TOPOGRAPH
Binary Quadratic Form Explorer
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Depth
Form Q(x,y) = ax² + bxy + cy²
A
1
B
0
C
1
Sign map (+ green / − red)
Show vectors (p,q)
Highlight home triad
D = b²−4ac =
-4
(positive-definite)
Home triad:
Q(1,0)=1 Q(0,1)=1 Q(1,1)=2
Reduced form:
1x² + 0xy + 1y²
(already reduced)
Topograph
Equivalence
Plain
River trace
Pell solutions
Q(x,y) = x² + y²
⊕
◉
◎
⛶
1
(1,0)
1
(0,1)
2
(1,1)
2
(1,-1)
5
(1,2)
5
(2,1)
5
(2,-1)
5
(1,-2)
10
(1,3)
13
(2,3)
13
(3,2)
10
(3,1)
D=-4 def+