Edit detail for QuadraticForm revision 1 of 4

(1) -> <spad>
QuadraticForm(n, K): T == Impl where
    n: PositiveInteger
    K: Field
    SM ==> SquareMatrix
    V  ==> DirectProduct

    T ==> AbelianGroup with
        quadraticForm: SM(n, K) -> %
            ++ quadraticForm(m) creates a quadratic form from a symmetric,
            ++ square matrix m.
        matrix: % -> SM(n, K)
            ++ matrix(qf) creates a square matrix from the quadratic form qf.
        elt: (%, V(n, K)) -> K
            ++ elt(qf,v) evaluates the quadratic form qf on the vector v,
            ++ producing a scalar.
        coerce: % -> InputForm

    Impl ==> SM(n,K) add
        Rep := SM(n,K)

        import List InputForm

        coerce(q:%):InputForm ==
            convert(['quadraticForm,algCoerceInteractive(q,SM(n,K),InputForm)$Lisp pretend InputForm])

        quadraticForm m ==
            not symmetric? m =>
                error "quadraticForm requires a symmetric matrix"
            m::%
        matrix q == q pretend SM(n,K)
        elt(q,v) == dot(v, (matrix q * v))</spad>

Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1043127575028836965-25px001.spad
      using old system compiler.
------------------------------------------------------------------------
   initializing NRLIB QFORM for QuadraticForm 
   compiling into NRLIB QFORM 
   importing List InputForm
   compiling exported coerce : % -> InputForm
****** comp fails at level 3 with expression: ******
error in function coerce 

(|convert|
 (|construct| '|quadraticForm| | << |
              (|pretend|
               ((|Sel| |Lisp| |algCoerceInteractive|) |q|
                (|SquareMatrix| |n| K) (|InputForm|))
               (|InputForm|))
              | >> |))
****** level 3  ******
x:= (pretend ((Sel Lisp algCoerceInteractive) q (SquareMatrix n K) (InputForm)) (InputForm))
m:= (Symbol)
f:=
((((|q| # #) (|#| #) (< #) (<= #) ...)))

   >> Apparent user error:
   Cannot coerce (algCoerceInteractive q (SquareMatrix n K) (InputForm)) 
      of mode (InputForm) 
      to mode (Symbol)

)show QuadraticForm

 QuadraticForm(n: PositiveInteger,K: Field) is a domain constructor
 Abbreviation for QuadraticForm is QFORM 
 This constructor is exposed in this frame.
------------------------------- Operations --------------------------------

 ?*? : (Integer, %) -> %               ?*? : (PositiveInteger, %) -> %
 ?+? : (%, %) -> %                     ?-? : (%, %) -> %
 -? : % -> %                           ?=? : (%, %) -> Boolean
 0 : () -> %                           coerce : % -> OutputForm
 latex : % -> String                   matrix : % -> SquareMatrix(n,K)
 opposite? : (%, %) -> Boolean         sample : () -> %
 zero? : % -> Boolean                  ?~=? : (%, %) -> Boolean
 ?*? : (NonNegativeInteger, %) -> %
 convert : % -> InputForm if SquareMatrix(n,K) has KONVERT(INFORM)
 elt : (%, DirectProduct(n,K)) -> K
 quadraticForm : SquareMatrix(n,K) -> %
 subtractIfCan : (%, %) -> Union(%,"failed")

Test

parse(s:String):InputForm == ncParseFromString(s)$Lisp pretend InputForm

   Function declaration parse : String -> InputForm has been added to 
      workspace.

parse("Integer")

Compiling function parse with type String -> InputForm

(1)

qf := quadraticForm matrix [[1,2],[2,-1]]

(2)

qf::InputForm

(3)

unparse %

(4)

parse %

(5)

interpret(%)$INFORM1(QuadraticForm(2,Fraction Integer))

(6)