algebrite

test_inner = -> run_test [ # since we don't know anything about # a and b, we have to leave this unevaluated # turning this into a normal multiplication (which is # commutative) would not be OK "inner(a,b)", "inner(a,b)", # this shouldn't ever go wrong # but one never knows "inner(b,a)", "inner(b,a)", "inner(2,a)", "2*a", "inner(a,2)", "2*a", "inner(a,[b1,b2])", "inner(a,[b1,b2])", "inner([a1,a2],b)", "inner([a1,a2],b)", "inner(2,[b1,b2])", "[2*b1,2*b2]", "inner([b1,b2],2)", "[2*b1,2*b2]", "inner([[a11,a12],[a21,a22]],[x1,x2])", "[a11*x1+a12*x2,a21*x1+a22*x2]", "inner([1,2],[3,4])", "11", # non-invertible matrix "inner([[2,2],[2,2]],[[0],[1]])", "[[2],[2]]", "inner(inner([1,2],[[3,4],[5,6]]),[7,8])", "219", "inner([1,2],inner([[3,4],[5,6]],[7,8]))", "219", "inner([1,2],[[3,4],[5,6]],[7,8])", "219", "inner(c,a1+b1)", "inner(c,a1)+inner(c,b1)", "inner(b1+c1,a)", "inner(b1,a)+inner(c1,a)", "inner(inner(a,b),c)", "inner(a,inner(b,c))", "inner(inner(a,b),c) - inner(a,inner(b,c))", "0", "inner(inner(a,b),c,d) - inner(a,b,inner(c,d))", "0", # trying some associativity and distributivity together "inner(inner(a,b),c,d+f) - ( (inner(a,inner(b,c),d)) + inner(inner(a,b),c,f) )", "0", # bring it to a canonical form # using associativity "inner(a,b,c)", "inner(a,inner(b,c))", "inner(a,b+c,d)", "inner(a,inner(b,d))+inner(a,inner(c,d))", "inner(inner(a,b),inner(c,d))", "inner(a,inner(b,inner(c,d)))", # scalar product of vectors: "inner([a, b, c], [x, y, z])", "a*x+b*y+c*z", # products of matrices and vectors: "inner([[a, b], [c,d]], [x, y])", "[a*x+b*y,c*x+d*y]", "inner([x, y], [[a, b], [c,d]])", "[a*x+c*y,b*x+d*y]", "inner([x, y], [[a, b], [c,d]], [r, s])", "a*r*x+b*s*x+c*r*y+d*s*y", # matrix product: "inner([[a,b],[c,d]],[[r,s],[t,u]])", "[[a*r+b*t,a*s+b*u],[c*r+d*t,c*s+d*u]]", # --------------------------------------- # using the dot # --------------------------------------- "a·b", "inner(a,b)", "a·b·c", "inner(a,inner(b,c))", "a·b*c", "c*inner(a,b)", # note how we use associativity to bring it all # to a canonical form "((a·b)·c)·d", "inner(a,inner(b,inner(c,d)))", "a*b·c", "a*inner(b,c)", "2*a·b", "2*inner(a,b)", "inv(a)·a", "I", "a·inv(a)", "I", "b·a·inv(a)·c", "inner(b,c)", "b·aᵀ·inv(aᵀ)·c", "inner(b,c)", "b·inv(aᵀ)·aᵀ·c", "inner(b,c)", "b·inv((a+b)ᵀ)·(b+a)ᵀ·c", "inner(b,c)", "(-a)·(-b)", "inner(a,b)", "I·I", "I", "I·Iᵀ", "I", "(-I)·(-I)", "I", "(-Iᵀ)·(-I)", "I", "c·(b+a)ᵀ·inv((a+b)ᵀ)·d", "inner(c,d)", "c·inv((b+a)ᵀ)·(a+b)ᵀ·d", "inner(c,d)", "c·(b+a)ᵀ·inv((a+b)ᵀ)·inv(c)", "I", "c·inv((b+a)ᵀ)·(a+b)ᵀ·inv(c)", "I", "inv(c)·(b+a)ᵀ·inv((a+b)ᵀ)·c", "I", "inv(c)·inv((b+a)ᵀ)·(a+b)ᵀ·c", "I", "c·d·(b+a)ᵀ·inv((a+b)ᵀ)", "inner(c,d)", "d·(b+a)ᵀ·inv((a+b)ᵀ)", "d", "(b+a)ᵀ·inv((a+b)ᵀ)", "I", "c·d·(b+a)ᵀ·inv((a+b)ᵀ)·inv(d)", "c", "c·d·(b+a)ᵀ·inv((a+b)ᵀ)·inv(d)·inv(c)", "I", "c·d·(b+a)ᵀ·inv((a+b)ᵀ)·inv(c·d)", "I", "c·d·(a+b)ᵀ·inv(c·d·(b+a)ᵀ)", "I", "inv(c)·c", "I", "inv(c·a)·c·a", "I", "inv(c·b·a)·c·b·a", "I", "inv(c)·d·(a+b)ᵀ·inv(inv(c)·d·(b+a)ᵀ)", "I", "inv(c+f)·d·(a+b)ᵀ·inv(inv(f+c)·d·(b+a)ᵀ)", "I", "c·d·inv(a)·inv(c·d·inv(a))", "I", ]