[HELP] Understanding the operation of CAS object types

[compsystems]

HOME MODE X (defined variable to 0), x -> "Syntax Error" (best undefined variable)

case1: Why only capital X is valid as a symbolic variable? If the CAS command tells it to operate as symbolic arg.

TYPE CMD & CAS.() CMD

TYPE( CAS.( f(X):=X+3 )) [ENTER] returns 8 // X uppercase &
TYPE( CAS.( f(x):=x+3 )) -> "Syntax Error" Why? // x lowercase

type CMD & CAS.() CMD

type( CAS.( f(X):=X+3 )) -> 8
type( CAS.( f(x):=x+3 )) -> "Syntax Error" Why? /

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case2: Within a chain is indifferent X or x

TYPE CMD & CAS( "" ) CMD

TYPE( CAS( "f(X):=X+3" )) -> 8 // X uppercase
TYPE( CAS( "f(x):=x+3" )) -> 8 // x lowercase

type CMD & CAS( "" ) CMD

type( CAS( "f(X):=X+3" )) -> 8
type( CAS( "f(x):=x+3" )) -> 8

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case3:

TYPE CMD

TYPE( f(X):=X+3 ) -> 8 // // X uppercase
TYPE( f(x):=x+3 ) -> "Syntax Error" Why? / // x lowercase

type CMD

type( f(X):=X+3 ) -> 2 ??
type( f(x):=x+3 ) -> "Syntax Error" Why? /


CAS MODE

TYPE( CAS( "f(X):=X+3" )) -> "Error: Unmatch control word"
TYPE( CAS( "f(x):=x+3" )) -> "Error: Unmatch control word"


TYPE( CAS.( f(X):=X+3 )) -> 8
TYPE( CAS.( f(x):=x+3 )) -> 8

TYPE( f(X):=X+3 ) -> "Error: Unmatch control word"
TYPE( f(x):=x+3 ) -> "Error: Unmatch control word"

type( CAS( "f(X):=X+3" )) -> DOM_SYMBOLIC Why?
type( CAS( "f(x):=x+3" )) -> DOM_SYMBOLIC Why?

type( CAS.( f(X):=X+3 )) -> DOM_IDENT Why?
type( CAS.( f(x):=x+3 )) -> DOM_IDENT Why?

type( f(X):=X+3 ) -> DOM_FUNC
type( f(x):=x+3 ) -> DOM_FUNC

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CAS:: () only CAS MODE

TYPE( CAS.( f(X):=X+3 )) [ENTER] returns 8 [UP] [UP] [COPY] TYPE(CAS::(f:=(X)->X+3))
TYPE(CAS:: (f:=(X)->X+3)) -> 8

type( CAS.( f(X):=X+3 )) [ENTER] returns DOM_IDENT [UP] [UP] [COPY] TYPE(CAS:: (f:=(X)->X+3))
type( CAS:: (f:=(X)->X+3)) -> DOM_IDENT