExpression[sol][[2]]===ToExpression[a1],True,False];