QuadraticForm(n, K)

clifford.spad line 18 [edit on github]

• n : PositiveInteger
• K : Field

This domain provides modest support for quadratic forms.

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

0 : () -> %

from AbelianMonoid

= : (%, %) -> Boolean

from BasicType

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

convert : % -> InputForm if SquareMatrix(n, K) has ConvertibleTo(InputForm)

from ConvertibleTo(InputForm)

elt : (%, DirectProduct(n, K)) -> K

elt(qf, v) evaluates the quadratic form qf on the vector v, producing a scalar.

latex : % -> String

from SetCategory

matrix : % -> SquareMatrix(n, K)

matrix(qf) creates a square matrix from the quadratic form qf.

opposite? : (%, %) -> Boolean

from AbelianMonoid

quadraticForm : SquareMatrix(n, K) -> %

quadraticForm(m) creates a quadratic form from a symmetric, square matrix m.

sample : () -> %

from AbelianMonoid

subtractIfCan : (%, %) -> Union(%, "failed")

from CancellationAbelianMonoid

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

CancellationAbelianMonoid

CoercibleTo(OutputForm)

AbelianMonoid

AbelianSemiGroup

ConvertibleTo(InputForm)

SetCategory

BasicType

AbelianGroup