test1 {Error: File: test1.m Line: 10 Column: 38 Unbalanced or unexpected parenthesis or bracket.} test1 Please enter your name: Leon van Dommelen {Error using test1 (line 1) Error: Unexpected MATLAB expression.} Please enter your name: {Operation terminated by user during test1 (line 1) } test1 Please enter your name: Leon van Dommelen choice = 1 choice = 2 choice = 0 choice = 3 choice = 4 test2 x = 1 expValue = 2.7183 expError = 0 % symbolic computations qNum=@(x) -4*x.^2+3*x+12; qInt02=integral(qNum,0,2) qInt02 = 19.3333 qNumRoot=fzero(qNum,1) qNumRoot = 2.1472 syms x qSym=-4*x^2+3*x+12 qSym = - 4*x^2 + 3*x + 12 qSymInt02=int(qSym,x,[0 2]) qSymInt02 = 58/3 qSymInt=int(qSym,x) qSymInt = (x*(- 8*x^2 + 9*x + 72))/6 expand(qSymInt) ans = - (4*x^3)/3 + (3*x^2)/2 + 12*x qSymDiff=diff(qSym,x) qSymDiff = 3 - 8*x qSymDiff=diff(qSym) qSymDiff = 3 - 8*x qSymInt=int(qSym) qSymInt = (x*(- 8*x^2 + 9*x + 72))/6 sympar(qSym) {Undefined function or variable 'sympar'.} symvar(qSym) ans = x qSymRoots=solve(qSym == 0,x) qSymRoots = 3/8 - 201^(1/2)/8 201^(1/2)/8 + 3/8 double(qSymRoots) ans = -1.3972 2.1472 qSymFactors=factor(qSym) qSymFactors = [ -1, 4*x^2 - 3*x - 12] help factor factor Prime factors. factor(N) returns a vector containing the prime factors of N. This function uses the simple sieve approach. It may require large memory allocation if the number given is too big. Technically it is possible to improve this algorithm, allocating less memory for most cases and resulting in a faster execution time. However, it will still have problems in the worst case. Class support for input N: float: double, single integer: uint8, int8, uint16, int16, uint32, int32, uint64, int64 See also primes, isprime. Reference page for factor Other functions named factor matlab.internal.language.introspective.overloads.displayOverloads('factor') sym/factor help sym/factor factor Symbolic factorization. factor(S), where S is a SYM, returns all irreducible factors of S. If S is an integer, the prime factorization is computed. To factor an integer N greater than 2^52, use factor(SYM('N')). factor(S, VARS), where VARS is a vector of variables, returns all irreducible factors of S, but does not split factors that do not contain VARS. factor(S, 'FACTORMODE', MODE) or factor(S, VARS, 'FACTORMODE', MODE) factors S in the factorization mode MODE. The modes differ only in the case of univariate polynomials. Possible values: 'rational' - rational factorization. Result can contain only those irrational subexpressions that occur already in the input. This is the default mode. 'full' - factor into symbolic linear factors. 'complex' - factor numerically into linear factors. 'real' - factor numerically into linear or quadratic real factors. Examples: factor(x^9-1) is [x - 1, x^2 + x + 1, x^6 + x^3 + 1] factor(sym('12345678901234567890')) is [2, 3, 3, 5, 101, 3541, 3607, 3803, 27961] factor(x^2 * y^2, x) is [y^2, x, x] factor(x^2 + 1, 'FactorMode', 'rational') is [x^2 + 1] factor(x^2 + 1, 'FactorMode', 'full') is [x - 1i, x + 1i] See also factor, sym/simplify, sym/expand, sym/collect, sym/partfrac. qSymFactors=factor(qSym,x,'FactorMode','full') qSymFactors = [ -1, x + 201^(1/2)/8 - 3/8, x - 201^(1/2)/8 - 3/8] prod(qSymFactors) ans = (x + 201^(1/2)/8 - 3/8)*(201^(1/2)/8 - x + 3/8) 629/969 ans = 0.6491 simplify(629/969) {Undefined function 'simplify' for input arguments of type 'double'.} simplify(sym('629/969')) ans = 37/57 % very high accuracy pi^6/6 ans = 160.2315 pi^2/6 ans = 1.6449 vpa(pi^2/6,50) ans = 1.6449340668482264060656916626612655818462371826172 vpa(sym('pi^2/6'),50) ans = 1.6449340668482264364724151666460251892189499012068 Solving equations {Undefined function or variable 'Solving'.} % Solving equations syms x a b c qGen qGen=a*x^2+b*x+c qGen = a*x^2 + b*x + c qGenRoots=solve(qGen == 0,x) qGenRoots = -(b + (b^2 - 4*a*c)^(1/2))/(2*a) -(b - (b^2 - 4*a*c)^(1/2))/(2*a) pretty(qGenRoots) / 2 \ | b + sqrt(b - 4 a c) | | - -------------------- | | 2 a | | | | 2 | | b - sqrt(b - 4 a c) | | - -------------------- | \ 2 a / qGenRootsTest=subs(qGenRoots,{a b c},{-4 3 12}) qGenRootsTest = 201^(1/2)/8 + 3/8 3/8 - 201^(1/2)/8 qGenRootsFun=matlabFunction(qGenRoots) qGenRootsFun = @(a,b,c)[(b.*(-1.0./2.0)-sqrt(a.*c.*-4.0+b.^2).*(1.0./2.0))./a;(b.*(-1.0./2.0)+sqrt(a.*c.*-4.0+b.^2).*(1.0./2.0))./a] qGenRootsFun(-4,3,12) ans = 2.1472 -1.3972 % solving non-polynomial equations syms x y solve(exp(x) == -1,x) ans = pi*1i qxySym=a*x*y-b*x-1 qxySym = a*x*y - b*x - 1 solve(a*x*y-b*x-1) ans = -1/(b - a*y) symvar(qxySym) ans = [ a, b, x, y] symvar(qxySym,3) ans = [ x, y, b] symvar(qxySym == 0,x) {Error using symengine DOUBLE cannot convert the input expression into a double array. If the input expression contains a symbolic variable, use VPA. Error in sym/double (line 588) Xstr = mupadmex('symobj::double', S.s, 0); Error in sym/symvar (line 31) n = double(n);} solve(qxySym == 0,x) ans = -1/(b - a*y) solve(qxySym == 0,y) ans = (b*x + 1)/(a*x) xCoefs=collect(qxySym,x) xCoefs = (a*y - b)*x - 1 ratPartFrac=(2x^2-3*x+1)/(x^3+2*x^2-9*x-18) ratPartFrac=(2x^2-3*x+1)/(x^3+2*x^2-9*x-18) {Error: Unexpected MATLAB expression. } ratPartFrac=(2*x^2-3*x+1)/(x^3+2*x^2-9*x-18) ratPartFrac = -(2*x^2 - 3*x + 1)/(- x^3 - 2*x^2 + 9*x + 18) factor(ratPartFrac) ans = [ 2*x - 1, x - 1, 1/(x - 3), 1/(x + 3), 1/(x + 2)] partfrac(ratPartFrac) ans = 1/(3*(x - 3)) - 3/(x + 2) + 14/(3*(x + 3)) intHard1=int(1/(x*(a*x^2+b*x+c)^(1/2))) intHard1 = -log(b/2 + c/x + (c^(1/2)*(a*x^2 + b*x + c)^(1/2))/x)/c^(1/2) intHard1=int(1/(x*(a*x^2+b*x+c)^(3/2))) intHard1 = int(1/(x*(a*x^2 + b*x + c)^(3/2)), x)