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makeDiagonalForm -- the Grothendieck-Witt class of a diagonal form

Synopsis

Description

Given a sequence of elements $a_1,\ldots,a_n \in k$ we can form the diagonal form $\langle a_1,\ldots,a_n\rangle$ defined to be the block sum of each of the rank one forms $\langle a_i \rangle \colon k \times k \to k,$ $(x,y) \mapsto a_i xy$.

i1 : makeDiagonalForm(QQ, (3,5,7))

o1 = | 3 0 0 |
     | 0 5 0 |
     | 0 0 7 |

o1 : GrothendieckWittClass

Inputting a ring element, an integer, or a rational number instead of a sequence will produce a rank one form instead. For instance:

i2 : makeDiagonalForm(GF(29), 5/13)

o2 = | -13 |

o2 : GrothendieckWittClass
i3 : makeDiagonalForm(RR, 2)

o3 = | 2 |

o3 : GrothendieckWittClass

See also

Ways to use makeDiagonalForm:

For the programmer

The object makeDiagonalForm is a method function.