algebrite

test_power = -> run_test [ # according to the notorious # "PEMDAS" mnemonic, the power # operator has the most precedence. # Strangely, Mathematica parses # a^1/2 as sqrt(a), not following PEMDAS, # probably because of some fancy # euristics, since, contrarily to the # case above, it also parses # a^b/2 as (a^b)/2. # I think this more standard/uniform handling # a-la-sympy is ok. "a^1/2 + a^1/2", "a", "2^(1/2)", "2^(1/2)", "2^(3/2)", "2*2^(1/2)", "(-2)^(1/2)", "i*2^(1/2)", "3^(4/3)", "3*3^(1/3)", "3^(-4/3)", "1/(3*3^(1/3))", "3^(5/3)", "3*3^(2/3)", "3^(2/3)-9^(1/3)", "0", "3^(10/3)", "27*3^(1/3)", "3^(-10/3)", "1/(27*3^(1/3))", "(1/3)^(10/3)", "1/(27*3^(1/3))", "(1/3)^(-10/3)", "27*3^(1/3)", "27^(2/3)", "9", "27^(-2/3)", "1/9", "102^(1/2)", "2^(1/2)*3^(1/2)*17^(1/2)", "32^(1/3)", "2*2^(2/3)", "9999^(1/2)", "3*11^(1/2)*101^(1/2)", "8^(1/2)", "2*2^(1/2)", "10000^(1/3)", "10*2^(1/3)*5^(1/3)", # we could take out a "18" from the radix but # we only handle this for small numbers in # "quickfactor" routine. TODO "8204861575751304355842204^(1/2)", "8204861575751304355842204^(1/2)", # see above "simplify(8204861575751304355842204^(1/2))", "8204861575751304355842204^(1/2)", "sqrt(-1/2 -1/2 * x)", "(-1/2*x-1/2)^(1/2)", "sqrt(x*y)", "(x*y)^(1/2)", "sqrt(1/x)", "(1/x)^(1/2)", "sqrt(x^y)", "(x^y)^(1/2)", "sqrt(x)^2", "x", "sqrt(x^2)", "abs(x)", # always true, whether x is real or not "sqrt(x^2)^2", "x^2", "3^(1/2)*i/9", "1/9*i*3^(1/2)", "(-4.0)^(1.5)", "-8.0*i", "(-4.0)^(3/2)", "-8.0*i", # usually the rectangular form is returned. "(-1)^(1/3)", #"(-1)^(1/3)", "1/2+1/2*i*3^(1/2)", # note how the "double" type # is toxic i.e. it propagates through # everything it touches. "(-1.0)^(2/3)", "-0.5+0.866025*i", # this also has a nested radical # form but we are not calculating # that. "(-1)^(1/3)*2^(1/4)", #"(-1)^(1/3)*2^(1/4)", "1/2*2^(1/4)+1/2*i*2^(1/4)*3^(1/2)", "(-1)^(1/2)", "i", "sqrt(1000000)", "1000", "sqrt(-1000000)", "1000*i", "sqrt(2^60)", "1073741824", # this is why we factor irrationals "6^(1/3) 3^(2/3)", "3*2^(1/3)", # inverse of complex numbers "1/(2+3*i)", "2/13-3/13*i", "1/(2+3*i)^2", "-5/169-12/169*i", "(-1+3i)/(2-i)", "-1+i", # other "(0.0)^(0.0)", "1.0", "(-4.0)^(0.5)", "2.0*i", "(-4.0)^(-0.5)", "-0.5*i", "(-4.0)^(-1.5)", "0.125*i", # more complex number cases "(1+i)^2", "2*i", "(1+i)^(-2)", "-1/2*i", "(1+i)^(1/2)", #"(-1)^(1/8)*2^(1/4)", "i*2^(1/4)*sin(1/8*pi)+2^(1/4)*cos(1/8*pi)", "(1+i)^(-1/2)", "-(-1)^(7/8)/(2^(1/4))", "(1+i)^(0.5)", "1.09868+0.45509*i", "(1+i)^(-0.5)", "0.776887-0.321797*i", # test cases for simplification of polar forms, counterclockwise "exp(i*pi/2)", "i", "exp(i*pi)", "-1", "exp(i*3*pi/2)", "-i", "exp(i*2*pi)", "1", "exp(i*5*pi/2)", "i", "exp(i*3*pi)", "-1", "exp(i*7*pi/2)", "-i", "exp(i*4*pi)", "1", "exp(A+i*pi/2)", "i*exp(A)", "exp(A+i*pi)", "-exp(A)", "exp(A+i*3*pi/2)", "-i*exp(A)", "exp(A+i*2*pi)", "exp(A)", "exp(A+i*5*pi/2)", "i*exp(A)", "exp(A+i*3*pi)", "-exp(A)", "exp(A+i*7*pi/2)", "-i*exp(A)", "exp(A+i*4*pi)", "exp(A)", # test cases for simplification of polar forms, clockwise "exp(-i*pi/2)", "-i", "exp(-i*pi)", "-1", "exp(-i*3*pi/2)", "i", "exp(-i*2*pi)", "1", "exp(-i*5*pi/2)", "-i", "exp(-i*3*pi)", "-1", "exp(-i*7*pi/2)", "i", "exp(-i*4*pi)", "1", "exp(A-i*pi/2)", "-i*exp(A)", "exp(A-i*pi)", "-exp(A)", "exp(A-i*3*pi/2)", "i*exp(A)", "exp(A-i*2*pi)", "exp(A)", "exp(A-i*5*pi/2)", "-i*exp(A)", "exp(A-i*3*pi)", "-exp(A)", "exp(A-i*7*pi/2)", "i*exp(A)", "exp(A-i*4*pi)", "exp(A)", ]