algebrite

test_simplify = -> run_test [ "simplify(A)", "A", "simplify(A+B)", "A+B", "simplify(A B)", "A*B", "simplify(A^B)", "A^B", "simplify(A/(A+B)+B/(A+B))", "1", "simplify((A-B)/(B-A))", "-1", "A=((A11,A12),(A21,A22))", "", "simplify(det(A) inv(A) - adj(A))", "0", "A=quote(A)", "", # this shows need for <= in try_factoring # "x*(1+a)", # "x+a*x", # "simplify(last)", # "x*(1+a)", "simplify(-3 exp(-1/3 r + i phi) cos(theta) / sin(theta)\ + 3 exp(-1/3 r + i phi) cos(theta) sin(theta)\ + 3 exp(-1/3 r + i phi) cos(theta)^3 / sin(theta))", "0", "simplify((A^2 C^2 + A^2 D^2 + B^2 C^2 + B^2 D^2)/(A^2+B^2)/(C^2+D^2))", "1", "simplify(d(arctan(y/x),y))", "x/(x^2+y^2)", "simplify(d(arctan(y/x),x))", "-y/(x^2+y^2)", "simplify(1-sin(x)^2)", "cos(x)^2", "simplify(1-cos(x)^2)", "sin(x)^2", "simplify(sin(x)^2-1)", "-cos(x)^2", "simplify(cos(x)^2-1)", "-sin(x)^2", #"simfac(n!/n)-(n-1)!", #"0", #"simfac(n/n!)-1/(n-1)!", #"0", #"simfac(rationalize((n+k+1)/(n+k+1)!))-1/(n+k)!", #"0", #"simfac(condense((n+1)*n!))-(n+1)!", #"0", #"simfac(1/((n+1)*n!))-1/(n+1)!", #"0", #"simfac((n+1)!/n!)-n-1", #"0", #"simfac(n!/(n+1)!)-1/(n+1)", #"0", #"simfac(binomial(n+1,k)/binomial(n,k))", #"(1+n)/(1-k+n)", #"simfac(binomial(n,k)/binomial(n+1,k))", #"(1-k+n)/(1+n)", #"F(nn,kk)=kk*binomial(nn,kk)", #"", #"simplify(simfac((F(n,k)+F(n,k-1))/F(n+1,k))-n/(n+1))", #"0", #"F=quote(F)", #"", "simplify(n!/n)-(n-1)!", "0", "simplify(n/n!)-1/(n-1)!", "0", "simplify(rationalize((n+k+1)/(n+k+1)!))-1/(n+k)!", "0", "simplify(condense((n+1)*n!))-(n+1)!", "0", "simplify(1/((n+1)*n!))-1/(n+1)!", "0", "simplify((n+1)!/n!)-n-1", "0", "simplify(n!/(n+1)!)-1/(n+1)", "0", "simplify(binomial(n+1,k)/binomial(n,k))", "(1+n)/(1-k+n)", "simplify(binomial(n,k)/binomial(n+1,k))", "(1-k+n)/(1+n)", "F(nn,kk)=kk*binomial(nn,kk)", "", "simplify((F(n,k)+F(n,k-1))/F(n+1,k))-n/(n+1)", "0", "F=quote(F)", "", "simplify((n+1)/(n+1)!)-1/n!", "0", "simplify(a*b+a*c)", "a*(b+c)", # Symbol's binding is evaluated, undoing simplify "x=simplify(a*b+a*c)", "", "x", "a*b+a*c", ]