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Quadratic Invariant Modulus

The quantity ps-rq obtained by letting

x=pX+qY
(1)
y=rX+sY
(2)

in

ax^2+2bxy+cy^2
(3)

so that

A=ap^2+2bpr+cr^2
(4)
B=apq+b(ps+qr)+crs
(5)
C=aq^2+2bqs+cs^2
(6)

and

B^2-AC=(ps-rq)^2(b^2-ac),
(7)

is called the modulus.

See also

Quadratic, Quadratic Invariant

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Cite this as:

Weisstein, Eric W. "Quadratic Invariant Modulus." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/QuadraticInvariantModulus.html

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