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tensor_ring.m2
A = QQ[a,b] B = QQ[x,y,z] C = tensor(A,B,Degrees=>{{1,1},{1,2},{1,3},{0,1},{1,-3}},DegreeRank=>2) assert( degrees C === {{1, 1}, {1, 2}, {1, 3}, {0, 1}, {1, -3}} ) -- tensor products A = QQ[vars(0..2)] B = QQ[x,y,Degrees=>{2:{0,1}}] A ** B B ** A tensor(A,B,Degrees=>{5:{1,2,3}}) assert( degrees oo === {{1, 2, 3}, {1, 2, 3}, {1, 2, 3}, {1, 2, 3}, {1, 2, 3}} ) A = QQ[vars(0..2),DegreeRank=>3] describe A toExternalString A A = QQ[vars(0..2),DegreeRank=>2] D = A ** A assert( degrees D === {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {0, 0, 0, 1}} ) tensor(A,A,MonomialOrder=>Eliminate numgens A) E = tensor(A,A,DegreeRank=>6) assert( degrees E === {{1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}} ) F = tensor(A,A, Degrees => degrees A | degrees A) assert( degrees F == {{1, 0}, {0, 1}, {0, 1}, {1, 0}, {0, 1}, {0, 1}} )