Helper

count_affine_solutions_rank1

File dumas2017dual/lib/rouche_capelli.v

Section FiniteSolutionCounting

Type Lemma

Proof Lines 106

Signature

Lemma count_affine_solutions_rank1 (x y z : K) : y != 0 -> #|[set p : K * K | x * p.1 + y * p.2 == z]| = #|K|.

Description

2D linear constraint cardinality: |{(a,b) | x*a + y*b = z}| = |K| when y ≠ 0. Special case for rank-1 systems: one equation in two unknowns has |K| solutions. Used directly in DSDP's constrained_pairs_card and dotp2_solutions. Proof converts the pair constraint to column form and applies the general theory.

Uses (0)

This lemma does not use any other lemmas from the stats.

Used By (0)

No lemmas in the stats use this lemma.

Coq Source Code

View on GitHub

Loading source code...

← Back to Stats