MathAction QuadraticForm

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- mathematical algorithms
  - FriCAS Algebra
    - QuadraticForm <-- You are here.

fricas

(1) -> )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")

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

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

Type: Void

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parse("Integer")

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Compiling function parse with type String -> InputForm

$\label{eq1}\hbox{\axiomType{Integer}\ }$

(1)

Type: InputForm

Test

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

$\label{eq2}\left[ \begin{array}{cc} 1 & 2 \ 2 & - 1$

(2)

Type: QuadraticForm(2,Fraction(Integer))

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qf::InputForm

$\label{eq3}\left({quadraticForm \ {\left({squareMatrix \ {\left({matrix \ {\left({ \begin{array}{@{}l} \displaystyle construct \ \cdot \ \ \displaystyle {\left({ \begin{array}{@{}l} \displaystyle construct \ \cdot \ \ \displaystyle 1 \ \cdot \ \ \displaystyle 2$

(3)

Type: InputForm

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unparse %

$\label{eq4}\verb#"quadraticForm(squareMatrix(matrix([[1,2],[2,-1]])))"#$

(4)

Type: String

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parse %

$\label{eq5}\left({quadraticForm \ {\left({squareMatrix \ {\left({matrix \ {\left({ \begin{array}{@{}l} \displaystyle construct \ \cdot \ \ \displaystyle {\left({ \begin{array}{@{}l} \displaystyle construct \ \cdot \ \ \displaystyle 1 \ \cdot \ \ \displaystyle 2$

(5)

Type: InputForm

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

$\label{eq6}\left[ \begin{array}{cc} 1 & 2 \ 2 & - 1$

(6)

Type: QuadraticForm(2,Fraction(Integer))

Subject: Be Bold !!

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