matlab實(shí)驗(yàn)五多項(xiàng)式和符號(hào)運(yùn)算.doc

實(shí)驗(yàn)五：Matlab多項(xiàng)式和符號(hào)運(yùn)算一、實(shí)驗(yàn)?zāi)康?掌握Matlab多項(xiàng)式的運(yùn)算。2了解符號(hào)運(yùn)算。二、實(shí)驗(yàn)內(nèi)容1將多項(xiàng)式化為x的降冪排列。syms x;y=(x-2)*(x+3)*(x-7)*(x+1);expand(y) ans = x4-5*x3-19*x2+29*x+422求一元高次方程的根。syms x y;y=x9-5*x8-30*x7+150*x6-1365*x4-820*x3+4100*x2+576*x-2880;solve(y,x) ans = 6.8194768794135839294004124431946 1.1365779764942761488953013276419+.15748095564819249061612981291831*i 2.8654872113200760683901828473839+2.4926334821808807616844446271927*i -1.8876051302159888775697938373354+1.0110818640881167605567812452594*i -.95151427733108350913000920547633 -5.0968827172792270997017839130991 -1.8876051302159888775697938373354-1.0110818640881167605567812452594*i 2.8654872113200760683901828473839-2.4926334821808807616844446271927*i 1.1365779764942761488953013276419-.15748095564819249061612981291831*i3求一元高次方程的根，并畫出左邊多項(xiàng)式函數(shù)在區(qū)間內(nèi)的曲線。a=1 0 -2 0 1;r=roots(a)syms x;x=-2:2;y=1 0 -2 0 1;plot(x,y)r = 1.0000 + 0.0000i 1.0000 - 0.0000i -1.0000 -1.0000 4對(duì)比用多項(xiàng)式函數(shù)的polyder函數(shù)及符號(hào)函數(shù)中的diff函數(shù)，求導(dǎo)x2+2x+3。y=1 2 3;polyder(y)ans = 2 2 5求多項(xiàng)式 在點(diǎn)2、4、5的值 a=1 3 -2 1;polyval(a,2,4,5)ans = 17 105 1916計(jì)算 a(x)=2x3+4x2+6x+8, b(x)=3x2+6x+9的多項(xiàng)式相加(試著編寫一個(gè)polyadd的函數(shù)，實(shí)現(xiàn)多項(xiàng)式相加的功能)functionpoly=polyadd(poly1,poly2)if length(poly1)0poly=zeros(1,mz),short+long; else poly=long+short;endpoly1=2 3 5 7;poly2=8 -6 4 -2;poly=polyadd(poly1,poly2)poly = 10 -3 9 57求多項(xiàng)式和的乘積；并求的商和余式。(conv() deconv()f1=1 3 5 7;f2=8 -6 4 -2;f=conv(f1,f2)f = 8 18 26 36 -28 18 -14 fll=zeros(1,length(f)-length(f1),f1fll = 0 0 0 1 3 5 7 q,r=deconv(f-fll,f2)q = 1.0000 3.0000 5.0000 6.8750r = 0 0 0 0 -3.7500 -4.5000 -7.25008求的符號(hào)導(dǎo)數(shù)。y=x5+tan(4*x2)+3; diff(y)ans = -26 -41 -10 73 -19 13 -70 12 -10 78 -26 -44 -9 2 89用符號(hào)運(yùn)算求實(shí)驗(yàn)內(nèi)容6中的的表達(dá)式。觀察在不使用collect(f)函數(shù)以及使用后的結(jié)果。 三、設(shè)計(jì)提示1關(guān)于多項(xiàng)式運(yùn)算的函數(shù)有poly、roots、diff、conv/deconv等。2多項(xiàng)式做加減運(yùn)算時(shí)要注意等長(zhǎng)度。3符號(hào)表達(dá)式的輸入可以用字符串方式，也可以用sym函數(shù), syms函數(shù)。4了解以下符號(hào)多項(xiàng)式函數(shù)1. collect(f): 函數(shù)用途是合并多項(xiàng)式中相同的項(xiàng), syms x tf=(1+x)*t+x*t;collect(f)2. expand(f):展開多項(xiàng)式, syms xf=x*(x*(x-1)+3)+2;expand(f);3. horner(f) 對(duì)轉(zhuǎn)換多項(xiàng)式為Horner形式, 這種形式的特點(diǎn)是乘法嵌套, 其有著不錯(cuò)的數(shù)值計(jì)算性質(zhì). syms x;f=x3+2*x2+5*x-2horner(f)4. factor(f): 多項(xiàng)式的因式分解. 如果無(wú)法在有理數(shù)的范圍內(nèi)作分解, 那么返回的結(jié)果還是輸入值.syms x;f=x3-6*x2+11*x-6;factor(f)5. simplify(f): 通過數(shù)學(xué)運(yùn)算化簡(jiǎn)符號(hào)表達(dá)式syms x; f=cos(x)2+sin(x)2simplify(f)6. simple(f): 威力比較強(qiáng)大, 它會(huì)嘗試各種辦法來(lái)化簡(jiǎn)符號(hào)表達(dá)式, 其化簡(jiǎn)的標(biāo)準(zhǔn)是使得符號(hào)表達(dá)式的長(zhǎng)度最短. syms x f=sin(x)2+cos(x)2; simple(f)7. subexpr(f): 通過計(jì)算機(jī)自動(dòng)尋找, 將表達(dá)式中多次出現(xiàn)的因式用簡(jiǎn)短的符號(hào)表示, 返回的結(jié)果中包含替換之后的表達(dá)式, 以及被替換的因式. syms x a; f=solve(x2+a*x-1);r=subexpr(f);8. pretty(f): 用我們?nèi)四芸吹蕉谋硎痉椒ū硎境龇?hào)表達(dá)式. syms a x; f=solve(x2+a*x-