Input = A P inv[A] A == A P inv[A] A P inv[A] == P inv[A] A^{T} (P inv[A])^{T} == P inv[A] A (P inv[A])^{T} A^{T} == A P inv[A] (P inv[A])^{T} == P inv[A^{T}] A^{T} A P inv[A] == A^{T} A P inv[A] P inv[A^{T}] == P inv[A^{T}] File Name = PinvA NCMakeGB Iterations = 6 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→False THE ORDER IS NOW THE FOLLOWING: A < A^{T} < P inv[A] < P inv[A^{T}] < (P inv[A])^{T}

YOUR SESSION HAS DIGESTED THE FOLLOWING RELATIONS

THE FOLLOWING VARIABLES HAVE BEEN SOLVED FOR: {(P inv[A])^{T} } The corresponding rules are the following: (P inv[A])^{T} → P inv[A^{T}]

The expressions with unknown variables {} and knowns {A, P inv[A], P inv[A^{T}], A^{T} } P inv[A] A → A^{T} P inv[A^{T}]

P inv[A^{T}] A^{T} → A P inv[A]

A P inv[A] P inv[A^{T}] → P inv[A^{T}]

A A^{T} P inv[A^{T}] → A

A^{T} A P inv[A] → A^{T}

A^{T} P inv[A^{T}] P inv[A] → P inv[A]

USER CREATIONS APPEAR BELOW

SOME RELATIONS WHICH APPEAR BELOW MAY BE UNDIGESTED THE FOLLOWING VARIABLES HAVE NOT BEEN SOLVED FOR: {A, P inv[A], P inv[A^{T}], A^{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 0:00:00 The time for RegularOutput was 0:00:00 The time for everything so far was 0:00:00