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complex.m2
-- Test of the various cases for sqrt of a complex number -- (in default precision) -- test multiplication -- debug Core testmult = (a,b) -> ( a1 = rawFromNumber(raw(CC_53),a); b1 = rawFromNumber(raw(CC_53),b); abs(rawToCC (a1*b1) - a*b) ) assert(testmult(1+ii,2+ii) < 1e-15) assert(testmult(2+ii,1+ii) < 1e-15) assert(testmult(1+2*ii,1-2*ii) < 1e-15) assert(testmult(2*ii,1-2*ii) < 1e-15) assert(testmult(3+2*ii,1-2*ii) < 1e-15) assert(testmult(20+2*ii,-1-2*ii) < 1e-15) assert(testmult(-1-2*ii,20+2*ii) < 1e-15) assert(testmult(0.0+0.0*ii,20+2*ii) < 1e-15) -- test division -- debug Core testdiv = (a,b) -> ( a1 = rawFromNumber(raw(CC_53),a); b1 = rawFromNumber(raw(CC_53),b); abs(rawToCC (a1//b1) - a/b) ) assert(testdiv(1+ii,2+ii) < 1e-15) assert(testdiv(2+ii,1+ii) < 1e-15) assert(testdiv(1+2*ii,1-2*ii) < 1e-15) assert(testdiv(2*ii,1-2*ii) < 1e-15) assert(testdiv(3+2*ii,1-2*ii) < 1e-15) assert(testdiv(20+2*ii,-1-2*ii) < 1e-15) assert(testdiv(-1-2*ii,20+2*ii) < 1e-15) -- test abs -- a = 1+ii b = abs(a) assert(b == sqrt(2)) a = -1+ii b = abs(a) assert(b == sqrt(2)) a = 1-ii b = abs(a) assert(b == sqrt(2)) a = -1-ii b = abs(a) assert(b == sqrt(2)) a = 1+0*ii b = abs(a) assert(b == 1) a = -1+0*ii b = abs(a) assert(b == 1) a = 0.0+ii b = abs(a) assert(b == 1) a = 0.0-ii b = abs(a) assert(b == 1) -- test sqrt -- a = 1+ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = -1+ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = 1-ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = -1-ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = 1+5*ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = -1+5*ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = 1-5*ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = -1-5*ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = 5+ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = 5-ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = -5+ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = -5-ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = 5*ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = -5*ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = 1.0+0.0*ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = -1+0.0*ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = 1.0*ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = 5-ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = -5+ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) a = -5-ii b = sqrt(a) assert(abs(b^2-a) < 1e-14) assert(b >= 0) assert(log1p ii == log(1 + ii)) assert(expm1 ii == exp ii - 1)