Input = − 1 c + (c a + d b) c − 1 d + (c a + d b) d c a + d b − a^{T} c^{T} − b^{T} d^{T} − 1 c a − d b + a^{T} c^{T} + b^{T} d^{T} a c − c^{T} a^{T} − 1 a c + c^{T} a^{T} a d − c^{T} b^{T} − 1 a d + c^{T} b^{T} b c − d^{T} a^{T} − 1 b c + d^{T} a^{T} b d − d^{T} b^{T} − 1 b d + d^{T} b^{T} (a^{T} a + b^{T} b) P inv[a^{T} a + b^{T} b] − (P inv[a^{T} a + b^{T} b])^{T} (a^{T} a + b^{T} b) − 1 (a^{T} a + b^{T} b) (P inv[a^{T} a + b^{T} b])^{T} + P inv[a^{T} a + b^{T} b] (a^{T} a + b^{T} b) (a^{T} a + b^{T} b) (P inv[a^{T} a + b^{T} b])^{T} − P inv[a^{T} a + b^{T} b] (a^{T} a + b^{T} b) − 1 (a^{T} a + b^{T} b) P inv[a^{T} a + b^{T} b] + (P inv[a^{T} a + b^{T} b])^{T} (a^{T} a + b^{T} b) − 1 a + a c a + a d b − 1 b + b c a + b d b − 1 a^{T} a − b^{T} b + (a^{T} a + b^{T} b) P inv[a^{T} a + b^{T} b] (a^{T} a + b^{T} b) − 1 a^{T} a − b^{T} b + (a^{T} a + b^{T} b) (P inv[a^{T} a + b^{T} b])^{T} (a^{T} a + b^{T} b) P inv[a^{T} a + b^{T} b] (a^{T} a + b^{T} b) P inv[a^{T} a + b^{T} b] − P inv[a^{T} a + b^{T} b] a^{T} c^{T} a^{T} + b^{T} d^{T} a^{T} − a^{T} a^{T} c^{T} b^{T} + b^{T} d^{T} b^{T} − b^{T} c^{T} (a^{T} c^{T} + b^{T} d^{T}) − c^{T} d^{T} (a^{T} c^{T} + b^{T} d^{T}) − d^{T} (P inv[a^{T} a + b^{T} b])^{T} (a^{T} a + b^{T} b) (P inv[a^{T} a + b^{T} b])^{T} − (P inv[a^{T} a + b^{T} b])^{T} P inv[a^{T} a + b^{T} b] − (P inv[a^{T} a + b^{T} b])^{T} − 1 P inv[a^{T} a + b^{T} b] + (P inv[a^{T} a + b^{T} b])^{T} File Name = PseudoInverseOfColumn NCMakeGB Iterations = 5 NCMakeGB on Digested Iterations = 0 SmallBasis Iterations = 0 SmallBasis on Knowns Iterations = 0 Deselect→ {} UserSelect→ {} UserUnknowns→ {} NCShortFormulas→-1 RR→False RRByCat→False SB→False SBByCat→False DegreeCap→-1 DegreeSumCap→-1 DegreeCapSB→-1 DegreeSumCapSB→-1 NCCV→True THE ORDER IS NOW THE FOLLOWING: a < a^{T} < b < b^{T} < P inv[a^{T} a+b^{T} b] < P inv[a^{T} a+b^{T} b] < (P inv[a^{T} a + b^{T} b])^{T} < (P inv[a^{T} a + b^{T} b])^{T} ≪ c < c^{T} ≪ d < d^{T}

YOUR SESSION HAS DIGESTED THE FOLLOWING RELATIONS THE FOLLOWING VARIABLES HAVE BEEN SOLVED FOR: {c, d, c^{T} , d^{T} , (P inv[a^{T} a + b^{T} b])^{T} } The corresponding rules are the following: c → P inv[a^{T} a + b^{T} b] a^{T}

d → P inv[a^{T} a + b^{T} b] b^{T}

c^{T} → a P inv[a^{T} a + b^{T} b]

d^{T} → b P inv[a^{T} a + b^{T} b]

(P inv[a^{T} a + b^{T} b])^{T} → P inv[a^{T} a + b^{T} b]

The expressions with unknown variables {} and knowns {a, b, P inv[a^{T} a + b^{T} b], a^{T} , b^{T} } P inv[a^{T} a + b^{T} b] b^{T} b → −1 P inv[a^{T} a + b^{T} b] a^{T} a + a^{T} a P inv[a^{T} a + b^{T} b] + b^{T} b P inv[a^{T} a + b^{T} b]

−1 a (1 − b^{T} b P inv[a^{T} a + b^{T} b]) + a a^{T} a P inv[a^{T} a + b^{T} b] == 0

−1 b (1 − a^{T} a P inv[a^{T} a + b^{T} b]) + b b^{T} b P inv[a^{T} a + b^{T} b] == 0

(a^{T} a + b^{T} b) P inv[a^{T} a + b^{T} b] P inv[a^{T} a + b^{T} b] − P inv[a^{T} a + b^{T} b] == 0

−1 (1 − b^{T} b P inv[a^{T} a + b^{T} b]) a^{T} + a^{T} a P inv[a^{T} a + b^{T} b] a^{T} == 0

−1 (1 − a^{T} a P inv[a^{T} a + b^{T} b]) b^{T} + b^{T} b P inv[a^{T} a + b^{T} b] b^{T} == 0

USER CREATIONS APPEAR BELOW

SOME RELATIONS WHICH APPEAR BELOW MAY BE UNDIGESTED

THE FOLLOWING VARIABLES HAVE NOT BEEN SOLVED FOR: {a, b, P inv[a^{T} a + b^{T} b], a^{T} , b^{T} }

The time for preliminaries was 0:00:00 The time for NCMakeGB 1 was 0:00:00 The time for Remove Redundant 1 was 0:00:00 The time for the main NCMakeGB was 0:00:00 The time for Remove Redundant 2 was 0:00:00 The time for reducing unknowns was 0:00:00 The time for clean up basis was 0:00:00 The time for SmallBasis was 0:00:00 The time for CreateCategories was 0:00:00 The time for NCCV was 0:00:03 The time for RegularOutput was 0:00:00 The time for everything so far was 0:00:04